Diss. ETH No. 13938
Unconventional Vortex
Dynamics
Superconducting States with Broken
Reversal Symmetry
A dissertation submitted to the
SWISS FEDERAL INSTITUTE OF TECHNOLOGY
ZURICH
for the
degree
of
Doctor of Natural Sciences
presented by
ELISABETH M. M. DUMONT
Dipl Phys.
born
on
the
ETH
2"d April
1973
citizen of Luxembourg
accepted
on
the recommendation of
Pi of. Dr. A. C. Mold, examiner
Prof Dr. T. M. Rice
,
co-examiner
Prof. Dr. M. Sisrist. co-examiner
Zürich 2000
in
Time
7b the memory of my
grandfather Paul
Reinert
Contents
List of
iii
Figures
Abstract
I
Kurzfassung
3
1
Introduction
5
2
Theoretical
3
4
5
9
Background
2.1
Unconventional
2.2
Superconductors
2.3
Domain walls and fractional vortices
General
Properties
Superconductivity
of
with broken time reversal symmetry
SriR11O4
3.1
Electronic and Normal State
3.2
Superconducting properties
Heavy
16
Properties
19
22
31
4.1
Normal state
4.2
Superconducting properties
4.3
Superconducting Properties
5.1
14
19
Ferniion Phenomena
Experimental
9
properties
31
36
of
Ut-^xTh,Ben
Details
38
45
Measuring System
45
5.1.1
The Dilution
5.1.2
The
5.1.3
Thermometry
Refrigerator
Experimental
45
Cell
48
52
1
ii
Contents
5.1.4
5.2
6
54
SQUID Measuring System
57
Measuring procedures
Results
Experimental
59
S12R11O4
on
59
6.1
Introduction
6.2
Description
6.3
Measurements of the lower critical field
67
6.4
Vortex creep measurements
76
6.5
7
The
of the S12R11O4
Magnetization
function of temperature and field
76
6.4.1
Remnant
6.4.2
Relaxation measurements
as a
function of temperature
82
6.4.3
Relaxation measurements
as a
function of
field
98
as a
cycling
.
.
101
Summary
Experimental
results
on
thoriated
103
UBei3
103
7.1
Introduction
7.2
Description
7.3
DC-Magnetization
7.4
Vortex creep measurements
7.5
61
samples
of the
U()972sThoo275Ben samples
105
and the lower critical field
109
Ill
Magnetization
7.4.1
Remnant
7.4.2
Relaxation measurements
as a
function of
temperature
7.4.3
Relaxation measurements
as a
function of
cycling
7.4.4
Field-cooled
versus
Summary
8
Summary
A
Experimental
and Conclusion
Data
as a
function of temperature and field
.
.
115
field
zero-fleld-cooled relaxation measurements
Ill
126
.
136
139
141
147
Bibliography
157
Acknowledgements
169
Curriculum Vitae
171
Publications
173
List of
Figures
of
diagram
3He
16
2.1
Phase
2.2
Sketch of two fractional vortices
3.1
Crystal
3.2
Fermi surface of
3.3
Electrical
3.4
Spin-lattice relaxation
3.5
^iSR-rate
4.1
Magnetic susceptibility
4.2
Electrical
4.3
Phase
diagram
of UPh
39
4.4
Phase
diagram
of thoriated UBen
40
4.5
Theoretical
5.1
Picture of the dilution
5.2
Cross section of the
5.3
Gradiometers of
5.4
Diagram
6.1
Picture of
Sr2Ru04 (C49)
61
6.2
ac-susccptibilityofSr2Ru04 (C49)
62
6.3
ac-susccptibility of SriRuG^ (C82)
64
6.4
Picture of
65
6.5
Electron
6.6
ac-susccptibility
6.7
Magnetization
curves
of
6.8
Magnetization
curves
of Sr2Ru04 (C49)
6.9
Magnetization
curves
of
structure
of
zero
20
SnRuCU
21
of SnRuCXj
rate
24
of S12RUO4
magnetic field
resistivity
of
of
our
26
34
CCAI3 and UBen
some
phase diagram
of the
19
S12R11O4
resistivity
in
17
heavy
fermion
compounds
41
of thoriated UBen
refrigerator
experimental
46
48
cell
50
measuring system
55
SQUID measuring system
Sr2Ru04(C81)
channeling diagram of Si'oRuCm. (C81)
of Sr2Ru04
35
65
66
(C81)
Sr2Ru04 (C49) for
H 1
fori-/!|
c
r
Sr2Ru04 (C81) for ff±c
111
67
68
69
iv
Lisi of Figures
6.10
Magnetization cycle
6.11
Illustration of the
6.12
The lower critical field of
sample (C49)
72
6.13
The lower critical field of
sample (C81)
73
6.14
Temperature dependence
6.15
Deviation of the reduced critical field from the
6.16
Remnant
6.17
The remnant
cling
of
two
Sr2Ru04 (C81) up
methods used
of
of
magnetization
to
of 300 Oe
70
obtain Hc[
70
k^(î)/k
74
Si'tRuC^ (C81)
magnetization
to a field
of SroRuC^
parabolic
as a
law
75
function of temperature
.
.
77
function of the maximum cy¬
as a
field
78
6.18
Illustration of the Bean model
6.19
Remnant
6.20
Temperature dependence
6.21
Decays
6.22
Decays of Sr2Ru04 (C81) with
6.23
Decays of Sr2Ru04 (C49)
6.24
Decays
of
Sr2Ru04 (C49) with
6.25
Decays
of
6.26
Creep
rates of
Sr2Ru04 (C49) for H
6.27
Creep
rates of
Si"2Ru04
6.28
Creep
rates
6.29
Comparison
6.30
Field
dependence
decays
in the
high-temperatuie regime
98
6.31
Field
dependence of decays
in the
low-temperature regime
99
7.1
Specific
7.2
ac-susceptibility
7.3
Thermal
7.4
ac-susceptibility
7.5
Magnetization
7.6
Thelower critical field of
7.7
Field
the
7.8
of
as a
function of the maximum
of the
Sr2Ru04 (C49)
remnant
magnetization
of
field after Bean 79
Si"2Ru04 (C49)
80
83
± c
84
|
c.
Region (I) and (IV)
87
H
\\
c.
Region (II)
88
Sr2Ru04 (C49) with II
||
c.
Region (III)
89
with H
as a
\\
c as a
function of temperature
L
c as a
of
expansion
of
94
97
YBa2Cii408
Uo972sThoo27sBen
105
Uo 9725Thoo275Bei3. sample I
106
coefficient of Uo
Be n
107
IT
108
9725
Tho
0275
U()9725Thoo275Ben-sample
curves
dependence
dependence
of
U972sTho275Bei3
109
U()972sThoo27sBen,
of the remnant
magnetization
110
of
Uo 9725^0 0275Ben
in
Ill
of the remnant
magnetization
of
Uo9725Thoo27sBen
low-temperature phase
Temperature dependence of
7.10
Decays
7.11
Illustration of
7.12
Deviation of the
the remnant
Uo9725Th()0275Ben
as a
magnetization
113
function of temperature
116
decay anai\ sis
decays
of
in
112
7.9
our
90
93
function of temperature
of creep rates between S12R11O4. and
of
....
function of temperature
Si*2Ru04 for//
of
heat data of
of
.
c
with // 2.
H
cycling
high-temperature phase
Field
the
magnetization
79
Uo972^Tho 0275BC13 from
117
the
logarithmic
time-law 118
Lisi of Figures
7.13
v
magnetization
Remnant
as a
of
Uo 9725TI10 027sBei3- taken
at two
different times
119
function of temperature
0275^613
Creep
rates
of U09725TI10
7.15
Creep
rates
of thoriated and pure UBen
7.16
Creep
rates of
7.17
Deviation of the
7.18
Field
as a
120
function of temperature
7.14
122
123
Uo 9725Tho 0275Ben and UPt3
decays
in UPt3 from the
dependence of the decays
of Uq
logarithmic
124
time-law
in the high-temperature
9725'fho 0275Ben
127
phase
7.19
Remnant
magnetization
of Uo
9725 Tho
02756013
at T
400 mK, taken at two
=
127
different times
7.20
Field
dependence of the decays
of Uo
in the
9725Tho 0275BC13
low-temperature
129
phase
7.21
Remnant
magnetization
at T
—
200 mK, taken at two different times,
as a
130
function of field
7.22
law
7.23
7.24
7.25
decays
Deviation of the
as a
in
Uo 972sTho 02756013 from the logarithmic time131
function of field
Deviation of the
decays
in the UPt^
single crystal
from the
logarithmic
133
function of field
time-law
as a
Remnant
magnetization
and deviation of the
decays
in the
UP13 powder
sample from
the
logarithmic time-law
as a
function of field
Comparison
between field-cooled and
zero
-field-cooled mode in the
134
high-
temperature phase
7.26
Comparison
136
between field-cooled and zero-field-cooled mode in the low
temperature phase
137
Abstract
In this thesis,
report investigations of
we
vortex
dynamics
in the unconventional super¬
conductors Si'2Ru04, thoriated UBen and compare them to earlier results of
UPt3 [I]. For this purpose,
netization from
metastable
a
field. In all three systems,
distinct from the standard
vortex
novel
several hours. Its
state of these
Sigrist
dependent,
and
strong that
no vortex
in
a
magnetic
a
completely
different
The
high-77c superconductors.
creep is observed in
This
a
time scale of
pinning
mechan¬
superconducting
as
being
the lack of vortex creep which
due to domain walls,
vortex
approaching
separating
of their line
former remain
energies
strongly pinned
occupied
with
different
superconductors
such
a
with fractional flux quanta. Since fractional vortices
main walls
or
of
mechanism which is very
but rather intrinsic to the unconventional
states. Such domain walls may form in
sum
pinning
decreasing temperature.
Agtcrbcrg [2] interpreted
symmetry. A conventional
and the
application
from the
defects. It manifests itself in
with
on
systems.
these materials
ducting
so
strength increases
ism is not material
a new
observed in classical,
one
mechanism is
pinning
have discovered
we
group
relaxation measurements of the remnant mag¬
configuration originating
pinning by
than the
dynamics
performed
we
our
only
is smaller than that of
decay
can
exist
one
degenerate
on
supercon¬
into vortices
the domain
walls,
conventional vortex, the
in the domain wall. Due to vortex-vortex
pinned
observe in
with broken time reversal
domain wall
can
we
repulsion,
do¬
fractional vortices, represent efficient barriers for vortex
motion and thus prevent flux flow.
In the
known to
case
occur
of UPC, and
of which the
Uo 9725Tho 0275ßen-
low-temperature
1
one
two consecutive
leads to
a
phase
transitions
superconducting phase
are
with
Abstract
2
broken time reversal symmetry [3-5]. In both systems,
creep rates
by
than three orders of
more
duction of creep
rates
pinning regime
only found in
in the
is
coincides
high-temperature phase
exactly
the
magnitude
with the
to
we
large
a
undetectabely
creep rates
are
sharp drop
of initial
low levels. This
re¬
transition. The novel
low-temperature
low-temperature phase
rather
observe
of UPtß and Uo
9725Tho 02756013,
observed, which increase with
increasing temperature.
In
S12R11O4 time reversal symmetry breaking is reported
However,
we
do not observe unconventional
ducting transition,
pinning
vortices,
as
the lowest
looks
zero
creep sets in
pinning immediately
only
much below Tc.
mechanism described in this thesis is caused
proposed by Sigrist
main walls in
lower
but
While in
superconducting
more
like
associated with
superconducting
Uo 9725^0 0275Bei3
then
and
below the supercon¬
If the unconventional
domain walls
one
right below Tc [6].
carrying
fractional
has to conclude that the do¬
temperatures, but only
UPt3, the drop in creep
rates at
at
the
transition temperature is very sudden and strong, in SroRuCU it
a crossover.
a
Agterberg [2],
by
cannot carry fractional vortices at all
S12R11O4
[7].
and
to occur
Sigrist
and
Agterberg suggest
that this
crossover
might
be
"transition" of domain wall states due to the multiband nature of the
state in
S12R11O4 [2].
Kurzfassung
Im Rahmen dieser Dissertation wurde die
nellen
Supraleitern Sr2RuC>4
Ergebnissen
unserer
Gruppe
und thoriertem
allen drei
sentlich
völlig
die durch
Systemen
von
Anlegen
haben wir einen
dem Standard-Haften
anderen
Flussdynamik
Supraleitern vorgefunden
als
wird.
gig,
neuartigen
an
Der
Temperatur
Um das Flusskriechverhalten
Magnetisierung
Ilaftmechanismus
gemessen. In
gefunden,
Defekten unterscheidet. Dieser
zeigt
welche in klassischen oder
neuartige
Haflmechanismus ist
zu
einer metastabilen
von
Magnetfeldes hervorgerufen wurde,
diejenige
Flusskriechen in einem Zeitraum
nimmt mit sinkender
UBen untersucht und mit vorangegangenen
remanenten
eines
Flusslinien in den unkonventio¬
von
UPI3 [1] verglichen.
an
erforschen, wurde die Relaxation der
Konfiguration,
Dynamik
der sich
we¬
sich in einer
Hochtemperatur-
so
stark, dass kein
von
mehreren Stunden beobachtet wird. Die Flaftkraft
zu.
Dieser Haftmechanismus ist nicht matcrialabhän-
sondern vielmehr dem unkonventionellen
supraleitenden Zustand
dieser
Systeme
in¬
härent.
und
Sigrist
Agterberg [2]
haben die
Unterdrückung
in diesen Materialien beobachten, der Existenz
verschiedene entartete
de können in
Supraleitern
tionelle Flusslinie
nicht
supraleitende
mit
als die
nur
von
Flusskriechen, welches wir
Domänenwänden
(Vortex) die
zugeschrieben,
die
Zustände voneinander trennen. Diese Domänenwän¬
gebrochener Zeitumkehrsymmetrie
eitstehen. Eine konven¬
auf eine solche Domänenwand trifft kann in Vortizes mit
ganzzahligen Flussquanten
existieren
von
von
zerfallen (fraktionierte
Vortizes). Fraktionierte Vortizes
auf den Domänenwänden. Da die Summe ihrer
Linienenergie
kleiner ist
einem konventionellen Vortex, bleiben die fraktionierten Flusslinien in den
Domänenwänden stecken.
Wegen
der
gegenseitigen Abstossung
der
Vortizes, stellen Do¬
mänenwände die mit fraktionierten Flusslinien besetzt sind sehr starke Haftzenlren
3
dar,
Kurzfassung
4
die wie
"Einzäunungen"
der Fluslinien
welchen der
chener
der
zur
Anfangskriechraten
eine
neue
zu
aufeinanderfolgende Phasenübergänge
einem
supraleitenden
aussergewähnlich
über mehr als drei
Der
zwei
Zustand mit
gebro¬
(3-5], In beiden Systemen beobachten wir exakt
führt
Tieftemperaturphasc
tierbar kleinen Wert.
von
es
Tieftemperatur-Übergang
Zeitumkehrsymmetric
Übergang
Bewegung
der Probe heraus unterbinden können.
UPt3 und Uo 9725TI10 02756013 gibt
In
von
aus
Vortizes in den Domänen umschliessen und damit die
starke und
Grössenordnungen,
Haltmechanismus wird
nur
bis
in der
abrupte
zu
am
Abnahme
einem undetek-
Tieftemperaturphase
UP13 und Uo 9725141002756013 aktiviert, in der Hochtemperaturphase werden endli¬
che Kriechraten gemessen, die mit
zunehmen.
S12R11O4 wurde die Brechung der Zeitumkehrsymmetrie direkt unterhalb der kri¬
In
tischen
steigender Temperatur
Temperatur
beobachtet
bene Haftmechanismus nicht
sondern
er setzt
erst bei viel
[6]. In diesem Material jedoch, wurde der oben beschrie¬
gleich
tieferen
supraleitenden Überganges
unterhalb des
Temperaturen
ein. Falls dieser
gemessen,
ungewöhnlich
starke
Haftmechanismus tatsächlich durch Domänenwände mit fraktionierten Vortizes hervor¬
gerufen wird,
wie
Sigrist
und
achtungen schlicsscn, dass
Agterberg [2] vorschlagen,
die Domänenwände in
Übergangstemperatur
Kriechraten
an
dem unterem
"Übergang"
von
Phasenübergang
Sigrist
und
Domäncnwandzuständen
Mehrbänder-Natur des
nur
weit unterhalb der
supraleiten¬
[7]. Während in Uo 9725^0 027sBei3 und UPts der Abfall der
S1-2RUO4 eher einem Crossover.
Art
diesen Beob¬
SoRu&j. nicht bei allen Temperaturen
fraktionierte Flusslinien enthalten können, sondern
den
so muss man aus
supraleitenden
sehr
abrupt
und scharf
Agterberg schlagen
zugeschrieben
ist,
so
gleicht
er
in
vor, dass dieser einer
werden
könnte, der
Zustandes in SnRuOzt L2] herrührt.
von
der
1
Introduction
Conventional
Cooper
superconductors,
and Schrieffer
fact, that
such
as
Al and Nb,
microscopic theory
of
are
well described
superconductivity [8].
on
the
ity
of the Fermi-sea, with respect to the formation of bound
Cooper pairs).
in
even a
electron-phonon coupling
internal
the
angular
favor
fluctuation mechanism is
p-wave
pairing.
As
with two different
a
magnetic
some
of the
Coulomb
field
and well studied
thought
in
zero
(labeled A 0
heavy
fermion
s-wavc
it
rather
Cooper pairs.
more
than
third class of unconventional
pairing
(called
origin
with
zero
example
responsible
is
example
^
unlikely,
rather
To
a\
oid
a
one
<. \ <
preferred.
0.045,
a
of the
interaction which differ', from pure
-
the
D
one
appearing
spin-
under
superconductors
and UBen). Due to
quasiparticlcs'
with different
high-Tc cuprates
-
are
large
of these systems
wave
second transition has been
electron-phonon
a
condensate with
In two of these systems,
superconducting phase
superconductors
third
heavy quasiparticlcs
large overlap
0 would be
a
where
complicated phase diagram
of unconventional
that the
interactions could
superfluid 3He,
for the creation of
a
not
superconductivity.
compounds (e.g. CeCmSio, UPt3
seems
based
instabil¬
of electrons
potential. Other
field (labeled A and B) and
UPt3 and Un ,Th3en with 0.019
evidence for
be
to
Another
.
tions, anisotropic pairing with /
giving
attractive
an
consequence this system has
phases
repulsion,
would form
a
causes an
spin-singlet Cooper pairs
in unconventional
pairing, resulting
prominent
theory is
the attractive interaction has its
and the electrons form
mechanism to obtain
non-s-wave
The most
superconductors,
pairs
the Bardcen,
(s-wave). However, the electron-phonon interaction is
momentum
only possible
Their
weak attractive interaction between electrons
In conventional
by
func¬
namely
observed,
symmetries.
has also shown
interaction. Indeed,
a
A
a
great
deal of
experimental
data
give
evidence that the
conductors has d-wavc character
Today,
a
of
example
more
is
Introduction
J.
6
One
are
olate T.
a
Rice and
early hypothesis by
feature of unconventional
proposed
They
the
are:
15]
and
to occur in the
examples
proposed
A-phase
Ui_-,Th,Ben with 0.019
to occur at
a vortex.
=
of
fic/2e.
However
is to be
superconducting
degrees
the
-
a
expected
analogy
to
0.045
<
< x
superconductors
finite vortex creep with
superconducting
attributed to
topological!}
(3,4),
types of vortices.
to now,
likely
vi¬
fermion
heavy
and the
this is the
than
In the
a rate
dis¬
recently
a
single
only possible form
where
new
field, is
and
seven
different
interesting
vor¬
Since in the latter, the
component, this yields many
one
more
stable defects.
was so
results of
vortex
that increased
creep"
our
pinning
group
on
UPt3 [1].
in the low-field low-
strong that the initial flux creep dropped
high-temperature phase,
pinning mechanism
-
superconductors.
by experimental
transition. The "zero
a new
which very
of the two
rotating superfluid 3He,
more
temperature phase of UPt?. The latter
zero.
[10,11]. Up
than its lower critical
higher
Mota, Amann and coworkers found unusually strong
practically
Tic
called vortices. Each vortex carries
in unconventional
order parameter has
of freedom to form
violation. The break¬
superconductors
field
magnetic
In conventional
in
is the fact that
surface of high-temperature superconductors [12,13].
The present work is motivated
down to
(T)
superfluid
types of vortices have been identified in the A- and Z?-phases
physics
Sr2Ru04
that
Sigrist,
It should be mentioned that T-violation has also
by quantized magnetic flux lines,
flux quantum &0
tex
Sf2Ru04.
discovered
superconductors
low-temperature superconducting phase
type II superconductor in
threaded
super¬
magnetic systems. Spontaneous 'I breaking
of unconventional
superconductor Si"2Ru04 [6].
covered
A
well known property of
three known
metals UPt3
for
recently
among them show spontaneous time reversal symmetry
has first been
been
is the
superconductor
confirm the
especially intriguing
down of T is
there
high-rc
superconductor.
p-wave
some
experiments
many
function of the
wave
(sec for example [9] and references cited therein). One
unconventional
an
pair
rapidly
in the
as
on
the other hand,
the temperature
they observed
approached
low-temperature phase
intrinsic to this
of
superconducting phase,
the
UPt3
was
and/or
new
1
Introduction
/.
A theoretical model
berg [2]. They proposed
formed in
states
explaining
approaching
vortex
repulsion,
such
domain walls
can
occupied
pinned
as an
indirect
probe
According
to this
for the nature of the
ing phase. Since, following this theory, superconducting phases
symmetry could then be identified by their lack of
vortices, represent effi¬
fractional
cient barriers for vortex motion and thus prevent flux flow.
model, lack of creep could be used
Agter¬
into fractional vortices. Due to vortex-
decay
with
and
A conventional
with broken time reversal symmetry.
domain wall
a
by Sigrist
degenerate superconducting
that domain walls between different
superconductors
vortex
this effect has been put forward
vortex
creep
theoretical
superconduct¬
that break time reversal
or
their anomalous strong
pinning.
Following
superconductors
the results of
our
group
UPt3.
on
we
with broken time reversal symmetry.
looked for other unconventional
The
only
other known
examples
are:
-
The
low-temperature phase
tion
regime (0.019
ing
transition is observed which leads to
ducting phase
<
x <
of
Ui_Vrh,Bci3 in the critical
0.045):
In this
system
a
a
second
concentra¬
superconduct¬
low-temperature
supercon¬
with broken time reversal symmetry, similar to the
case
inUPt3.
-
The unconventional
superconductor S12R11O4:
down of time reversal symmetry is
So far there is
transition in
In this work,
no
experimental
evidence for
a
to occur
second
right
below Tc.
superconducting
S12R11O4.
we
have
investigated
ition temperatures, and also two
which the two
reported
In the latter the break¬
superconducting
three
S12R11O4 single crystals with different trans¬
single crystals
of
transitions could be
Ui^/fh^Ben with
x
clearly distinguished
0.0275, for
=
in
specific
heat
measurements.
This thesis is
Chapter
are
2 In this
organized
chapter
as
some
the
following:
theoretical concepts of unconventional
defined, the main focus
being
on
symmetry. Then the unconventional
reversal symmetry
breaking
superconducting
vortex
is illuminated.
dynamics
superconductivity
states that break time reversal
in
superconductors with
time
8
1.
Chapter
3 presents
Chapter
4
on
gives
the
previous experimental,
brief summary of
a
properties
5 describes the
Chapter
6 In this
critical field
Chapter
7 In this
experimental setup
chapter
chapter
susceptibility,
field and
are
Chapter
experimental
Besides
and, above all,
Uo 9725Tho 0275Be 13
dynamics.
the
presented.
are
heavy
well
as
fermion
theoretical work
the
are
we
and the
results
Si"2Ru04.
superconductivity, focusing mainly
have
presented.
a
on
investigated
experimental
performed
experimental procedures.
low-field
ac-susceptibility.
results
on
we
vortex
we
dynamics.
mainly
our
of other groups.
we
measured
concentrated
on
as a
of
ac-
on vortex
function of
Uo.9725Tho
0275
Be n
group.
8 summarizes and discusses the main results with
experimental results
magnetic properties
of the latter, both
temperature. In this chapter, the results obtained
UPt? of
of
have measured the lower
low-field
have
systematic study
to earlier results on
magnetic properties
Also in this system, have
the lower critical field, but
We have
compared
on
of thoriated UBen.
Chapter
S1-2R11O4
as
Introduction
comparison
to
theory
and
2
Theoretical
The aim of this
chapter
focusing mainly
on
Background
is to define
a
few concepts of unconventional
which break time reversal symmetry. We will
superconductors
that violation of time reversal svmmetrv
been shown
by Sigrist
and
superconductivity,
can
Agterberg [2].
have
In the
striking effects
following
on
I will
flux motion,
follow
closely
as
see
has
Sigrist
andUeda[l4].
2.1
A
Unconventional
widely spread
definition of unconventional
considerations: When
U(\)
only
a
sample undergoes
is broken, because the
the whole
Superconductivity
specimen [15].
gauge symmetry
phase
a
of the order parameter has the
other hand,
ductor, if the order parameter breaks
-
is based
superconducting transition,
It is customary to call
[ 14]. On the
superconductivity
a
superconductor
one
refers to
an
same
gauge symmetry
value
unconventional supercon¬
in addition to gauge symmetry
invariant system. So. above its
us
superfluid
consider
superfluid 3He,
-
at
least
<£
P)
which is
or
a
one more
parity
P.
rotationally
transition temperature, it has the total symmetry
group:
(r 0 S0f}
throughout
conventional if it breaks
symmetry of the crystal point group, for instance time reversal symmetry 1
To illustrate these concepts, let
symmetry
on
<5>
S0f 0 ('/(g) U{ 1 ))
9
2.
10
where
/
is the group of translations,
rotation group. The conventional
is not realized due to hard
symmetry. Because of the
3He
breaks
SO^
core
the group of space
superconducting
repulsion.
nonzero
Due to
.
SO\
In
Theoretical
rotations,
superfluid ^He, Cooper pairs
i nternal orbital momentum of the
spin triplet pairing,
SO^
Time reversal symmetry is conserved
not
the
for
case
3Hc-A.
The
only symmetry,
only
for
a
spin
state, which
have p-wavc
=
1
),
Since the orbital
part is antisymmetric, the order parameter changes sign under parity.
broken.
the
Cooper pairs (L
is also broken.
'
'
S03
singlet
would be the
state
Background
Thus, P is also
real order parameter, this is
that remains unviolated is the iranslational
symmetry [16].
In
generalized
a
written in
mean
field
where
c/C0is
spin
Vsisgcj {k.k')
s.
the
BCS
the
theory
approximation
pair potential (also
which
-
states,
taking
In the
spin.
case
into account
of
stales,
A(k)
—
by
an
a
small range
is
arc
er
are
a
general
effective electron-
the Fermi surface.
split
into
antisymmetry
singlet
and
triplet
condition.
function in momentum k and odd in
antisymmetric matrix,
characterized
by
an even
scalar
y/(&) :
denoting the
the conventional
also in
the
an even
Pauli matrices. The
superconductors,
-xir(k)
most
(2.1)
0
prominent examples
which follow BCS in its
h\gh-Tc superconductors, singlet pairing
with J-wave symmetry.
y/(k)
0
A(k)-- /ô:y(jt)z
with
be
electron of momentum k and
near
pair potentials
—A1 (—k),
singlet pairing, A(k)
It is described
function
removes an
is the matrix element of the operator V.
electron interaction which is attractive in
spin
can
as:
annihilation-operator
Classifying superconducting
function)
called gap
is believed to
of
singlet pairing
original
occur
version. But
in connection
Unconventional
2. /
In the
-
case
of triplet
The matrix is
spin.
11
Superconductivity
pairing,
A
symmetric
(k)
is
and
odd function in the momentum k and
an
be
can
parameterized by
even
in
odd vector function
an
d(k).
—dx
l{k)-i(d{k))ô)ô2
Triplet pairing
also
likely
is realized in
to occur
4-
idy
1.2)
d~
superfluid
in unconventional
-'He.
dy + idy
On the other hand,
superconductors,
e.g.
triplet pairing
is
Si"2Ru04, UBen and
UPt3.
However, it should be noted, that in superconductors with strong spin-orbit coupling, the
spin
is
states
no
longer
valid quantum number, since the
spin-operator
of the
spins [14].
a
In
crystals
states, rather than
anymore. Nevertheless, the states
with inversion symmetry,
and
matrix
A(k)
nonunitary
2x2 unit matrix a0.
triplet pairing
is
most cases,
sight
to a
defined
can
be
microscopic
into unconventional
as
B-phase
are
unitary
odd-parity
origin of unconventional
Landau
theory.
is
gained by
The
representations.
representations
assume
In that
that this Tc
case,
r k
the stable
Ai-phase
explicitly.
one
much
to the
superfluid 3He
of
a
is unknown in
However,
F of
that
larger
a
certain in¬
phcnomenological approach
possible superconducting
F there is
We
pair potential
evident, that only
It is
superconductivity
Hamiltonian.
the
between two types:
states.
représentations
other
cigen-
by pseudo-
and
states for which the
classified with respect to the irreducible
Among
distinguish
For instance, the
non-unitary.
superconductivity
using generalized Ginzburg
r.
even-parity
non-unitary.
the Hamiltonian cannot be written out
temperature" Tc
of
be labeled
can
unitary matrix, i.e. the product A À is proportional
while the A- and
Since the
speaks
has to
Otherwise the state is called
matrices
non-unitary,
one
stales. The former are
proportional
is
one
states are no
singlet, respectively triplet pairing.
Furthermore, among odd-parity states,
unitary
single particle
Q,
gives
the total group of the
the
highest
than the other
superconducting
state
states can be
"transition
Tcj
immediately
of all the
below
T(
Theoretical
2.
12
is described
by
linear combination of the basis functions
a
Background
A(F;k):
A(k)---^n(r,m)A(l\m;k)
m
r\{Fpn)
where
meter of the
are
complex
{p(Fjn)} plays
numbers. The set
The iree energy F is constructed
system.
by
the role of the order para¬
single restriction,
with respect to the order parameter with the
general expansion
the most
that F is scalar under all
symmetry transformations. Since the gauge and the time reversal transformations
certain among these
The second order
order.
with temperature
free energy,
The
one
all terms of this
expansion
have to be real and of
of the free energy
expansion
is
symmetries,
term
dependent
finds the
coefficients
stable
possible
superconducting
Ar(T)
a'(T
=
-
order parameter cannot be observed
the nature of the order parameter manifests itself
of the
experiments giving
bilinear form
diagonal
Tcr). By
even
minimization of the
superconducting phases.
identification of the latter rather difficult. However, there
some
a
for
are
directly.
several
are
In the
indirectly.
evidence of unconventional
This makes
experiments
an
where
following paragraph
superconductivity
will be
discussed.
In conventional
A(k)
which is
of various
superconductors,
.v-wave
non-vanishing
for all k. This
physical quantities,
such
hand, in unconventional superconductors
surface. In this case,
of
case
of
a
lead to
gapless
a
example, in
modification of the BCS
for
a
finite range of
impurity
unambiguous
dependencies
are
is not
or
points
or
fines
on
can
strongly
gap
at T <C
the Fermi
Tc. This is
Fermi surface. However, the observation
a
conclusive evidence for
an unconven¬
superconductors magnetic impurities
superconductor becomes
concentration below the critical value which
This
a
NMR relaxation rate. On the other
of states such, that the
also lead
influenced
power-law
destroys
behaviours. Moreover,
by impurities [14]. This
makes
an
identification of the order parameter difficult.
More cogent evidence for unconventional
istence of
excitations have
exponential temperature dependence
may vanish for
conventional
density
superconductivity completely [17],
the temperature
heat
spherical
power-law temperature dependencies
tional gap structure. For
A(k)
an
low-energy
specific power-law 7"-dependcncies
one measures
illustrated in Table 2.1 for the
yields
specific
as
the
multiple superconducting phases
-
superconductivity
e.g.
are
for
example
in UPh and thoriated
the
ex¬
UBen in the
2.1
Unconventional
13
Superconductivity
physical quantity
specific
heat (C)
NMR relax at i on rate
(1/70
T1
T°>
T}
T5
penetration depth (X ~)
Tabic 2.1:
line
or
ivity
regime
time reversal
sensitivity
is
where the
phase
impurities
act as
to
-
of the gap function
pair
changes sign
breakers which
does not affect
approaches
the
Phase sensitive
order parameter,
.9-wave
7<.
dirty
one
metry [23-25].
on
magnetism (i.e.
superconduct¬
are
anisotropic,
in unconventional
for
indispensable
have been
a
proposed
the
predicted
to occur
in
isotropic
gap,
non-magnetic
an s-wave
supercon¬
of directions which
occurs
and lowers T(. But this effect is
the symmetry of the
superconduct¬
definite identification of the latter. Andreev
in order to determine the
sign
for unconventional
for />-wave [22],
zero
^-dependence
as
well
as
energy bound states in
of
(non s-wave)
r/-wave sym¬
tunneling
high—7^ superconductors [26, 27],
an
transition
superconductors [20].
and also in
j27|, revealed
pairing
an
averaging
isotropic
states are a
Indeed, the observation of
BSCCO
with
non-magnetic
superconducting
It should however be noted that for
and have been
evidence for J-wave
suppress the
superconductors
superconductor UBen [28],
experiments
strongly
limit makes the gap
troscopy has been reported
fermion
can
[21]. Subgap Andreev bound
superconductivity
with intrinsic
around the Fermi surface,
experiments, directly probing
scattering experiments
the gap
Fermi surface and either
non-magnetic impurities. Since, in unconventional superconductors
much weaker than the
ing
spherical
Another indication of unconventional
ductor whose gap in the pure state is
as one
a
superconducting phase
or a
symmetry).
temperature. Whereas, in
scattering
calculated assuming
are
at
point nodes in the gap. after [18] and [19].
critical concentration
violating
T1
T
temperature dependencies of several physical quantities
Theoretical
Tc. The properties
T <
nodes
T2
conductivity (k)
thermal
point
line nodes
in the
spec¬
heavy
Si'2Ru04 [29]. Furthermore, tunneling
in-plane crystallographic dependence, giving
in BSCCO. In this context, it is
important to
mention another
type of phase sensitive experiments, which have been very successful in identifying the
symmetry of the order parameter of YBCO
single-junction,
van
Harlingen
as
and coworkers
being dp_p.: (1) Using dc-SQUID
[9] ha\e observed
a
phase
and
shift of order
k
Theoretical
2.
14
in the order parameter between
and
«//-plane; (2) Kirtlcy
losephson junctions.
Superconductors with broken time reversal symmetry
2.2
with,
To start
olation".
and
directions of the
[30] have reported half integer flux quantization in superconducting rings with
coworkers
three
orthogonal
Background
we
give
definition for what is meant with "time reversal symmetry vi¬
a
Under the time reversal
behave
(2.2)
according
operation K,
(T)
Time reversal symmetry
classified
states are
former have
a
relations
by
(2.1)
to:
Kyr(k)^xi/{k)
is different from the
the functions defined
original state,
according
and
Kû(k)
is \iolated, if the stale
i.e. if
\j/(k) ^ ty'ik),
"ferromagnetic"
to
finite, and the latter
d"(k)
-=
a
emerging
resp
from this
operation
û(k) ^ d+(&). T-breaking
"antiferromagnetic" types.
and
vanishing angular
(2.3)
momentum
L of the
The
Cooper pairs:
f {w\k)(-Nxk)V(k))¥S
L=
I
[
where
types
(... )ps
are
the
nonunitary
by
S
—
denotes the average
"antiferromagnetic"
with
wave states
even-parity.
states arc
nonunitary
The
states lies in
s
4
There
The most
only
in
state in zero
major
over
idp_p-\\'d\e
also
are
an
external
possess
a
spin degree
is the
field. In
examples
for both
"ferromagnetic" dx2_v2
examples for odd-parity
magnetic
states:
of
Aj-phase
general,
+
id^,-
for instance
freedom, defined
of
superfluid 3He
it is difficult to stabilize
field.
difference between the
angular
and the
prominent example
the fact, that the former
its net orbital
the Fermi surface. Well known
always T-breaking. They
(d*(k)d(k))ps.
which is stabilized
a
(luàu(k){-iVxk)(lu(k))Fs
ferromagnetic
can
momentum or
and
directly couple
spin.
If the
antiferromagnctic T-violating
to an external
magnetic
superconducting phase
field via
is uniform
on
length
scales much
momentum
ging
the
of the
than the London
longer
penetration depth,
order parameter
short
on
magnetism.
magnetic
detected with
fields at
spin polarized
injected
spin
evolves in the local
time
of these
teraction of the
muon's
muon
positrons,
spin
one
at
may deduce the
with its environment
Pfl
-
called
so
-
^
-(I
muons
an
external
yields
the
œ
mm). The
0.1
decay emitting
magnetic field,
following
time
<
0.045) [3,4]
set at the second
and
a
positron,
as a
the
function
dipole
in¬
for the
Kubo-Toyabe function) [31]:
-
ruA-t-)exp{--ruA-r)
a
clear increase of the relaxation rate in
transition temperature has been observed. In
hand, this increase of the
the presence of
muon
muon
gyromag-
low-temperature, low-field phase of UPt3 [5] andUi^Th^Ben (with
netic ratio. In the
„v
a
dependence
where A is the width of the local internal field distribution and yß is the
0.019 <
be
decay. By accumulating
polarization
muon
can
latter, spin polarized pos¬
In the
the moment of the
In the absence of
spin polarization (the
The
environment.
is the presence of
impurities. They
sample (typical penetration depth
magnetic
implantation.
experiment.
uSR
a
into the direction of the
histograms
of time after
in
muons
into the
muons are
breaking
domain walls and also around
edges,
itive
preferentially
chan¬
inhomogeneitics
scales lead to local variations
length
The strongest manifestation of time reversal symmetry
local
angular
the internal orbital
remains unobservable. However,
Cooper pairs
superconducting
of the internal
15
with broken time reversal symmetry
Superconductors
2.2
zero
field uSR rate starts
right
zero
field with
on
the other
finding
indicates
Sr2Ru04 [6]
below 77c. This
an on¬
spontaneous magnetic field appearing within the superconducting phase
thus, the breakdown of time reversal symmetry.
These
metry
can
are
examples
for T-violation in bulk
also be violated locally.
superconductors,
As mentioned
m
the
but time reversal sym¬
previous section,
due to the
anisotropy
of the rf-wavc order parameter, surface bound states form, which manifest
themselves
as a
zero-bias
YBCO and BSCCO
peak
in the
m-plane
[26.27]. The zero-bias
netic field. However, the Greene group has
low temperatures in
surface state with
:ero
field
conductance of
conductance
spontaneous!)
peak (ZBCP) splits
recently reported
112,32]. This is
an
tunneling experiments
a
splitting
indication for
a
a
mag¬
of the ZBCP at
phase
broken time reversal symmetry [13].
in
on
transition to
a
It is believed to
Theoretical
2.
16
Background
40
solid
superfltiid B-phase
30
-
A-phase
-core
\
cd
\
e2o
vortex
double-core vortex
10
-
-1He normal
0
0
2.1:
Figure
diagram
Phase
in 3He-B
structure
of rotating
(dashed line) is
temperature side vortices have
have
a
single
result from
and which
2.3
an
core
L
T (mK)
a
a
"He in
zero
first order
with the character of the
topological
On the
double-core.
The
field.
in vortex
change
transition.
On the low-
high-temperature side,
vortices
A-phase.
additional subdominant order parameter, which is stabilized
spontaneously
core
by
the
surface,
breaks time reversal symmetry.
Domain walls and fractional vortices in time reversal
symmetry breaking superconductors
be
regarded
A vortex
can
getically
stabilized
by
an
order parameter goes to
around the line
netic flux of
by
one
only possible
as
a
line defect of the
externally applied
zero,
flux quantum ®0
form of
a
field.
thereby yielding
2?r. This results in
vortex.
—
a
a
hc,'2c.
However, in
singularity
view, since the phase of each component
in its
superconductors
can
phase.
manifested
In conventional
are
which is
ener¬
At the center of the vortex core, the
topological charge,
der parameter, various other types of vortices
of
superconducting phase,
by quantized
superconductors,
with
a
conceivable from
wind
The latter winds
separately.
mag¬
this is the
multicomponent
a
or¬
topological point
This concept has been
2.3 Domain walls and fractional vortices
tl
e^(l,
=
y
+7i/2
=
_^g)
1-1
studied
(I.—;).
c'°
=
tected
two
picture
This
predicted (for
lines,
vortex
NMR
by
^(1,-1)
=
(for
superfluid 3He.
separates
degenerate superconducting
it. taken from
a
review
review
a
see
n
e'é(],+i)
=
where
Lounasmaa and
phase
a
Figure 2.1.
In
a
great variety of topological defects
Point
singularities,
textures have been
with double-core vortices from
cannot
be transferred
vortices in -'He
nonsingular
one
by
intimately
are
phase
a
phase separation
with
one to
the
single-core
case
linked to the
de¬
and references cited
Thuneberg [33,34]
have drawn the the
we
and
|35].
Salomaa and Volovik [16]).
see
domain wall
a
on
states
sheets, domain walls and three-dimensional
These concepts
because
(marked by <g>)
Seven different types of vortices have been identified in the A- and
therein).
of
-71/2
extensively in rotating superfluid 3He.
have been
vortex
=
A sketch of two fractional vortices
(solid line), separating the
?]
vg}~7Tzy
__
y
Figure 2.2:
+i)
of
a
complete
B-phase
line which
vortices.
superconductor,
rotational sym¬
metry of the system. Nevertheless, in unconventional superconductors, vortices deviating
from the standard
the
case
of
ing
states
by
described above,
;j
=
e'ç(\.-ld)
analogue
or
from
have to be
of
n
=
a
ji/2
v=
to
/r/2.
0. The
e'ù
a
state, two different
(1. --/))
spin
are
degenerate superconduct¬
separated by
domain wall. This
a
where the Weiss domains
reverses
gradually. Inside
a
the internal phase y of the order parameter
But this
phase change
two structures are
separated by
under well defined circumstances. In
occur
ferromagnet.
domain walls inside which the
through
case
and
to the case of a
T-breaking superconductor,
ously
can
T-breaking superconducting
(e.g.
situation is
ated
a
one
line defect,
T-breaking superconductor,
can
either
present in the
analogous
to a
occur
same
to
a
Bloch line in
complete <P0,
domain wall of
changes
a
continu¬
passing through
a
this line defect is identical to
obtain
separ¬
y=
rt
domain wall and therefore,
of the order parameter components winds around this line, the
fraction of <f>(>. Since, in order
are
ferromagnet.
a
vortex. As
resulting
For the
only
flux has
one
only
a
both order parameter components
18
would have to wind. Such fractional vortices
approaching
such
a
domain wall,
fraction of &0 and the
Because the
one
sum
flux quantum,
sum
of their fluxes
of their line
they
two
only
on
domain walls. A vortex
fractional vortices, each
being equal
energies
exist
Theoretical
to
carrying only
occupied
is lower than that of
with fractional
conventional vortices [2]. Thus,
symmetry breaking superconductors is
to
an
be
a
(P0.
a
conventional vortex with
do not recombine and leave the domain walls. Since vortices
each other, these domain walls
oncoming
into
decays
can
Background
2.
vortices,
can
repel
act like "fences"
for
inhibition of the vortex flow in time reversal
expected.
of
3
General
3.1
Electronic and Normal State
The
crystal
structure
of SriRuCA- is
structure as that of the
Si*oRu04
are a
—
b
—
Properties
depicted
in
Sr2Ru04
Properties
Figure
3.1. It is the
high-7^ superconductor La:- xBa^Cudj.
0.387
and
nm
c
=
1.274
nra
at room
Band structure calculations [38.39] revealed that the
surface is
orbitals
governed by
hybridize
orbitals of O,
2p
temperature [361.
density of states
#i
rise to
giving
*#
»»
„*.»
**
'-*-
Figuie
a
3.1:
-*-
Crystal
structuic of
19
Si*
Ru
O
S0RUO4.
near
the Fermi
{diV, dv:> d:x).
antibonding
i
i——
K2NiF4-type
The lattice parameters of
the four Ru 4J electrons in the /:? orbitals
with the
same
These
tC bands.
De
3.
20
3.2: Fermi surface of
Figure
ß and y) centered
the 1Z line and
of the Bnllouin
corners
zone.
Picture taken from
one
surface is shown in
cylinder
Figure
[37].
that the Fermi surface consists of three
a
are
close structural
very different. Unlike
3.3 shows the
larger than
similarity
out-of-plane
becomes non-metalhc with
On the other hand, below 25 K. the
p
JrAT2
po
along
and
The
effective
in all directions,
perpendicular
specific
mass
the calculated
ones.
This
metallic behavior in its stoichiometric
and
in-plane resistivity
a
as a
starts to deviate
negative slope dpc/clT
<
function of
from the
one
0 above 130K.
from three-dimensional to two-dimensional metallic conduction takes
place.
=
form
high-7^ superconductors,
with the
temperature. Above 65 K. the temperature dependence of pc
a crossover
They
7).
La:Cu04, which is Mott insulating and
doping, Si*2Ru04 displays
finally
and
important.
only
composition. Figure
to the c-axis. A
about four times
are
upon
ß
calculations,
parallel
properties
metallic
running around the
3.2. This result agrees well with the band structure
masses are
there is
though
the electronic
Here
a
cylinders (labeled
of the Fermi
indicates, that electron correlations
of pnij and
electron
of Si~2 R11O4
picture
surfaces
cylindrical,
but the observed effective
turns
large
Properties
hole-like (labeled a) and two electron-like (labeled
three concentric, almost
Even
two
hole
one narrow
Alphen oscillations [37.40] revealed,
Haas-van
sheets,
on
S12R11O4 composed of
General
vv
resistivity
follows the
hich is characteristic of a Fermi
to the c-axis differ
by
a
liquid. Still,
factor of about 550
heat in the normal state is well described
estimated from the electronic
77-squared dependence
specific
by
C
—
the
resistivity
[41].
yT
4-
pT3 [42].
heat coefficient y is enhanced
The
by
a
t
*T
!
1
21
Properties
3.1 Electronic and Normal State
I
T
T"
1
1
1
I
1—I—I—p
10-
9 ab
X
55(L
10"2
o
Cl
,0-3
r
10„4
J
1
I
I
I
I
,
3.3:
resistivity
istivity
one
pa], is
electrical
multiplied
as
compared
all the
ers
as
well
as on
a
Pauli
I...
compared
=
300K. The
with the
susceptibility
the Van Vleck term in the
Alphen
to
the Pauli
7rit^0/3ugyof
enhanced
by
spin susceptibility
enhancement would be lower.
in-plane
out-of-plane
res¬
[41].
a
accordance with
measurements mentioned above.
the direction of the
paramagnetic susceptibility
gives
of SriRuC^ up to T
magnetic susceptibility showed,
calculated the Wilson ratio
This
resistivity
obtained from the De Haas-van
temperature
i,,..
to band structure calculations. This value is in
Measurements of the
on
1
T(K)
b\ 550 in order to be
pc. The data is taken from
factor of 3.6
the
Anisotropie
1.„,...,„„.,„
102
10J
Figure
1
that it
externally applied
spin susceptibility,
depends only weakly
field
[42]. Assigning
Maeno and cowork¬
SnRuCU and found it equal
factor of about
could be
eight.
to 1.8
[36].
Note however, that
non-negligible.
In that
case
the
3.
22
mal state
electron correlation effects
though
In summary,
superconducting
above the
just
dimensional Fermi
are
General
of SV2R11O4
Properties
important
in
S12R11O4, the
transition is well described
by
quasi
a
nor¬
two-
liquid.
Superconducting properties
3.2
Si'2Ru04 is
clean
samples.
critical
given
type II superconductor with
a
The
superconductivity
of
a
critical temperature of T,
1.5 K in very
«
Sr:Ru04 is strongly anisotropic. Values of the
fields, penetration depth and coherence length along the different directions
in Table 3.1. The
anisotropy parameters
anisotropy parameter 1/e
amounts to
high-Tc superconductors
in
attain
23-26. For
values of
are
comparison,
the
[43]:
l/e^5forYBa2Cih07
-
1
-
/e
>
50 for
Bi2Sr2CaCu208
1 /e > 100 for
-
Tl2Ba2CaCuOs
Moreover, it is important
to
notice, that the coherence length along the c-axis,
than the
intcrlaycr spacing
d
0.64
c,c
(0)
=
4.0nm
Thus, superconductivity
is
substantially longer
in
Si*2Ru04 is three-dimensional in spite of the large anisotropy. It is also interesting
to note that the
kc
?a
1.2
[44]
Ginzburg
to kc
^
2.0
Landau parameter
proposed
was
on
by
pound SrRu03
is
In the
a
pairing
a
years, many
matter
experimental
Sf2Rll04.
l/v/2
realized in this system [49,50].
specific
one m
mass-
3He. And
Their
hypothesis
spin susceptibility-
and Pauli
moreover,
that
related
a
com¬
ferromagnetic.
indicate that Si":Ru04 is
some
was
factor similar to the
following
this state is still
k=
from
superconductors.
the fact that Sr:Ru04 shows
enhancements
ranging
the c-axis is rather low,
discovery of superconductivity in Si*2Ru04 [36], Rice and Sigrist
the
that p-wave
based
nm.
This value very close to the critical value of
[45].
which separates type I from type II
Shortly after
along
=
an
of
results
experimental
unconventional
investigation.
vv
evidences have
superconductor.
In the
appeared,
which
clearly
But the detailed nature of
following paragraph,
hich reveal the unconventional nature of
we
will summarize
superconductivity
in
3.2
23
Superconducting properties
along
ab
along
c
0.03070.058'
0.787 1.4+
ID
1.4*
Hc (0) (mT)
180"
180s
feL(0)(nm)
4-
105772|:
3300"
13071521
Hc2(0)(T)
Hcl(0)(mT)
A(0)(nm)
1.27
k
2.0!
37
Table 3.1: Critical fields, coherence length and penetration depth of \Sr2R1tO4.
•
sample
a
sample with fc
7
from /76/ for
7
from 147] and [48] for samples with 1.4
specific
(RDOS).
as
Since the
quality
was
heat measurements
large
due,
as
specific
samples
of the
•
heat goes to
Early Ru-NQR
the
spin-lattice
ducting
Figure
state,
an
studies
zero
by
Ishida
decreases
observed in conventional
a
et
1/7)
al.
as a
it
of Tc
was
residual
=
in the
zero
an
states
1.14K
[51].
concluded that the
superconducting
density
state
revealed that
of states [52].
of the electronic
heat
specific
superconducting
gap.
unconventional behaviour of
function of temperature. In the supercon¬
without coherence
predicted by
superconductors just
on a
peak,
BCS
as can
theory
be
seen
and is
from
usually
below Tc.
high quality single crystal
revealed
a
of the relaxation rate down to 150mK.This is another indication
Sr:Ru04.
An unusual
strong dependence of Tc
reported by
several authors
Sr:Ru04 is suppressed
moreover,
sample
high,
no
[53] showed
has been
v-wave
a
772-depcndence
sharply,
peak
for line-nodes in the gap of
and,
large residual density of
higher quality crystals
0, leaving
Ru-NQR experiments [54]
773-dependence
•
->
on
indication for lines of
3.4. This coherence
More recent
a
< 1.5K.
Tc
<
but intrinsic to the
experiments
for T
relaxation rate
1/7)
1,39 K.
-
reported
impurity effects,
not to
temperatures,
-
believed to be
was
These measurements also revealed
at low
=
607c of the normal DOS in
of S12R11O4. Flowever, recent
the
0.9 K.
from [44] for
The first
RDOS
with T(
a
7
by
not
on
residual
resistivity of S12RUO4
has been
[47. 55]. Their results show that superconductivity in
only by magnetic,
defects of the
crystal.
but also
by non-magnetic impurities
General
3.
24
1U
1
1
1
1
1
_
1
1
1
II
1
1111|
1
1
1
"_
:
\ Sr2Ru04
;
1
"i"i"i"i
1
of S12R11O4
Properties
*
101Ru
-
Y
10[
-
-
:
/
-
1
fc?
-
-
*/
-
.
4
10°
1
ii
1111
-
»ii
1
ml
iii
1
10°
Vl
101
7'(K)
Figure
3.4:
rate of
Spin-lattice relaxation
taken from [53]. Note the absence of
With the
a
field
vortex
lattice structure has been
However,
not
we
et
to the
would like to
by
below
al.
emphasize,
77
[56] observed
Ru-0
planes.
verv
crystallographic
a
unit cell. This
within the framework
that unconventional
a
superconductivity
square flux line lattice in
strong [59].
superconductors (e.g. superconducting
square flux
model [58].
the observation of
of the flux-line lattice is
a
The unit cell of the
Moreover, in low-k materials1, the influence of the crystal lattice
logy
NQR, data
NMR and
predicted by Agterberg [57]
dependent superconductivity
necessarily implied by
peak
45D with respect to the
lattice is rotated
by
measured
Hebel-SJichter
applied perpendicular
vortex
of the orbital
as
of neutron diffraction, Riseman
help
line lattice in
a
St^RuC^
Experiments
on
on
elements Nb, V. Tc and Pb
is
S12R11O4.
the
morpho¬
low-zc type II
alloys),
revealed
strong correlation between the orientation of the flux-line lattice and the crystal
Note, that SriRuO.; has
obtained from X and
!;
a
low
k\
alue
range from v,
w
~
ith the held
1 2
(441
applied along the
to kc
~
2 0
[451.
c-axis.
Expérimental results for
jo
25
Superconducting properties
lattice, such that the symmetry of the flux—line lattice fits the
lattice
[59). If
tices form
a
tice
of the
crystal
transition from the
predicted by
parallel
neglecting particular
With
highly anisotropic
is based
features
fourfold axis of the
to
on
flux-line lattice to the
of
an
crystal,
indicate
triangular
theory [59].
•
Zero field
as
of the
crystal
relaxation
observed
onset
temperature around 77,,
has been
O-NMR
affected
interpreted
by
experiences
a
Knight
result of
shift in
case
of
(as
most
as
shown in
a
Figure
a
exponential exp(-At)
spontaneous internal magnetic
3.5.
zero
field with
of the
to zero al
the
to
This
to zero as
long
r;/;-plane.
to the
applied parallel
as
goes to
entering
pairing
the
zero
for T
On the other hand, in
high-7"c superconductors)
the
is
singlet,
experimental
Thus,
spin susceptibility [65 [.
Xs follows the Yosida function
low temperatures. The
upon
the electronic
exp(—A/kT).
un¬
from the field that the nucleus
spin susceptibility
superconductor,
realized in the
spin susceptibility
plied along
state.
of oxygen nuclei remains
if the field is
originates
proportional
77 at low temperatures. As
is reduced
an
This indicates the presence
interaction with conduction electrons.
the electronic
an ,s--wave
Knight shift
shift
Knight
hyperfine
metal, is
probably
to
spontaneous time reversal symmetry violation of the
superconductivity
metal, the
low températures goes
state
to
as
a
to
spin singlet pairing
a
For the
at
as
showed that the
the transition
In
For
additional
pSR data
St*2Ru04.
state in
experiments
ab~p\anc |64].
the
al. fitted their
spontaneous magnetic field appearing within the superconducting
superconducting
17
a
et
clear increase of the relaxation rate A in
They
finding
•
an
additional relaxation due to
field.
a
high-K
measurements revealed the appearance of a
(//SR)
function (see page 15) and
to characterize the
of
lat¬
V^Si [60] and borocarbides [61-63].
muon-spin
Kubo-Toyabe
lat¬
isotropic superconductor,
anisotropic properties
spontaneous internal magnetic field below Tc [6]. Luke
the
a
But this
tice. On the other hand, square flux line lattices have also been observed in
materials, such
vor¬
the influence
experiments
The
Landau and London
from
arising
threefold axis of the
a
[59].
assumption
the
crystal
the
crystal,
increasing jc-value,
lattice decreases
original Ginzburg
the
description
theoretical
to a
flux-line lattice is observed.
anisotropy
gradual
parallel
square lattice. If the field is
a
hexagonal
of the
field is
magnetic
the
of the
one
the
Xs is
0.
[66J and
a
dp_p
proportional
spin susceptibility
result shows
superconducting
-±
state
no
change
if the field is ap¬
The data is consistent with the p-wave state
proposed by
General
3.
26
Figure 3.5:
Sigrist.
spins
Tvluon
spin
relaxation rate in
Rice and coworkers
of the
[67]. The
Cooper pairs j ft)
susceptibility
is
expected
the c-axis. However, the
and
magnetic field,
zero
latter is
144.}
to follow the
Knight shift
an
lie in the
been obtained
a
to
on
ob-planc.
shift does not decrease
state
is realized in UPh.
Mao
et
al.
for this field direction is
reported
an
second
measurements
showed that in the
of the
regardless
principle,
the
spin
applied along
experimentally
Hc2(\\ c)
~
not
780 Oe.
in-plane anisotropy
superconducting
transition
an
by
Tou et al.
[68,69]
superconducting
crystal
The authors conclude that
symmetry [481. They have also observed
to a
state, where the
Yosida function if the field is
UPk,. Pt-Knight shift
conducting multiphases.
•
In
[6|.
draw the reader's attention to the fact, that similar results have
high quality single crystal UP7,
Knight
of Si^R11O4
data taken from
equal spin pairing
accessible, because of the small upper critical field value
We would like
Properties
near
state, the
orientation and the super¬
odd-parity superconducting
of the upper critical field with
a
on
feature in Xcu
{H),
which
a
they
fourfold
attribute
HL2- Their observation is in qualitative
agreement with theoretical predictions [57], except for the temperature depend¬
ence.
In contrast to that theorv. Mao et al. did not observe the
H(2 anisotropy,
nor
3.2
27
Superconducting properties
the second transition, down to
TC{II
=
0).
and the second transition is not detectable for T
that
have found
they
parallel
T < 800 mK and the field
to
superconducting
a new
to the
anisotropy
The 77,2
800 mK. Their conclusion is,
>
Hci with
state near
line node gap at
a
In this context, it is
ab-phne.
reduced
strongly
is
interesting
notice, that anisotropics of HC2 have also been observed in conventional super¬
Nb and V
conductors (e.g.
superconductors [72].
isotropy
[70] and V^Si). in borocarbides [71] and in high-Tc
In these
of the Fermi surface
materials, the anisotropy of Hci is attributed
[73]
or
to
anisotropy
the
to an¬
of the order parameter in the
high-7^- superconductors [72].
•
investigated
Laube et al.
They
Andreev reflection of
[29],
contacts
observed two distinct types of spectra:
Spectra with a double-minimum
1.
Si"2Ru04-Pt point
point contacts
structure, for
with
a
high trans¬
parency.
2.
Spectra
with
a zero
transparency
The
experimental
on
bias conductance
anomaly,
barrier
lying
The
strength,
a
feature,
gap-like
as
ob¬
superconductors.
strength, spectra
with
Andreev bound states
the order parameter
predict
[74.75]:
served in conventional
to low
contacts with low
results agree well with theoretical calculations. The latter
1. For contacts with low interface barrier
high
point
the other hand.
also two types of spectra
2. For
for
at
bias
a zero
anomaly.
the surface, caused
The latter is due
by
a
sign change
of
[22].
experiments strongly support
the existence of
an
unconventional
non-s-wave
order parameter in S1-2R11O4. However, the authors could not discriminate between
different
ance
pairing
states.
Moreover, it should be noted, that such
anomalies have also been
predicted
and have indeed been observed in
ductance
peak
zero
bias conduct¬
in the framework of the d-wave
high-T^ cupratcs [26]. Recently,
has also been observed in the
fermion
heavy
a zero
model,
bias
con¬
superconductor UBe^
byWatu>/6-/. [28].
Several theoretical models have been put forward
superconducting
state
in
describe the exact nature of the
to
S1-2R11O4. As mentioned above,
a
large
residual
density
of
states
is observed in S12R11O4, which
(RDOS)
ing
First,
state.
3He,
was
model
the
General
3.
28
a
non-unitary
proposed by Sigrist
the
explains
odd
et
large RDOS
stabilize in
to
Agterberg,
believed
state,
be intrinsic to the
to
analogous
to
the
a
state is rather
nonunitary
unlikely
of Sr^RuC^
superconduct¬
Ai-phase
[76] and simultaneously by Machida
of about 50%, because the
et
of
superfluid
al.
[77].
The
state leaves half of
be realized, since it is
to
[67].
field
zero
Rice and
cd.
parity
But such
quasi-particlcs ungapped.
difficult
-
was
Properties
Sigrist [58] proposed
RDOS. Their model is called "orbital
alternative
an
explanation
dependent superconductivity" [58].
for the
large
As mentioned
above, the Fermi surface consists of three sheets: the y-band (characterized by the Ru
and the
dxy orbital)
Agterberg
scattering
al.
et
a-
and
via
a
suggested
~
that the
on
larger
for the
proximity
highly planar
a.ß
one
The
momentum
parities
under
the
the
hand, and
y-band
on
gap of these two
state, while the other
of states. The identification of the dominant
Agterberg [57]
two vortex
(he field is
iments
examined the vortex lattice structure of
lattice
applied along
a
phases separated by
high-symmetry
applied parallel
to
[56] suggested, that the
which would
imply,
that the
a
second
direction in the
the c-axis.
vortex
7-sheet
that the two lattices
orbital could not be
definitely identified
Rice and coworkers
as a
to be done
Sr2Ru04
superconducting
r//?-plane,
and
was
a
near
up to
an
of
residual dens¬
experimentally.
transition for the field
square vortex lattice if
aligned parallel
misaligned by
one
is
ELp- He predicts
scattering
to the
the relevant orbital. However,
are
subsystems
essentially gapless
The first report of neutron
lattice
was
periments showed,
Sigrist,
band(s) has
re¬
participates only
one
The presence of
space.
one
Therefore, only
than for the other.
excitations for temperatures greater than the smaller gap, will appear
ity
<7-x-orbitals).
their different
superconducting
superconducting
effect in
to
subsystems:
subsystem
and
dv:-
the Ru
character of S12RUO4 would prevent
owing
sheets,
have two
we
the other.
forms the
subsystems
kind of
—c). So
h->
/3-bands
assumed to be
the two
ß- bands (characterized by
and
between the y and the
flection (that is.
the
a-
angle
exper¬
crystal lattice,
more
recent ex¬
of 45°. The relevant
now.
[671 proposed
the
odd-parity
state
characterized
by
the
following pair potential:
dfk)-z(/lx±/Ay)
(3.1)
3.2
written here in the vector
implies
an
isotropic
sequence of orbital
for the two
The
gap without nodes
over
the whole Fermi surface. However,
dependent superconductivity,
group of
point
can
be classified
odd-parity. They
are
according
one
(k) (for odd-parity)
and di
given
as
corresponding
magnitudes
on a
Al,
1
Ain
xky +yky
A-2,
kM^-^)
A2ll
xky —ykx
Bi,
k2^k2
Bl,t
xkx
B2g
kA
B2ll
xky Pyk,
Eu
{zkx,zk\}
-
are
well
//SR [6]
A-phase
is the
belonging
to
are
representation.
As mentioned
[64] experiments suggest
us
an
different
unlikely.
This
above, experi¬
odd-parity
state
that
consider the two-dimensional repres¬
a
combination of the
listed below:
A
phase
cl{k) ^z(k,±ik\)
B
phase
d{k) ^z(k,±k\)
C
phase
d{k)
only
basis functions
is very
particular. Three possible phases, that result from
basis functions
and
-yky
separated, interlayer pairing
and NMR
even
Fermi surface. The
cylindrical
drik)
layers
F of D4/,. There
for both
corresponding
F
sible time reversal symmetry
states
as a con¬
linear combination of these basis functions.
breaks time reversal symmetry. Therefore, let
entation 77» in
representations
Wr(k)
the two-dimensional E„
mental results from
representations
r
E,
already
the irreducible
o-dimensional
tw
orbital part of the gap function is then
Since the Ru-0
to
listed in the table below with the
\j/r(k) (for even-parity)
The
this gap may have different
(3.1)
S1-2R11O4 is the tetragonal group D4/,. Therefore, the possible
four one-dimensional and
excludes
Relation
representation, assuming cylindrical symmetry.
subsystems.
pairing states
are
29
Superconducting properties
state
—
zhx.zk\
which violates time reversal symmetry.
breaking
states
representations.
would involve
In
general
complex
Other pos¬
combinations of two
this would lead to
a
second
phase
30
3.
General
Properties ofSi'2RuÖ4
transition, below which the time reversal symmetry violation appears. This leaves
the order parameter of
equation (3.1).
breaks time reversal symmetry. It
A-phase
of
superfluid
can
It describes
be viewed
L52] revealed lines of
Maki and coworkers
But the
problems
proposed
a so
zero
called
recent
NQR experiments [54]
"f-wavc"
state
explain
intrinsically
unstable [79],
and
this
and
secondly,
specific heal
experimental fact,
havingB\g<S>E„
of this model lie in the fact that first of all. the
are
state, which
two-dimensional analogue to the
in the gap. To
rigorous microscopic derivation in Si'2Ru04;
from this model
as a
odd-parity, unitary
with
JHe.
However, it should be noted that very
measurements
an
us
symmetry [78].
"/'-wave"
the lines of
state
zero
lacks
a
resulting
Heavy Fermion
4
Heavy fermion materials
exhibit
a
Phenomena
huge spectrum
great variety of their properties, it is difficult
heavy
understanding
characteristic
be found in
heavy
of
lermion
heavy
phenomena
fermion metals
are
Due to the
intriguing properties.
an
overall
picture including
and theoretical
is still
lacking.
efforts,
a
all the
compre¬
In this section
some
summarized. Extensive reviews
can
| J 8,80-82].
liquid theory,
In Fermi
density
of
properties
give
Despite great experimental
electron systems.
hensive
to
of
the Sommerfeld coefficient is
of states at the Fermi energy and
thereby
to the
and
D(ef )
directly proportional
effective
mass
nP of the
to
the
quasi¬
particlcs:
2/r
y-
In
heavy
by
about
fermion systems
one
corresponds
the
name
4.1
A
or two
"heavy
at
paramagnetic,
magnitude compared
masses as
-^kFin
large
as
to
those of
yis
ordinary
enhanced
metals.
This
thousand times the free clecctron mass, thus
fermions".
Normal state
large variety
2
=
low temperatures, the Sommerfeld coefficient
orders of
effective
to
,
-—kßD{er)
of
ground
properties
states
is found in
anti ferromagnetic and
heavy
fermion systems:
semiconducting.
31
Table 4.1 lists
superconducting,
some
of the
heavy
Heavy Feimion Phenomena
4.
32
01
giound
7MK)
71(K)
compound
stale
deimg; lempeiatuic
Ce A h
paiamagnetic
YbAgCiu
U0Z1117
UCdn
'
CeCuß
0 002
_
10
-
CePd2Si22
10
-
CeRhln-r
4
-
CeCu2Ge22
4
_
CeRli2Si22
pei conducting
15 2
-
Celm2
su
50
_
UCus
antilenomagnetic
97
-
36
-
CeCu2Si2
0 7
_
CeColm
23
-
Celiln,-
04
uPh
0 5
UBen
09
UR112S12
1 5
17
UPd2AH
2 0
14
-
50
_
semicoiiiductoi
gap
60
CeNiSn
semiconducting
Table 4 1
feiinion systems with then
is
mteiestmg
to note, that
stales
and
has
been
lecenth
compounds
ol piessuic
application
dingiam
gi\ ing
aie
18-4—86[
ev
and then siound stale
oideung lempeiatuics
and
where appiopiiate It
antitenomagnetism often
lound
and theunal expansion measuiements
These Ce based
ptcssuic
giound
reunion sv stents
supeiconductivity
Antilenomagnetic oideung
susccplibihty
35 0
Ce?Bi4Ph
Some he aw
(K)
111
CeCu,,
at
2 mK
based
idence loi
magnetic
ac-
mediated
supetconducting
upon
paitiuilaily inteiesting tempciatuiesupeiionductn îty m these matenals [871
and Cel7bSn exhibit
magneticalh
on
[S3]
antileiiomacnets at ambient pie^uie and turn
Celn
coexist
a
4. J
Norm a l
s ta te
33
properties
ïiT)
material
(I/molK2)
X(Tc)
(pQ cm)
(10 ~3emu/mol)
2
<380
0.7-1.1
CeCii2Si2
P(T)
-)-
UPt3
0.45
180
UBe]3
1.10
260
0.3
-
110/60
0.02
3
15
18
-
105
1.2
U()97Thoo3Ben
0.1-0.3
3
0.290
CeCohis
(ßß)
80
65
-
u
_
URu2Si2
0.065
140
12-70
1.2/4.9
0.03
UPd2Ah
0.145
60
4
110/30
0.85
UNi2Al3
0.120
48
7
45/30
0.24
Table 4.2:
Low-temperature
normal state
properties
systems, after [18.80.81]. Values separated by
Heavy
fermion metals
are
partially
superconducting heavy
slash indicate a-axis/c-axis
compounds
in which
filled 4/"
5/
intermetallic
ents is a rare-earth or actinide with
a
of
or
fermion
anisotropy.
of the constitu¬
one
electron shells. The
high-
temperature properties of these materials resemble those of weakly interacting magnetic
moments,
immersed in
a sea
of conduction electrons.
served in conventional rare-earth and actinide
the atomic moments, due to the
ever, in
heavy fermions,
a narrow
ults in
high density
masses
compounds.
a
behaviour
If the latter
are
usually
ob¬
cooled down
/'-electrons, order, mostly antiferromagnctically. How¬
/-electrons hybridize with conduction electrons and together
energy band at the Fermi level. The
produce
a
the
This is
of states
narrow
width of such
the Fermi energy. A metallic stale with
at
a
heavy
band
res¬
effective
results.
The
crossover
ent in the
from
a
local-moment to the dclocalized
magnetic susceptibilty.
Near
room
regime
becomes most appar¬
temperature, the susceptibility follows the
Curie-Weiss law:
X(T)
where
n
is the
density of
df
3kR{T-Tc\v)
local moments, nct1 the size of the local moment and Tew
the Curie-Weiss temperature.
At low
temperatures,
xST)
becomes almost
temperature
Heavy Fermion
4.
34
Phenomena
300
200
-
O
100
^
-
200
Figure 4.1:
The Curie-Weiss behaviour of the
UBci3 above 100
taken from
are
very
Figure
tems.
In
gives
large compared
4.2 shows
room
of
only
a
a
spin susceptibility xj>
—
behaviour of the electrical
p takes values around 1
finally
temperatures,
several hundred pQ
istivity shows
The data is
PbN(Ef).
cm
saturates
a
large,
for T
->
—
resistivity
0.
In
few p£2cm below 50 K. At
verv
(e.g. UPt3, CeCtnSii)
p{T)
most
heavy
is well described
rrl
fermion sys¬
fermion systems, the
resistivity
Fermi
of
of
res¬
to
values
some
heavy
dropping drastically
by
very
independent, resistivity
low temperatures, the
=A.-pt.öT
heavy
heavy fermions, p(T) is
almost temperature
is observed. For
of
lOußcm at 300 K, and decreases
broad maximum at low temperatures, before
fermion materials
The saturation values
with those of normal metals.
typical
with temperature until it
typically
evidence for localized local moment behaviour.
resembles Pauli
ordinary metals,
unusual: At
of CeAF and
[82].
independent and
of x
K
magnetic susceptibility
liquid theory:
4.1
Normal state
35
properties
Figure 4.2: Temperature dependence
below
compounds
room
resistivity of CeAf;.
Also, the
resistivity
of the electrical
p of
some
heavy fermion
temperature. The inset reveals the Fermi liquid behaviour of the
The data
is
taken from [82].
low-temperature specific
heat differs
dramatically
from that of
ordinary
an
metal, where the low-temperature specific heat follows:
C(T)^yT+ß'^
In many
heavy
tronic part
ther
y(T)
fermion
~
C(T),'T
cooling down,
7« 1
J/molK2
rare-earth
parts.
based
or
—">
0. For
by equation
Most theories,
are
shows
a
-
trying
on
actinide
to
e.g.
CeCuiSi?, UBei3, CeAf3, CeCug
strong upturn with
weak maximum
a
for T
very well described
mions,
compounds
might
appear, but
comparison,
4.1 with y^ 1
explain
the
in
The first part resembles
a
a
-
the elec¬
decreasing temperature. By
eventually
specific
it tends to
a
fur¬
value of
heat of copper below 10 K is
mJ/molK2.
the unusual normal state
the Hamiltonian introduced
impurity
(4.1)
by
Anderson
properties
[881.
of
heavy
It describe
a
fer¬
single
conventional metal. The Hamiltonian consists of three
free-electron Hamiltonian and defines the conduction
36
electrons in the
to
and p-states. The second considers
s-
describe the /'-electrons. Because the
repulsion
the Coulomb
/'-states
filled and this
yields
repulsion
For the
conduction states.
analytically
and is known
system displays local
moments
of
case
as
Kondo-effect; it
moment
ground
leads to
state
is
non
single
specific
compounds
fest
are
a
becomes much
impurities
and
heat coefficient y and
major discrepancies
maximum in
heavy
the
the
with
an
atoms
more
predict
a
finite
p(T).
assume a
with
At low
Moreover, there is
no
and
has been solved
A Kondo
temperatures, the
linear
magnetic susceptibility,
carrying
specific
the
heat for T
a
This results in
concerning
peri¬
[ 82]. This
which this coherence
K).
0.
approaches
the formation of Bloch states
on
—»
/-electrons form
involved. Some theoretical
Kondo model, but
The third
/-states
alloys [89].
large magnetic susceptibility.
experimental
state.
between
problem
from
/-states
with the conduction electrons.
enhanced
the energy scale
a
ground
well to dilute
site Kondo energy, which is small ( 10-100
it is reasonable to
model for the
occurs
a
large
For the Ce-based
the U-bascd
ones,
facts: for instance UPt3 does not mani¬
rigorous microscopic
derivation of this
fermion metals [82].
Superconducting properties
4.2
One of the most
There
exciting aspects
some
compounds.
are
eight
known
listed in Table 4.3,
parison,
and the
we
of
in
conductivity
are
which prevents the
hybridization
applies
degenerate,
vanishing resistivity. Secondly,
electronic
there
problem
lattice of Kondo
would be the
energy levels
degenerate
high temperatures.
behaviour at
However, in heavy fermion systems, the
odic lattice and the
Phenomena
localized around the atomic core,
single-site impurity,
a
temperature dependence of the specific heat, and
a
of
compensated via antiferromagnetic exchange
are
In this case, the
consider
set
possibilities for
several
of the Anderson Hamiltonian accounts for the
term
Heavy Fermion
between these electrons is strong, and is hence included in the
Hamiltonian. It is also the strong Coulomb
being completely
are
a
4.
heavy
together
heavy
fermions is the
fermion
with
some
superconductors
of their
have also included conventional
compound V3Si.
Several trends
are
possible
at
unconventional super¬
ambient pressure.
superconducting properties.
superconductors:
For
They
com¬
the elements Al and Nb,
apparent: All heavy fermion superconductors
37
Superconducting properties
4.2
Tc (K)
-AA4
ç (nm)
l(nm)
k
rci.0(mT)
Al
1.18
1.60
1600
50
0.03
77r
Nb
9.25
2.07
40
50
1.25
181
16
16
6.2
78
18-20
CeCu2Si2
0.7
1.3
9
CeColn.s
2.3
4.5
Celrlns
0.4
UPt3
0.5
1.0
20
UBen
0.9
2.5
10
Uo97Thoo3Be13
0.5
1.95
URu2Si2
1.2
0.6
10
UPd2Al3
2.0
1.2
UNi2Al3
1.0
material
V3Si
Table 4.3: Critical temperature,
Ginzburg
V3Si
-
[18.43.
are
added for
50
56
-
0.0 IT
0.2
2.0/2.4
2.3
-/5
360
1.9
20
100
4.6
10
37
4
4
700
105
1.6
8
8.5
500
105
1.0
3.0/3.6
24
>300
1.5
1,5
specific
81].
80.
5
450
>
heat
800
jump,
Landau parameters and critical fields of
Data taken from
and
3
=
Hc2/J(T)
coherence
some
length, penetration depth,
heavy fermion superconductors.
Values of the conventional
comparison.
Values
separated by
superconductors Al,
Nb
slash indicate a-axis/c-axis
a
anisotropy.
have
relatively
low transition temperatures,
small coherence
the
exception
lengths
of UBci
^
ç, which is due to their
-
conventional BCS value
comparatively high penetration depths
they
exhibit
AC(TL)
—
specific
large
heat
effective
jumps,
the critical temperature scales with the normal state value
mass
quasiparticles
with /'-character (i.e. the
states)
are
involved in
ample,
the
Chevrel-phase
magnetism
by,
the
by
In the
magnetic
heavy
and the
superconducting
from
measurements
an
of
on
close to the
AC(TC)
that the
important
at
heavy-
difference to for
magnetic superconductors [82].
earth moments. But
fermion metals,
are
heat jump
yTc, indicates
superconductivity
conduction electrons which interact
The earliest evidence for
originates
rare
specific
However- with
hybridized /-electron/conduction-electron
Therein lies the
and ternary boride
the local
essentially separate
moments.
the
is carried
superconduetiv ity.
.
whose values
The fact that the
F43yFc.
mass m
X and
In the latter,
is
governed
only weakly with
the contrary, it is the
same
ex¬
the local
electrons, that form
state.
unconventional
specific heat,
superconductivity
in
heavy
sound attenuation and NMR
fermions
spin-lattice
Heavy Fermion
4.
38
In
therein).
relaxation rate (see [81 ] and references
power law
non s-wave
gap without nodes
of the above mentioned
7-depcndencies
indication for
a
in
pairing
the Fermi surface.
on
properties
fermions is the
heavy
fermion super¬
heavy
exponential temperature beha¬
conductors did these measurements show the conventional
viour, which would be expected for
of the
none
Phenomena
were
Indeed,
observed. Another
suppression
of
superconduct¬
ivity by non-magnetic impurities.
While these
power-law
indicators for
only
in UPt3 and thoriatcd UBen in
Specific
heat measurements
the existence of
strongly suggested
of UPt3, shown in
phase diagram
superconducting phases,
ent
earlier, uSR
been mentioned
B-phase
can
a
be
nm.
heavy fermions,
in
discovery
the
a
are
definite evidence for
of multiple
superconducting
critical concentration range.
UPt3 revealed the existence of
an
abrupt change
a
double
multiple superconducting phases.
Figure 4.3,
is
firmly
measurements
peak
struc¬
[91],
in the upper critical field
Nowadays, the
established. It contains three differ¬
labeled A.B and C, which meet at
seen
from Table 4.3, the cubic
a
yielding
coherence
indicated that the
point.
tetracritical
a
low-temperature,
As has
low-field
a
Ginzburg
larger
than the weak
effects [92]. The
ition follows
indication for
dependence
a
specific
of the
nodes in the gap
and
k
a
penetration depth A(0)
Specific
First of all, the
BCS value, which is
temperature-dependence
nodes in the
superconducting
penetration depth X{T)
[93]. NMR
follows
measurements gave
the absence of the Hebel Slichter
peak L94].
a
with
gap
a
type II super¬
extreme
an
of about f 00.
BCS behaviour.
coupling
is
a
a
of
heat
specific
than
more
measure¬
heat
jump
sign for strong coupling
heat data at temperatures well below the
power law
point
nm
Landau parameter
non
of Ui-xThTBei3
compound UBen
ç0 of 10
length
gave clear evidence for
is much
non-magnetic impurities
to
of UPt3 violates time reversal symmetry.
conductor, with
ments
state
Superconducting Properties
4.3
800
on
[90]. This finding, together with
ture
As
anisotropic pairing
sensitivity
superconductivity was given by
unconventional
phases
an
behaviours and
superconducting
cubic
term
T:\
trans¬
which is
an
[92]. Moreover, the temperature
T2 law,
another indication for
relaxation rate
1/7)
oc
point
T3 and revealed
On the other hand, ultrasonic attenuation
of
Superconducting Properties
4.3
100
0
17/
_x
diagram of UPh for
Phase
(mK)
fields in the basal
plane.
Three different super¬
They
labeled A.B and C. have been identified.
conducting phases,
600
500
400
300
200
T
Figure 4.3:
39
ThxBeu
meet at
a
tetracritical
point.
measurements do show a
order parameter
of
UBen-Au
was
in the attenuation below Tc
the observation of
given by
contacts
[28]. But the
most
[95],
feature which docs not
a
very recent, indication for
superconductors. Another,
in conventional
occur
peak
bias
a zero
spectacular
a non s-wave
anomaly in the conductivity
observation
was
done upon substi¬
tution of uranium for thorium.
Thorium,
with
ivity
meter.
even as a
increasing
It does
so,
non-magnetic impurity,
concentration if the
has been
region (I) for
proposed
0
transition
The
at .v2
sharp
a
^
minimum at \\
^
^
heal measurements revealed
a
second
was
attributed to
transition temperatures
are
a
labeled
7,"
i,
an
be
from
seen
an
order para¬
Figure
additional
region (III)
peak
superconduct¬
anisotropic
0.019 and
\2; and
second
has
suppress
phase diagram
0.045. This divides the
region (II)
to
as can
.\
.vi;
[96]. This finding
respective
superconductor
for x\ <
< x <
gion (10 specific
expected
but the decrease is non-monotonic.
The transition temperature has
point
is
into three
for x2 <
below the
irregular
regions:
x.
In
re¬
superconducting
superconducting phase
respectively Tc2.
4.4.
transition.
4.
40
Heavy
Fermion Phenomena
U^Th^-Be^
.0
(b)
(a)
a
\
"\
Tcl(x)
\
-—,
r*
0.5
-
\
Tciix)
(d
-
0
i
i
i
0
i
i
OD
:
1
1
0.02
0
phase diagram
and model
Experimental phase diagram
taken from
susceptibility
measurements; open circles:
triangles: /2
obtained from the kink
specific
from
atures
0.04
at ,\ i
0.06
in
[4]:
of thoriated
UBe^.
Tc\ obtained from
open squares:
77 obtained from magnetization
77,
(J2);
]
solid
Figure (a):
triangles: TL\
M(H);
ac-
open
Tt2 obtained
and
heat measurements.
Figure (17:
Theoretical model: The transition temper¬
superconducting
states with
different symmetry
of the two
~
1
-Y
.V
Figure 4.4: Experimental
(m)-
:
11,1,
1
0.06
0.04
0.02
X2
'?1
0.ÜJ 9 and a2
~
0.045. dix
the
idtng
phase diagram
(J'and 7)
three
tn
are
crossing
labeled with
regions,
(I), (II) and (III). Picture taken from [14],
In the years
existence of
origin
This
of
a
following
this
discovery,
second transition.
But
they
more
have also
was
ascribed to
an
anti ferromagnetic transition,
and
antiferromagnetic
in at
7;.2. Hcffner
et
cd.
7^2 and is restricted only
attributed to
ing
with the
a
observed
to
more
state
state.
rise to controversy
sharp
leading
attenuation
to a state
peak
at
the
Tc2.
with coexistence
evidence for
magnetic
correlations set¬
occurring
region (II) |3].
in
region (II)
This
finding
was
first
below T(2 and coexist¬
However, this result could also be
low-temperature superconducting phase
over
increase of uSR relaxation rate which sets in
concentrations in
spin-density-wave
superconducting
an
a
evidence confirmed the
order below 7)2 [97].
Zero field uSR measurements prov ided
at
given
of the latter. Ultrasonic sound attenuation showed
superconductivity
ting
experimental
explained by
which violates time reversal symmetry
[98].
a
4.3
of
Superconducting Properties
The
urements
superconducting origin
of the second transition
of the lower critical field
critical field H(\ at T(2
ducting condensation
was
41
Ü)„^ThxBei3
[99].
was
observed. It has been ascribed to
phase diagram
the transition from F5 to F\
the transition lies in
anomaly
states
-
7
region (Ilk
of
Tc(x)
and Ueda identified it with the
perconducting
meas¬
slope of the
lower
increase in the supercon¬
an
energy.
4.5: Theoretical
Since the
inferred from
A distinct increase in the
Thorium concentration
Figure
again
for the
x
representations I)
and r$. Two
considered: (a) the transition lies in
are
Picture taken from
for
region (1); (b)
[14].
at.vi around 0.019 is
crossing point
cases
so
sharp
and
cusplike, Joynt,
of transition temperatures
of different symmetry (characterized
by
Fand
belonging
Rice
to su¬
E in Figure 4.4 [100].
Later, Rice and Sigrist assumed the existence of three different phases for concentrations
.v
The
< A'2.
phase
with two distinct
phase
state
in
high-temperature phase
of region (I) and the
single representations: F\.
region (II)
results then
as a
at x2
around 0.045
can
then be
lines:
Tc,r(x)
>
T(_r(\)
in the
region
,v
^
V2.
Tc,r(x)
<
Tcji (a)
in the
region
a
"^
a2.
point
region (II)
respectively.
combination of the two
violates time reversal symmetry. This
anomaly
and 7">
in
as a
identified
low-temperature
representations [98].
is illustrated in
readily explained
The
are
Figure
second
This
4.5. The other
crossing of the
two
Heavy Fermion
4.
42
This model is in accordance with the
to the
model, the transition from the highbe
accompanied by
by
the
Hc\
increase in the
an
experimental
according
facts. First of all,
low-temperature phase
superconducting
in
Phenomena
region (II)
this
to
should
condensation energy, confirmed
measurements mentioned above.
Furthermore, the model is
significantly
different in
supported by
region (I)
371(a)
_
and (II):
j
0.022K/kbar
.for
x<x{
0.07 K/kbar
.for
y
~1
dP
of 77, which is
dependence
the pressure
> .ri
where P is the pressure [101].
The model is also
specific
in
supported by specific
the
magnitude
transition has different
superconducting
heat at the
heat measurements, i.e.
in
in the
jump
region (I)
than
region (II) [96]:
j
AC
~
Tc
.for
v
=
0
F9J/molK
.for
v
=
0.033 >vi
)
Another evidence in favor of this model
urements.
pure
such
As mentioned before,
a
sharp
or
comes
from ultrasound attenuation
ultrasonic attenuation
peak
peak
a
was
upper transition
not observed at the
TC\C\)
Tc2(x). loynt.
due to
consequence of domain wall motion
damping
In
as a
state can
by
produce
muons
nor
Sigrist.
a
because
local internal
a
magnetic
is
supported by
in thoriated
UBen in region (I),
nor
no
in
the other
peak
at
hand,
but instead at
7"C2 would be
[100].
can
field around
the fact that
on
region (II),
that the
very well be
time reversal symmetry
in uSR measurements, which leads
interpretation
UBen,
proposed
addition, the results of the uSR experiments
model of Rice and
sensed
Rice and Fleda
in
meas¬
has been observed in
UBen below the superconducting transition. In thoriated UBen,
the lower transition
This
0.0017 <x{
F56J/molK
to an
explained by
the
breaking superconducting
impurities.
The latter
can
be
increase of the relaxation rate.
similar effect
region (III).
was
observed in pure
4.3
Superconducting Properties
Very recently,
by
iments in
region (1)
for 0 <
<
.v
0.019 is
conclude that their
transition,
as
of the
a
a new
'line of
nature of the second transition has been
anomaly'' Ti(x) in
7*(a) phase diagram [ 102J.
precursor of the lower
findings
would rule out
proposed by Rice
and
43
Ui -xThxBe;3
controversy about the
discovery of
rekindled
the
the
of
a
phase
thermal
exper¬
These authors propose, that
transition
Tci{x)
superconducting origin
Sigrist [98].
expansion
at
„r
>
77,(.v)
0.019 and
of the lower
phase
I
,
$""4
I
v|
I
i
f\
|
iv
I Vs/
fi "T
w*
*
Experimental
5
In the
the
following chapter,
Details
experimental setup
and the
used in the scope of this thesis, will be described.
formed with
cryostat is based
ded
by
an
on
a
cell,
designed
the custom made
imental setup for low-field and
effect in
has been described in detail
proximity
by
a
NS wires
former members of
This
[103].
the Mota group
mesoscopic
The
chamber has been exten¬
powerful
For
inductive measurments.
low-temperature
experimental setup
cell,
exper¬
example
L105-107]. The
our
group in their
[103-105. f 07,108],
Measuring System
5.1.1
A
mixing
were
have been per¬
3He/4He dilution refrigerator.
a
by
experiments
SQUID magnetometer [104] provide
study
5.1
the
and built
it has been used to
PhD theses
The
commercial model, where the
experimental
together with
built inside
rf-SQUID magnetometer
an
that
measuring procedures
The Dilution
picture
of
S.H.E. dilution
it is able to
transfers
cryostat
our
Refrigerator
at
ETH Zurich is shown in
refrigerator (model 420).
keep
Figure
5.1. It is based
Its minimum temperature is
the temperature constant for about two
da)
s,
as
on a
low
commercial
as
5 mK and
the time between two He-
l.
Immediately
aftei the lunstei. the tempeiatuie
icached within
a
can
lew horns
45
change b>
a
few percent, but theimal
equilibiium
is
5.
Experimental Details
coldplate
still
continuous flow
heat exchanger
SnPb shield of the
flux transformer
-
step heat exchanger
„
—
baseplate
mixing
chamber heater
CM N-thermometer
body of
the copper
mixing chamber
sample
___
—
Figure 5.1: Picture of the dilution refrigerator in
our
tower
sample plug
laboratory
at
ETH Zürich.
47
Measuring System
5.1
In order to reach low temperatures,
due to vibrations, radiations,
necessary. Our dilution
and gas
eddy
one
handling system,
the
Therefore,
currents.
refrigerator system
Great
a
a
heavy
These tubes
are
firmly
the other hand, is
The
2.
as
and
tubings.
The He-dewar. The He-dewar is
a
day.
with
liquid nitrogen.
At this rate it is
transferring liquid
The
a
only
possible
follows
one
and
pumping
superinsulated,
helium
so
there is
consumption
relatively
exchangers
and
exchanger,
are
located
on
lines
pumping
a
are
no
need for
precool-
a
lies between 6 and 7 liters
days continuously
two
without
small: At lOOmK, the
good
one
cooling
cooling performance
power-
is due to
thermal isolation. Besides its role
base
as
first heat
plate
heat
exchanger.
exchanger
Then
and three
of Frossati type.
vacuum-can
thermally
isolates the dilution insert from the
sur¬
He-bath.
Measurements of the \ibration
ani
The mechanical pumps
-74e. the still also functions
exchangers
A stainless-steal
rounding
is bolted to the
It is connected to the cryostat and
operate the machine
to
continuous flow heat
sintered silver heat
on
building.
handling system
150 uW which is reduced to 5 uW at 20 mK. The
evaporating
laboratory-floor
helium.
very elaborate system of heat
of
The
from the main foundation. All
liquid
The dilution insert. This unit is
is
building.
anchored and have soft flexible sections.
carefully mechanically
ing stage
top
on
four sand filled concrete tubes.
on
The gas
refrigerator support.
vibrational!)' decoupled
pumping
The cryostat is mounted
from the rest of the
gashandling system.
the dilution
free
the foundation of the
to
the mechanical pumps with flexible
floor which is
standing
vibrational!)' decoupled
pumping
foundation
same
attached
of the cryostat is
has been taken for the setup of the cryostat in
care
aluminum structure, which is
design
e.g.
dewar and the dilution insert.
order to avoid heat leaks due to mechanical vibrations
of
careful
inputs,
consists of the cryostat support, the
superinsulatcd
The cryostat support.
has to avoid all kinds of heat
(1051.
amplitude
on
top of
ourcnostat are
presented
in the PhD thesis of P. Vis-
Experimental
5.
48
Details
He-outlet
SHE-CMN-thermometer,
He-inlet
chamber
mixing
heater
Ge-lhermometer
vacuum can
-—
0.7K radiation
silver heat
-
exchanger
shield
mixing chamber
carbon resistor
thermometers
sample
space
SQUID
pick-up
coils
primary
coils
field coils
soap
Figure
At the
the
at
still,
The
a
a cross
given
sample
in
and is manufactured from
one
from
warmer
Figure
5.2.
by
refrigerator
are
positioned
towers and
on
mixing
in
our
chamber and
parts of the cryostat.
non-magnetic
major advantage:
different
closed
leak-tight
custom-made
epoxy resin
one
specimens
top of removable
a
It holds three
and would disturb the ac-measurements.
towers allows to measure up to three
of the
coming
chamber is extended
mixing
epoxy rather than metal has
Samples
cell of the dilution
Cell
section of which is
produce heating
experimental
cell from radiations
Experimental
(sample towers)
ing
Stvcasl 1266
the
copper thermal shield is attached and protects
The commercial copper
cell,
Copper
D
ETH Zurich.
experimental
5.1.2
D
Cross section of the
5.2:
laboratory
sea
plugs
avoids
measuring
which
devices
(Stycast 1266).
eddy
currents
Our setup with three
in the
with soap seal
experimental
Us¬
which
sample
same run.
are
then screwed into
[109]. Thus,
the
samples
one
are
49
Measuring System
5.1
liquid 3He/4He
in direct contact with the
ages: The
or
samples
clamping
hinders fast
thermal
can
be
mixture. This method has the
them. However, the thermal
establishing
boundary
and
easily exchanged
of thermal
one
avoids
advant¬
possible damage by welding
resistance between helium and solids
boundary
equilibrium between
resistance, also called
following
the mixture and the
Kapitza resistance,
is
sample.
The
given by:
RK^\/(AT})
where A is the contact surface and T the temperature. Below 50 mK, the
results in
a
rather
long
Each of the three
-
-
-
a
field coil
a
primary
a
secondary
time constant until thermal
sample
has
towers
a
coil
coil (also called
out of NbTi wire. We use
gradiometer)
NbTi wire without
between NbTi and copper. The
150,am
tubes.
are
thick
They
nine
pairs
designed
mylar
foil.
mode.
continuously
source
is needed in order
The
driven
by
mixing
not to
an
made
proximity
effect
separated by
three
layers
twisted and shielded with Pb-Sn
located
on
top of the
tubes. The thermal
chamber does
not
vacuum can.
path
There
of the circuit
exceed 2
of this setup is that the
disturb the SQUID
external 12V
arc
to the
are
later)
•
was
10~3,uW,
is used in the coil system and neither of the coils
advantage
apply
coils
are
up and down. With this method,
The field coils allow to
are
secondary
shielding
such that the heat load to the
be described
copper mantel, due
a
SQUID probe
of NbTi leads and nine
persistent
and
(which will
All leads to the coils
connected to the
varied
They
primary
superconducting shielding
No
used in
are
is reached.
of three concentric coils:
set
All the coils and the dc-flux transformers
of
equilibrium
T} dependence
a
a
24 V
field
can
be
custom-made low-noise current
signal.
variable external
or
magnetic
are
battery
magnetic
dc-field up to 2500Oe.
and the current is variated
using
one
of three variable resistances:
-
the
so
called small CCS: 12V, three different ranges with
fO, and 100 mA;
a
maximal current of f,
Experimental Details
5.
50
Sample location
Figure
5.3:
Second order
(left)
and first order
(right) gradiometers
of
our
measuring
system, after [103].
-
-
the
so
called BIG CCS: 12 V
three resistors in series which
Both CCS contain
an
different for each of the three
sample.
can
primary
The
(depicted
The
during
sample
coils generate
operated manually.
a
the measurement.
towers and
given
small ac-field
or
The current-to-field ratio is
in Table 5.1.
to measure
the
ac-susceptibility
of the
frequency
160 Hz.
secondary coils consist of
in
be
is variable in hxed steps between 0.07 and 33 mOe. The
amplitude
be set at 16, 32, 80
The
can
active circuit for stabilization of the desired current. A computer
programm controls the resistors
The
24 V, maximal current 500mA:
or
one
first order and two second order
gradiometers
Figure 5.3):
gradiometer
coilgroups:
two
of
sample
tower
groups of three
Z: and 7a
windings
are
and
second order. It consists of three
one
group of six turns wound in the
5. /
51
Measuring System
L(uH)
gradiometer
number
type
of turns
CMN
second order
8-16-8
z2
second order
3-6-3
0.7
z3
second order
3-6-3
0.7
tower
^secondary
field to
<PSQUID
current
2
260
0.8 f Oe/mA
0.66 Oe/mA
200
Table 5.1:
is such that the
field
magnetic
disturbances do not
to-noise ratio
a
a
linearly varying
produce
single loop gradiometer [110J.
samples (œ 3mm)
In order to
der
gradiometer.
direction and has
magnetic
plied.
a
does not vary if
measuring system.
factor of about
However,
one can
106
only
coilgroups
tower
Z4
uniform
a
second order external
signal-
In this way the
over
that achieved with
measure
relatively
gradiometer does
was
equipped with
short
not vary
if
Thus, first order external disturbances do not
a
a
first order
or¬
opposite
gradiometer,
the
magnetic
field is ap¬
noise in this
measuring
uniform
produce
first
a
of four turns each, wound in
total inductance of 0.6 uH [103]. In
flux inside the
[103]. This astatic design
applied. Thus,
larger specimens, sample
It consists of two
a
towers.
high sensitivity.
with this
measure
gradiometer
field is
noise in this
improved by
be
can
experimental
total inductance of 0.7 uH
flux inside the
magnetic
or a
of the
Specifications
It has
direction.
opposite
0.68 Oe/mA
0.6
4-4
first order
z4
ratio
svstem.
is
If the
sample
resp.
inside the
the
magnetic
A
68
cm
placed
coilgroup
field at the
/./-metal
inside
one
with six
sample
can
shield has been
long cylinder
of 12.8
cm
of the coil groups of the first order
turns
of the second order
gradiometer
gradiometer
-
-
changes of
be measured.
placed
inside the
inner diameter and
liquid
a
helium dewar. It consists of
wall-width of 0.5
cm.
The
a
cylinder
is closed at the bottom and made out of CRYOPERM 10. After its installation, the residual
field at the
sample
space
was
measured to be less than 2 mOe.
5.
52
5.1.3
Experimental
Details
Thermometry
Six carbon resistors
are
located at different parts of the cryostat:
1. at the col dpi ate,
2.
at the
3. at the
still,
baseplate
heat
4. at the last step heat
5.
one
exchanger.
exchanger,
inside,
6. and another outside the
They
are
used to monitor the
mixing
chamber.
of the
performance
refrigerator during
cooldown and opera¬
tion.
Temperature
three calibrated
measurements in the range from 6 K down to 50 mK
attached to the copper part of the
germanium resistors,
For temperatures below 50 mK.
magnetic
of CMN follows
ferromagnetically.
moments of the
In
we use
salt of the chemical formula
susceptibility
general,
Its low
a
Cerium
Magnesium
performed with
mixing
Nitrate
chamber.
(CMN),
a
para¬
[2 CefNTAFri 3 Mg (N03)2 24 H2OF The magnetic
•
Curie-Weiss law down to 2mK. below which it orders
magnetic ordering temperature
Cerium ion and the
the
are
number of
large
susceptibility of
a
paramagnetic
water
is due to the small
molecules in the
magnetic
crystal.
salt follows the Curie-Weiss law:
C
X~"
JZ-XQ
where C is the Curie constant. xo the temperature
and T+ is the
magnetic temperature.
The letter is
independent
given by:
A/;«pe
~7n/?mw(
Van Vleck
susceptibility,
5. /
where
Aawpe
~
(zln N)C and Awsniinw
—
quantity, which
is
for
zero
to have some non-zero
against
for
53
Measuring System
a
and diameter, A
to
the
value of order
of CMN,
mixing
the
with
demagnetization
unity. By calibrating
packed
a
resistor,
inside
thermodynamic temperature
rectangular cylinder
provided by
N is the
a
our crvostat
equal
the
Whcatley
3He/4He
tightly clamped
T down to 5 mK
consists of
diameter and
to the
a
is
practically
[112].
powdered CMN, contained in
height.
exchanger through
mixing
powder
a
in the copper
chamber. The
The Curie constant C and the temperature
cooldown from
be assumed
and coworkers showed, that
magnetic temperature T"
It is mounted
mixture. For this the thermometer
sintered copper
calibration
against
a
magnetic temperature T*
on
10
cm
housing
long capillary
housing
susceptibility
independent
a
right
the outside of
body
is
is connected to the
diameter. The thermal contact between the helium and the outside of the
by
can
chamber. Thermal contact between the CMN and the copper
dilute inlet of the coldest heat
is realized
factor and y is
right rectangular cylinder with equal height
0±0.12 mK [111]. Thus, the
The thermometer in
the copper
yC.
cubic lattice, but which in non-cubic CMN
the Johnson noise temperature of
powder sample
equal
a
-
tube of 0.25
mixing
cm
chamber
of the thermometer, which is
is measured with the
offset xo
are
SQUID.
determined for every
the sermanium resistors below J K.
The
5.1.4
for measurements of
netic flux
ments
small
as
n
Gauss
experimental setup
SQUIDS,
two
flux. Commercial
magnetic
10
as
which
each
are
for
cm2.
offer
rf-SQUID s
An extensive work
on
Webb and
by Giffard.
inductively coupled to
a
sensitiv¬
extremely high
are
able to detect mag¬
the first
magnetic
measure¬
Wheatley [113].
SQUID magnetomelry is depicted
following
The latter contains the
(SQUID)
Interference Devices
with SQUIDs has been written
Our
Details
SQUID Measuring System
Superconducting QUantum
ity
Experimental
5.
54
in
Figure 5.4.
We
use
superconducting dc-fluxtransformer.
(see also
elements connected in series
diagram
the
in
Figure 5.4):
coil, also called
-
one
pick-up
-
one
balancing coil,
-
sample
and of
SQUID:2
•
and
A flux
formed to
•
10~9
to measure
inductively coupled
to
four
each
is 1 uH.
samples,
two
secondaries
SQUID:
a
is
inductively coupled
to
the
sample
coils of
secondary
towers
Z3
Z4
change
flux
of
2000,,
change
Gauss
one
Z2
tower
of
cm2 for
in 7a and
one
our
spot,
so
that it
07
at the
Z4
-
respectively 260</>o
This results in
SQUID.
experimental setup.
currents inside the wire of the
latter at
balancing coils
SQUID-1 is inductively coupled to the secondary coils of the CMN-thermometer
•
of 2
the mutual inductance of the
connected in series and
are
coil
coils in series. In order
secondary
two
signal
can
fluxtransformer,
a
In order to
in
a
Z\ and Z2
sensitivity
remove
any
-
is trans¬
of the order
trapped
super-
resistance heater is wound around the
be driven normal when desired.
5.1
55
Measuring System
Quadrature
ln-phase
Ranee
Div ide
.
n
3!
'•
a
Multiply
a
o
R,
=10kO
CI
CI
PC
\
A
B
Forward
-
Reverse
X
SHE Bridge
Model RBI I
reference
out
fluxtransformer
/
A
secondary A
3
-,
^
<:
3
secondary B
r—
pick-up
coil
cryogenic
'environment
-dT
SQUID
reference in
S.H.E.-SQUID
Control Unit
model 30
S.H.E.-Biphase
Detector
model BPD
AC output
computer
DFC
DC output
Figure
5.4: Schematic
diagram
of the
SQUID measuring system.
56
5.
dc-magnetic
A flux
to
a
Digital
A
the
secondary coil induces
the flux-conservation in the
generates
Details
measurements
change in
proportional
Experimental
to
the flux
change
Flux Counter
the
at
which is
voltage output
(DFC)
the
loop,
a
current in the
SQUID
sample
The
space.
directly proportional
converts
the
flux
senses a
to
Due
superconducting loop.
the flux
directly
control unit
SQUID
dc-output voltage
which is
change
change
at
the
(SCU)
SQUID.
of the SCFJ into units of
flux quantum <p„.
ac-magnetic
The
measurements
complex susceptibility
amplifier (BPD) together
of the latter is
The
a
current
R[. This
with
of the
ined
by
working principles
proportional
current
loop.
A
settings
and Co. The
voltage
amplifier.
goes
primary
voltage
of the
in-phase
(V^
or
and
V/j)
The
primary
as a
secondary,
A7 and Co.
a
lock-in
simplified diagram
and X-
ß
are
—
-
balancing
X
(/,
coil A
and is
proportional
mutual is induced
out-of-phase (quadrature)
—
Vm generates
inductively by
null-detector. The
/
a
A
of
or
B is excited
to
the
SQUID
a
(m-R\/R2)
X-ß-(ni-C2co)
by
on
determ¬
ratio transformers
and fed to the
R2
superconducting
input
by setting
to zero.
the
susceptibil¬
a current
current in the
is measured
conditions
to the
by
the resistor
Vr in the secondary coil, which depends
susceptibility of the sample
x'
where X-
means
inversely proportional
ratio transformers such, that the output of the BPD is balanced
is used
by
bridge (RBU).
V and
balancing
and
J-
following:
voltage
the
across
difference
The
the
as
voltage VA
a
This current is sensed
lock-in
is measured
mutual inductance
the oscillator
to
induces
sample.
the
a
sample
°* ^c
ix
given in Figure 5.4.
mutual inductance between
ity
x +
of the BPD
the values of the
Thus, the SQUID
are:
In-phase
(5.1)
Quadrature
(5.2)
the fractions of the oscillator excitation
voltage
V
applied
to
i?j,
57
5.2 Mcas uring procedures
Measuring procedures
5.2
The
investigation
of
magnetic properties
of unconventional
dc-magnetization
this thesis consist of two main classes of measurements:
relaxation of the remnant
Magnetization
For isothermal
ature
in
zero
magnetization
the
field. The field is
sample
by
cycled
a
fields. The
temperature in
zero
maximum value
The
field.
voltage
104
time t
seconds
two helium
a
or
is
initially
maximum value
cooled to the desired temper¬
H,mx and back
at
the DFC. The latter is
performed
using
cycling field,
magnetization
—
to zero
again.
current at the
proportional
to
the flux
different temperatures and for differ¬
one
minute.
as
to
the desired
After
a
waiting
the field has been reduced to
has been recorded
0 is defined
Tr
measuring
manual resistors, the field has been raised to
as a
zero
function of time
time of
typically
been
performed
approximately
a
a
few
within seconds.
by
a
computer.
the moment when the external field reaches
10"' seconds (the latter is
transfers).
at
has been cooled from above
Then,
Relaxation measurements have
to
to
H,mn within approximately
remnant
starting
sample
magnetization
sample
seconds at this maximum
Then, the
"decays'*):
computer, which drives the change of the
Relaxation measurements have been
cycling
and
space.
Relaxation of the remnant
ent
the
curves,
CCS and reads out the output
at
curves
in
measurements
This process is controlled
change
called
magnetization (also
superconductors presented
zero.
in the time window of 1 second
two
days, i.e.
the time between
Seite Leer1 /
Blank leaf
6
Experimental
6.1
Introduction
In
our
Results
on
investigations of the magnetic properties of SriRuO-t,
we
Sr2Ru04
started from the
following
hypotheses:
two
-
In the framework of
a
ave
p-x\
model for
transition has been
conducting
Sr^RuO.;,
proposed [58].
the
possibility
In the
of
second
is
superconducting phase
field [1.99]. In
analogy
to
accompanied by
these systems,
we
second super¬
multiphase superconductors
UPh and thoriated UBen in the critical concentration regime, the
to a
a
a
phase transition
kink in the lower critical
decided to look for
an
anomaly
in the
temperature dependence of the lower critical field.
-
According
Sigrist
to
perconducting
states
and
Agterberg,
should form in
domain walls,
superconductors
metry [2]. As follows from this theory and
results of
ted
our
through
group
on
can
as
on
vortex
dynamics:
degenerate
su¬
suggested
can
domain walls
from
be
experimental
indirectly
occupied
with
detec¬
pinned
be efficient barriers for vortex motion and prevent flux flow.
In the view of this theorv. anomalous strong
right
has been
two
that break time reversal sym¬
UP7, the presence of domain walls
their influence
fractional vortices
separating
below T(. since the bulk
pinning should be
superconducting phase
observed in
SroRu04
of Si^RuCU is believed to vi¬
olate time reversal symmetn.
For that purpose
netic field, and
we
performed
studied vortex
dynamics
measurements
as a
function of temperature and mag¬
of the lower critical field. These measurements
59
60
6.
have been done with the
c-axis, and in
This
samples
lyzed.
is
a
magnetic field oriented both parallel
given.
Then follow
and
on
Sr2Ru04
perpendicular
In the
same
course
as
follow
s:
In the first section,
of this thesis, three
section, the results of
dc-magnetization
a
the
description of the SroRuQ^
St"2RuC>4 single crystals
ac-susceptibility
measurements as a
have been
measurements are
function of
applied
field.
creep measurements, both
as a
function of temperature and maximum
ana¬
presented.
From the
latter, values of the lower critical field have been obtained. In the third section,
presented.
to
temperature range between 7 mK and Tc.
chapter is organized
In the
Experimental Results
vortex
cycling field,
are
Description
6.2
of the
61
Si^RuO4 samples
Sample Description
6.2
Si"2Ru04 single crystals
of this thesis, three
In the
course
atures
have been measured. All of them
the group of Y. Maeno at
1.
were
with different transition temper¬
prepared by floating
zone
technique [36]
in
Kyoto University.
Sample (C49)
Figure 6.1:
applied perpendicular
first been
angle
Sideview and topview of the
of 15° from the
The first
sample
sample
are
crystal
we
shown in
was
measured
Figure
oriented
ments, the field has been
which
ure
means at an
6.1 ).
sample's largest dimension,
Secondly,
angle
was
Figure
6.1. It has
and its
mm
by
an
mass
takes
at an
of 15° from the
it has been
place
at
Tc
ellipsoidal shape
and its size is
is 11.5 mg.
applied perpendicular
^
-
as
-
to the
to
measure¬
sample's largest dimension,
<r//;-plane (see picture
applied parallel
6.2. T( has been taken
sample
almost
Fane x-ray diffraction. In the first series of
ATC results from using the 1077
the
means
Si-2Ru04 (C49). A top- and sideview of the
Wo determined the transition temperature
in
which
fl£>-plane.
2.63minx 1.52 mmx0.98
The
the
to
Sr4luC7 (C49) single crystal. The field has
on
the left in
the c-axis.
by ac-susceptibility measurements,
the middle
point
907o criterion. The
1.03 K and has
a
Fig¬
of the
transition, the value for
superconducting
width A7^
shown
œ
300mK.
transition of
62
x
0.0
-0.5
-1.0
0.02
0.01
0.00
-1
1
1
1
1
Hllc
H
1
1
1
1
h
and
1
6.
1
H
1
1
1
1
1
1
1
—
on
r
the
S12R11O4
ac-
33mOc in the
of
F
1
Results
1
:500
Experimental
000
temperature.
has been renormalized.
ae-amplitude HCIL
at the lowest
susceptibility
an
out-of-phase component
I(mK)
Sr2Ru04 (C49)
_,—1—1_
The
measured with
in-phase component
Sr>Ru04 (C49)
6.2:
Figure
of
susceptibilitv
mOe of the crvostat. The
susceptibility
2
H'dL'3
the minimal value of the
^
residual dc-rield
using
6.2
of the
Description
2.
S12R11O4 samples
63
Sample (C82)
In the years
improved,
important
sample
following
to
with
confirm
a
a
our
results
is
an
thin
extremely
transition of the
width of
only 27,
~
sample
(C49),
the
sample quality
1.5 K have been achieved.
So
we
It
was
another
analyzed
of
channeling diagram,
Figure
of the size 1 mmx3mmx0.25mm. The
takes
place
at
Tc
~
1.5 K, and is very
60 mK. Both values have been determined
shown in
electron
as
on
high quality crystal.
platelet
susceptibility,
an
high
as
on a
experiments
higher Tc.
superconducting
with
first scries of
and critical temperatures
Sample (C82)
row
our
6.3. The orientation
was
by
determined with the
the c-axis turned out to be
along
nar¬
ac-
help
the shortest
dimension.
A
big experimental difficulty
field
applied along
fact that the
drive the
the data
the c-axis
was
very poor.
A. It is
previous
and
was
critical field
sample critical:
Appendix
the
higher
the fact that the
was
27T
extremely high.
77t2
^
~
to
H(2. Also, due
our
emphasize,
following samples.
Because of this
300 Oe is rather small,
The results of
important
demagnetization
to the small
we
factor with the
reason
had
that
they
problems
size of this
relaxation measurements
and the
arc
to
sample,
given
in
do not contradict the results of
64
6.
_,
,,!
1
!
!
!
1
|
,
!
Experimen tal
{
!
|
,p
Res ul ts
on
Si'2 R u O4
,,j-
0.0
S17R11O4 (C82)
H II
*
c
-0.5
1.0 •m*
»
»--
1
i
1
i
i
i
i
1
0.10
V*
0.05
0.00
J
500
7'
Figure
6.3:
susceptibility
The
of
residual dc-field
using
in-phase component
i_
fOOO
< 2 mOe
the minimal value of the
and
out-of-phase component
an
of the crvostat. The
susceptibilitv
Î000
(mK)
Sr:Ru04 (C82) measured with
E'JS
1500
at
ac-amplitudc Hllc
—
of the
ac-
33mOe in the
susceptibilitv has been renormalized,
the lowest temperature.
6 2
Desciiption
3
of the
65
S12RUO4 samples
Sample (C81)
Because oi the
pioblems
pictuie ol the sample
figure 6
closed
Top-
4
by
can
shown
the white line indicates
be
seen
with lounded
m
and sideview oi the
giam oi 1 iguie 6 S
As
is
stated above,
was
ft
om
angle
the
comeis,
figui e,
This
sample
and
the
atea on
I he
sample
which the
tectangle
channeling
*>
the
Flection
depicted
1( slightly low et.
athei
big
chunk
m
the foim of
A
en¬
dia
in
ol
an
flè-pkmes
election
can
easily
mass
channeling diagiam,
be
129mg
shown
m
iccogmzed Theyfoiman
sample
channeling diagiam of S11R11O4 (C81)
m
Figuie
which
help
paiallelepipcd
a
ol dimensions 4 8 mmv2 2mmx2 6mm and
has been annealed
urements aie
thud
below
SitRuCai (C8I) single crystal
it is a 1
ol 7" with the face oi the
I iguie 6
measute a
taken
Ft om the lattei
5
figuie
appioxtmatelv
It has also been onented with the
Figuic 6
the
decided to
we
is
oxygen (oi
one
month [114]
6 6 The twmsition
piobabl)
due to
a
is
Susceptibility
bioadei than
latgei
111
meas¬
sample (C82)
amount of delects than
m
66
6.
the
previous crystal.
almost
as
large
as
We found
in the
Tc
Experimental
1.4K and the width
~
Results
ATC
pc
on
S12R11O4
230 mK, which is
low-IJ sample (C49).
->—1—1—<-
_,
0.0
,
,
,-
4^^^r~
Sr2Ru04(C81)
1 J.
,,„
1
w
j
-0.5
-*
/
-—"
-1.0
I
F
-J—I—H—h-1—b
1
1
0.015
0.010
k
0.005
0.000
^^^
-
_i
1
1
0
L
1
I
-1
500
I
i_
1000
1500
2000
T (mK)
Figure 6.6:
susceptibility
The
of
residual dc-field
using
in-phase component
SriRuCXt (C81)
H',[s
and
measured with
out-of-phase component
an
< 2 mOe of the cryostat. The
the minimal value of the
susceptibilitv
at the
ac-amplitude HCIL
susceptibility
=
of the
ac-
33mOe in the
has been rcnormalized,
lowest temperature.
6.3 Measurements of the lower critical field
6.3
67
Measurements of the lower critical field
Values of the lower critical field of
isothermal
magnetization
been measured up to
a
our
have been determined with the
samples
measurements as a
function of field.
maximum field of either 65 Oe,
or
help
Magnetization cycles
300 Oe in
a
of
have
temperature range
from 7 mK to 77.
H (Oe)
Figure
field
6.7:
Magnetization
applied parallel
o/;-plane.
Here the
to the
longest
tion
at an
cycles
it shows
a
in
angle
of 15e from the
Figure 6.7.
Sr^RuCti (C49)
dimension of the
demagnetization
Typical magnetization curves
applied
of
curves
of
1 actor has been
sample (C49)
a^-plane.
is their strong
An
different temperatures with the
at
sample,
entering freely
are
depicted
important
irreversibility.
into the
sample
curves
does not
change significantly
with
in
Figure
the
6.7 for the field
feature of all the
Instead of
a
sharp
magnetiza¬
minimum at Hc\.
large pinning, which prevents
and inhibits free vortex motion. In view
of the vortex creep measurements discussed below, it is
of the
angle of 15° from
neglected.
very broad cusp. This is due to the presence of
the vortices from
at an
important
to note,
decreasing temperature.
that the
shape
Experimental Results
6.
68
Figure
field
As
Magnetization
6.8:
parallel
the c-axis. The
to
be
can
creasing
branches
are
be attributable to the
Macno group
Figure 6.8,
almost
to
different temperatures with the
factor has been
the minimum of the
the c-axis. At
The
parallel.
at
neglected.
increasing
higher fields,
magnetization cycles
the
show
branch is much
increasing
a
less
and de¬
pronounced
an
additional feature appears
"peak
effect*' observed in
at
higher
fields.
ac-susceptibility
This
"hump"
measurements
could
by
the
[44],
6.9 shows
field of 65 Oe and
also
St^RuCF (C49)
demagnetization
applied parallel
above T > 400 mK,
In both
of
(Oe)
than in the other field direction. It should be noted, that for temperatures
irreversibility
Figure
from
seen
for the field
sharper,
curves
Sr2Ru04
300
200
H
on
magnetization cycles
Figure
6.10
one
the field has been
graphs
strongly irreversible,
as can
of
sample (C81)
magnetization cycle
up
to a
applied
in the
«/;-plane.
be
from
Figure
seen
up to
maximum
cycling
maximum field of 300 Oe.
The
6.10.
a
magnetization
Due to
curves
large pinning,
is
the
minimum of the ascending branch is much broadened.
Ideally,
infinite.
the
So, in
read from the
slope
an
of the
magnetization
ideal type 11
magnetization
curve
superconductor,
curve
as
at the lower critical field should be
the lower critical field
can
directly
the minimum of its increasing branch.
be
But, due
6.3 Measurements of the lower critical field
I
1
69
'
1
1
^
5
"'••-...,_
-
Sr2Ru04(C81)
-
H±c
0
^
-
—<
•
_D
cd
ï
-5
^0~-XX
-1
400mK
^^^-X
'
i
,
0
i
,
40
20
8mK
i
i
-
"
,
60
80
H(Oe)
figure 6.9: Magnetization cycles of Sr:Ru04 (C81) up
to
a
field of 65 Oe at different
temperatures. The magnetic field has been applied along the a/>-planc. The demagnet¬
ization factor has been
to
neglected.
strong pinning, this minimum is very much broadened and lies
higher than Hc\,
impracticable.
which makes this
Nevertheless,
the field of first flux
straightforward determination
quantitative analysis
a
penetration.
In this method,
as
of
HC\(T)
determines the field, where the deviation AM from the initial
curve
A/(77)
takes
beginning
of the
that the
field H
also used
we
magnetic
H > Hc\.
a
by subtracting
the
raw
a
at
induction of
line
the
possible by measuring
Figure 6.11,
slope
a
intersecting
straight
data M (H).
the
shows
of the
always
which enhance the field at the
edges
of the
second method based
one
simply
magnetization
on
some
corners
sample already
curvature.
of the
at very
sample.
small fields.
the Bean model. The latter
predicts
type 11 superconductor increases quadratically for fields
Consequently, plotting
yields
magnetization cycle
demagnetization effects
Thus, vortex penetration starts
Therefore,
considerably
place.
Flowever, the
This is due to
value
of the lower critical field
is
sketched in
at a
the square root of the deviation AM
the 77-axis
at
H
=
versus
HL\. The deviation AM
line fit to the low-field part of the
the
was
magnetization
applied
calculated
curve
from
6.
70
1
1
1
1
1
1
1
Experimental
1
'
!
1
Results
1
on
S12RUO4
1
1
-
Sr2Ru04(C81)
10
-
H12 c
-
•§
0
\
\
7'=8mK
1
1
1
1
1
0
1
1
1
1
1
The magnetic field has been
SigRuC^ (C81) up
cle ot
applied along
300
(Oe)
H
cv
1
1
1
200
100
Figure 6.10: Magnetization
1
the
to a field
oft-plane.
The
of 300 Oe at T
demagnetization
=
8 mK.
factor has
been neglected.
i
i
•
IV
1
<
1
-
i
-
80
'
£
3
S 40
/
—
'S
l<
1
-
~
/
*>
-0 1
/
Hcï
/
S "0.2
-
-
/
/ill
i
,
i
10
-0.3
30
20
//(Oe)
Figure
6.11: Illustration of the
data is taken horn
applied along
the
a
values of H,
of ±0.5 Oe
\
or
magnetization
aft-plane.
Both methods lot
resulting
two
In this
obtaining
ol
graph
the
er
to
obtain ïlL\ (see text for
sample (C49)
ctnve
the low
from the two
±1 Oe close to T,.
methods used
-
500 mK, with the field
demagnetization factor
critical field
anal)ses
at T
are
the
are
same
details). The
has been
illustrated in
within
our
neglected.
Figure
6.11. The
experimental
error
6.3 Measurements of the lower critical field
The values of the lower critical field
both field directions.
field
applied
in the
demagnetization
an
are
Figure
given
are
6.13 presents the
aft-plane.
In both
factor. The latter
ellipsoid and using
71
Hi
data obtained
\
on
approximating
Comparing
the
in-plane
data of both
sample (C49)
sample (C81)
the
tables of [115]. The values of the estimated
in Table 6.1.
for
the data has been corrected
cases
obtained via
is
Figure 6.12
shown in
by
in
for the
respective
the
sample's shape
with
demagnetization factors
samples
one
notices, that
77f i (0) of the high quality sample (C81), is about three times higher than that of the lowTc sample (C49). The values of the lower critical field
sample(C8i)
1.03
1.4
^i(o)1; c(Oe)
31.270.5
#cl(0)|| t?ft(Oe)
Table 6.1
:
\
(0)
been estimated
the field
Fet
Using
us
has been
according
ab
applied
in the
H( \ (0) and the estimated demagnetization
our
Landau
ones
theory,
Along
HL\{0)
(0) ||
ab
namely 77Li(0) )
ab
value is HL
Hc\
(0) ||
It
\
measured
ab
was
=
-
=
larger: HLi{0)
\
c
'
c
on a
only
—
in our
by
Yoshida
al. [44J.
et
larger
than
we
a
rather low T(
=
0.9 K.
our
oft-plane,
their calculated
value for the
low-T( sample,
obtained
on
the
high quality crystal
to their calculated value.
discovered many years ago, that the decrease of the
field with temperature is
data available with
low-77 sample, whereas, their
llOOe. In the
6A Oe. However, the value,
comparable
with
sample
31.2 Oe
=
14 Oe, which is much
18.6 Oe is
is
D has
the authors of the latter paper calculate their
Ht2-daVà. taken
estimated value is much
demagnetization factor
in Table 3.1 obtained
lower critical field values from
we
data. The
rtft-plane.
Ginzburg
the c-axis,
0.18
[ 115]. For sample (C81) there
compare these values to the
BCS and
-
0.31
extrapolated from
to
18.6 ±0.5
0.23
Values of the lower critical field
factor D. If
-
6.170.5
k
D for 77
summarized in Table 6.1.
samplc(C49)
Tc (K)
D for II
are
approximately proportional
thermodynamical
to the square of the
perature. This temperature dependence is quite well described by the
two
critical
reduced
tem¬
fluid model of
Experimental
6.
72
1
'
1
'
1
1
1
Results
1
1
|
S12R11O4
on
-
Sr2Ru04 (C49)
Ï
30.0
r-
-
\
\
S
Id
Hclllc
S
20.0
O
\
-
k
?
\
10.0
\
\
\
W!>-
00
1
1
.,.
1
1
1
800
T
along
(mK)
6.12: Values of the lower critical field of
is scaled with
the
a
demagnetization
aft-planes.
?^2,
1
,
400
0
Figure
\
ï
factor of D
—
sample (C49)
with Tc
=
\ -03 K. The data
0.23 in the c-direction, resp. D
The dashed lines represent the fit with
a
simple parabolic
=
0.31
law.
Goiter and Casimir [116]:
tft(T)-tf((0)
In
for
a
first
simplicity
are
and
approach,
a
we
tried
to
fit
our
(6.1)
77,1 data
to a
simple parabolic law, assuming
temperature independent Ginzburg Landau parameter
plotted together
with the data in
Tc used for this fit
arc
given
Figure
6.12 and
in Table 6.1. As
could not satisfactorilv be fitted to this law.
Figure
can
be
v.
The fitted
curves
6.13. The values of Hc\
seen
from the
graphs,
(0)
the data
6.3 Measurements of the lower critical field
20.0
1
1
1
!
1
j
1
1
1
!
f
73
!
1
!
[_
-,
1
,
,
,
,
1
,
r
Sr2Ru04(C81)
Hlc
15.0
<D
o
10.0
tf
5.0
0.0
J
I
I
0
I
I
I
I
200
L_J
L
I
T
Figure
a
a
demagnetization factor of
simple parabolic
regime,
the
phase
not
give
A
theory.
of the
two
any
transition
more
L
I
i,„ I
1200
i„
-i
1400
sample (C81)
with 7^
1.4 K. The data
—
0.18 The dashed line represents the fit
and thoriated UBois in the critical
In
superconducting phase
analogy
to
these systems,
with different constants
77ci(0).
is
concen¬
accompanied by
we
also tried to fit
But this
procedure did
result either.
thorough analysis
is obtained from the
In the framework of BCS.
thermodynamical
=
second
to a
[1.99].
^-dependencies
satisfactory
I
1000
law.
kink in the lower critical field
the data to
I
(mK)
D
multiphase superconductors UP7
In the
tration
a
Il
I
800
6.13: Values of the lower critical field of
is scaled with
with
L_J
600
400
Mühlschlegel
critical field IIL
i t h as t he fo 11 ow i n g fo r m :
comparison
of
our
results with BCS
calculated the temperature
numerically [117).
In the
dependence
low-temperature limit,
74
6.
Experimental Results
Sr2Ru04
on
i.i
-
.
\.
/Ȃo
1.0
ï 0
1
1
0.0
0.5
1.0
(')
Figure 6.14: Temperature dependence of v-,(/) 77n
He
—
In order to be able to compare
ical critical field
Hc of
relation (valid in the
our
1-2.115
Hn
[118J.
—
77
our
samples.
the clean limit
results to BCS,
As kc
calculated the
we
31 in Sr;>Ru04.
thermodynam-
used the
following
This relation is similar to the
Ginzburg
^
we
high—k: limit) [118]:
7 2
Hcl^^^Hci^hlKiit)/^)
where /
=
T/Tc
is the reduced temperature.
Landau formula, but the
by
a
r-independent Ginzburg
temperature dependent function
because in
our case
/ 7>
jc?(f). plotted
Landau parameter jchas been
in
Figure
replaced
6.14 for the clean limit
[118],
ç7 [47].
It is customary to present the temperature
dependence
of the deviation from the Goiter and Casimir relation
(6.1):
1-
T,
of the critical field in terms
75
6.3 Measurements of the lower critical field
0.05
Sr2Ru04(C81)
-0.20
0.0
1.0
0.5
(TITC)2
Figure
squared.
function of reduced temperature
high quality sample (C81)
The lines
through
For
taken from
|20j.
The open diamonds
points
these data
we
are
guides
have also
together
w
ith £>
( f-)
to the eye.
plotted
We determined this deviation for both
6.15
represent the
The solid
SroRuOj samples.
for the BCS
phonon coupling.
than
predicted by
In
SriRu04
law is
on
positive.
as a
values of the
curve
is the BCS
(dashed line),
The result is
given
in
theory.
as
Al, follow BCS theory. In the
latter, the deviation T> from the Gorier Casimir relation is rather weak,
parabolic
plotted
sample (C49).
the deviation of lead
Conventional, weak coupling superconductors, such
the deviation from the
law
and the closed diamonds those of the low-7)
comparison,
deviation.
Figure
parabolic
6.15: Deviation of the reduced critical field from the
at most
4%. In Pb,
This may be attributed to strong electron-
the other hand, the deviation is
negative,
but much
larger
BCS theory. It amounts to 15-20%. This is another indication for the
unconventional nature of
superconductivity
in
SroRi^.
6.
Experimental
the lo\v-Tc
sample (C49),
76
6.4
parallel
and
perpendicular
to the
the field
applied perpendicular to
6.4.1
Remnant
In
on
S1-2R11O4
Vortex creep measurements
In this section flux creep measurements
both
Results
6.16 and
Figure
is shown
cycling
as a
on
c-axis, and
the c-axis, will be
Magnetization
the
high quality sample (C82),
with
presented.
magnetization M,cm
function of temperature and in
applied
function of temperature and field
as a
6.20 the remnant
Figure
on
with the field
Figure
6.17
as a
of die SriRu04
samples
function of the maximum
field Himn.
This behaviour
can
be
qualitatively
described in the framework of the Bean model
[119,120].
In the critical state, the Lorentz force
the
force and
pinning
generates
current
a
a
change
of
acting
field leads
magnetic
on
the vortices is balanced
flux
to a
density gradient,
by
which
density:
4;r
c
The Bean model
that
a
small
superconductor
straight
of the
lines of
Let
us
from
(a)
current to
limiting superconducting
current
density jc
Any electromotive force,
even an
arbitrarily
flow
locally.
field. Thus, in this model the flux
in
zero
example
field. To
an
infinitely
density profiles
are
jc
is
simply
simplify
density profiles
extended slab of thickness d with
the calculations,
and the remnant
three different external maximum fields
to
Bean assumed further that
slope 4rtjc/c.
sketched the flux
to
a
carry without loss.
magnetic
consider for
magnetization
sample
can
that there exists
will induce this full
one,
independent
we
assumes,
(c). Drawing (a) represents the
critical state and (c) the
fully
critical state.
so
we
neglect Hc\.
magnetization
Hmn.
The field
In
after
zero
Figure 6.18,
cycling
the
Hmax is increasing
called undereritical state,
(b) the partially
6.4
Vortex creep measurements
15-104
T
1
1
77
1
1
1
1
1
1
t
f
r
Sr2Ru04 (C81)
I0-104
5-104
0
1500
1000
500
0
T(mK)
Figure
6.16: Remnant
for the field
as to
applied in
be in the
fully
magnetization of SnRu&t (C81)
the
r/ft-planc.
critical
state
ID is the maximum field that
superconducting
sample
The
The line
can
serves as
„,
4/r
---
—-
c
It is the field at which, for
undercritical to the
partially
critical state at 77
that the flux
guide
a
function of temperature,
cycled
to
in
high enough fields,
the eyes.
screened out at the
midplane
of the
slab:
H
fully
has been
completely
be
as
—
.
ic
d
i
increasing cycling fields Hmn,
critical state.
For fields Hmn
0. Case (a) and (b) differ from
density gradient changes sign
inside the
the
>
case
sample.
sample
277", the
passes from the
sample
is in the
(c) by the important fact,
Results
Experimental
6.
78
on
S12RUO4
-1—1—1—1—1—1—1—1—1—1—1—1—1—1—j—1—1—1—1—j—1—1—1—1—1—1—1—1—1—1—1—r
15
10
Sr2Ru04(C81)
-
Hlc
1, af
0
1
1
1
l
1
1
1
100
0
1
I
1
1
1
1
I
1
1
1
300
200
1
I
1
1
1
1
I
1
1
1
500
400
1
l—1
l
600
«max (Oe)
Figure 6.17: Typical example
of the
the maximum cycling field. The line
remnant
magnetization of S12R11O4
serves as
«aide
as a
function of
to the eves.
The remnant magnetization is defined bv:
M1tm^~f-B{x)dX
Mmn depends
case, it is
on
the
given by:
sample's geometry
and size and also
on
its
magnetic history.
In
our
6.4
Vortex creep measurements
79
"max
2H*
2jyr+
2W7__
\
\
''mav
X
\
v
f7
/
N
\
rlmax
\
/
\
/
XZv
\
\
\
/
A//\
\
/
/
\
\
'
H=0
t/
—'-
\
'
A
(c)
(a)
Figure 6.18: Drawings (a)
to
(c) sketch the flux
slab of thickness d. for three different
magnetization,
again.
completely
Hc\
is
II
\
/
to zero
'
/
X
/
'
the remnant
'
'
'
'
\
—
11—0
'
'
/
\
\
'
/
X
\
after
The field denoted
screened out
at
the
density profiles
cycling fields Tlmax.
cycling
the slab to
a
in
an
infinitely extended
The shaded
area
represents
maximum field Hmax and back
by 77" is the maximum external field which
midplane
of the
superconducting
slab. For
can
be
simplification,
neglected
//nm///*
Figure
an
6.19:
Remnanl
infinitely
partially
cases
magnetization
extended slab [121].
critical state (PCS) and the
as
a
function of the maximum
Also marked
fully
critical
are
state
cycling field for
the undercritical state (UCS), the
(FCS), corresponding
to the three
in Figure 6.18.
4/T 8 ,t<//(
M rem
=
-Hr„,
max
for
Hmax
<
77"
{
l iJcd
(6.2)
for
H > 2H"
6.
80
Experimental Results
S12RUO4
on
I.O-IO4
r(iriK)
Figure
6.20:
Temperature dependence
with the field
shown here,
applied
were
both
taken with such
critical state. Hie lines
The field
remnant
magnetization
guides
perpendicular
to the c-axis.
high fields, that the sample
All the data
always in
was
points
the
fully
to the eyes.
of the remnant
increases
fully
and
magnetization of S12R11O4 (C49)
as a
magnetization
function of the
is
cycling
critical state, i.e. for fields H
>
plotted
in
Figure
6.19. The
field H,mn, until Hmn reaches
2/77, the
remnant
magnetiza¬
M,em becomes independent of Hmix.
tion
In
ure
are
dependence
the value 2/77 In the
parallel
of the remnant
6.17
is in the
spite
can
be
fully
pendent of
is then
of the
simplifying assumption,
qualitatively interpreted
critical state for H
the maximum
proportional
to the
2/7
=
cycling
critical
the field
dependence
of
with the Bean model. At T
^
200 Oe, and the remnant
field. As
current
can
/).
be
seen
Mmn(Hmax)
=
in
Fig¬
70mK, the sample
magnetization
from the above
is inde¬
expression, Mrem
6.4
Vortex creep measurements
Due to the
density.
samples' irregular shape,
It cannot be
we
it is difficult to estimate the critical current
read from relation
(6.2), because
with the field
sample (C49)
4.8
—
mm.
has almost the
In this case, it is
of
shape
appropriate
to use
Mnm^^Jc
depends strongly
applied parallel
with radius R
cylinder
a
this value
to the
c-axis,
104A/cm2.
obtain values of the critical current of the order of
Sample (C81)
ft
directly
the chosen thickness d. For
on
81
the formula for
1.3
=
mm
and
height
cylinder given by:
a
H->2H"
for
3c
This
gives
In
in the
so
a
value of the critical
Figure
6. J
6,
we
plotted
current
the
high quality sample (C81).
that the
sample is
dependence
/)(())
^
2000
A/cm2.
temperature dependence of the
All the
points
are
in the critical state. Therefore,
taken for
cycling
of the critical current. It shows, that the critical
current
This behaviour is
system: it is also observed in sample (C49),
as can
shape
of the
curve
does not
be
seen
change significantly with
Figure
high enough,
the temperature
varies
typical
from
magnetization
fields
Figure 6.16 represents
and saturates for the lowest temperatures.
the
remnant
continuously
for the
Si"2Ru04
6.20. Moreover,
field orientation.
82
6.
6.4.2
Relaxation measurements
as a
Experimental Results
ent
response to the
(122, 123]. The resulting
creep rates
are
proportional
to
driving
jump
force of the current and
creep has
vortex
Sr2Ru04
function of temperature
At finite temperatures, thermal energy may allow flux lines to
center to another in
on
a
logarithmic
time
from
pinning
one
flux-density gradi¬
dependence
and the
temperature:
dhiM
kBT
_
dint !
Such
a
Uf,
behaviour has for instance been observed in classical
Isothermal relaxation
measurements on
perature range between 7 mK and 7;. in
a
time
superconductors.
S1WR11O4 have been performed in the
w
indow from I second to
104 —103
tem¬
seconds.
In order to be able to compare relaxation measurements at different
temperatures, great
care
has been taken to ensure, that the
cays. The
state.
Only
sample
samples
density gradient,
outside of the
fully
critical
and hence
sample
probably
Figure
decays,
cycled
in this case, do the flux
is not in the
and would
have been
(see
not
6.21 for
to a
starting conditions
in
high enough
fields
as
regime, part
of the
Figure 6.18).
sample
sample (C49),
resp.
our
measuring
Figure
critical
sample.
exposed
If the
to a flux
to
the inside of the
sample
time.
6.22 for
taken at different temperatures, with the field
of the
fully
towards the inside instead of the
Those vortices relax
in
out
in the
vortices is
trapped
pointing
identical for all the de¬
to be
density gradients point solely
Lorentz force,
leave the
were
sample (C81),
applied
in the
show
z/ft-plane.
typical
6.4 Vortex creep
measurements
TTTT]
1
1
I
I
83
I I
ll|
1
1
I
I
I I
1
ll|
1
I
I
I I
1
111
1
I
I
I I I
1
11
TT
1.000
6.7 mK'
26 mK
40 mK
^
50 mK
0.995
0.990
A
600 mK.
Sr2Ru04 (C49)
Hlc
800 mK'
0.985
i
ml
i
101
i
i
i
i
ml
i
i
i
i i
ml
KT-
i
i
i
i i
10^
ml
i
i,
i
i i
ml
104
i
l_l
105
t(&)
Figure 6 21: Relaxation
ured
on
ol the temnant magnetization at different
temperatures
StjRuOj (C49) with the field applied
at an
angle
ol 15° horn the
meas¬
oft-plane.
6.
84
I
ITT'III'I
1
I'lllllj
1
1
ITIII|
I
1
Experimental Results
1
II M
I
1
11
1
I
1
I "I'M
on
11
S12RUO4
r
20 mK
60 mK
1.000
90 mK
120 mK
0.999
50 mK
CO
I
0.99*
200 mK
250 mK
0.997
0.996
300 mK
Hlc
700 mK
0.995
1
1
11
ml
101
1
1
1
11
nil
l(£
1
1
1
1
1
ml
1
1
1
11
ml
104
10-1
i
i
i
11
ml
i_
10-"1
f(s)
6.22: Relaxation of the remnant
Figure
ured
on
magnetization
Si'iRuCU (C81) with the field in the oft-plane.
at
différent temperatures
meas¬
6.4
Let
are
85
Vortex creep measurements
first consider the lovv-77
us
sample (C49)
in
6.21. The
Figure
following
features
observed:
1. In the first
104s,
deviating from
start
decays
accelerate
follow
decays
the
and follow
unusual
a
2. Below 26mK, the vortex creep of the first
main
strongly pinned
so
that
After the first few hours,
they
time
dependence,
cannot
they
104s.
the
non-logarithmic time dependence.
i04s
is
practically
escape from the
sample
vortices manage to leave the
some
but then
After the first
logarithmic behaviour.
this classical
suddenly
logarithmic
a
zero, vortices
re¬
in this time range.
sample
in
a so
called
avalanche.
Let
As
is
in
can
us
be
compare these results to the
from
seen
sample (C49),
cays start
is
Below
speculation.
time
ilarities, there is
Below
a
detected:
This lack of
only
vortex
creep to
sample (C81)
logarithmic
dependence
at
important
longer
in
vortex
at low
creep is
creep is
our
start
times
high-quality sample (C81).
zero
an
in
Therefore,
our
we
time window. It
flattening
to
case
at
law
might be,
longer
as
observed
that the de¬
times, but this is
mere
short limes and deviate from
the
one
60mK,
observed in the
no
visible
low-77 sample:
decay
could be
time window.
indication for
new
logarithmic
dependence
(see also Figure 6.31). Despite this dissim¬
feature similar
temperatures. The
zero.
the
behaviour at much
certain temperature, in this
vortex
tivated
in
150mK, the decays
one
on
No such strong deviation from the
from this
deviating
logarithmic
seen
obtained
6.22, for temperatures above 150mK, the time
Figure
practically logarithmic.
ones
an
unconventional
pinning
call this
mechanism is
phenomenon
'"zero
pinning
so
mechanism
ac¬
strong that it reduces
creep".
6.
86
What
Figure
6.25 show
oriented
if
happens
along
we
apply
of
decays
logarithmic
time
sample (C49)
as
the c-axis?
a
in
decreases
Figure 6.24:
ith
6.24 and
function of temperature with the field
regimes
The fraction of remnant
w
S12R11O4
on
Figure 6.23, Figure
can
be
distinguished:
For temperatures 300 mK< T < 900 mK, the
dependence.
measuring time
Region (II)
along
the c-axis. Four different temperature
Region (I) in Figure 6.23:
our
the field
Results
Experimental
decays
follow
magnetization that decays
a
in
decreasing temperature.
In the range 75mK< T <
300mK, the beginning of the
decays is logarithmic, but
after the first thousands of seconds the relaxation slows
down and deviate from the
purely logarithmic
here, is the fact that the fraction of remnant
our
measuring
Region (111)
could
time increases with
Figure 6.25:
in
quite
=
=
4s)
Region (IV)
in
magnetization
at
sample
in
< 50
mK, the
decays
exponentials:
~)
long
times, the
decays
+
M(0).
(6.3)
deviate from the stretched
law.
Figure
6.23: At
even
lower temperatures, for 7" < 20 mK,
cay could be detected in the first tenthousands of seconds.
strongly pinned
some
What is remarkable
that leaves the
temperatures 28.5 mK< T
[M(oo)-M(0)}. 1 1-exp
It should however be noted, that
exponential
dependence.
decreasing temperature.
well be fitted to stretched
M,cm(t)
M,em{t
At low
time
inside the
vortices manage
to
sample.
After this time
escape and leave the
sample
Thus, "zero creep" is observed for both field directions.
no
visible de¬
The vortices remain
(approximately eight hours),
in
a so
called avalanche.
6.4
Vortex creep measurements
-i—i
nui
i
i
1
87
i
renin
'—'
'
'
''''I
'—'
i
i
mi|
1—i
i
11
1
ui|
i
i
run
Region (IV)
7mK
8mK
16mK
LOO
20mK
Region (I)
0.99
300mK
CZ)
400mK
500mK
S 0.98
600mK
5
0.97
700mK
Sr2Ru04 (C49)
H He
^
900mK
0.96
'
'
10°
'
'
"*
t
»
'
101
'
'
'
102
'
"Mil-
103
i
|
i
i
til
i
JO4
.
i
i
I
800mK
ml
I
U..JLJLJLJ.1.J,,
106
10:
r(s)
Figure
time
6.23: In
Region (1)
dependence.
In
with 300mK< 7* < 900 mK, the
Region
(IV) with T
first tenthousands of seconds, alter
in
a so
called avalanche.
<
20mK, the
roughly eight
decays follow
decays
are
a
logarithmic
practically
hours the relaxation recovers,
flat in the
resulting
6.
1n
-1—1
111{
1
1—1
in|
11
1—1
1
Experimental Results
11111[
1—1
1
in]
11
1
1—1
on
11
S12RUO4
nry
Region (II)
1.000
^
0.990
II
2
0.980
0.970
Sr2Ru04 (C49)
Hllc
0960 1
1
1
1
I010
11
ml
1
1,1
1
1
nil
is
In
logarithmic,
dependence.
our
Region (II)
but then
1
with 75mK< T
they slow
increases with
nut
1
1,
).i
10J
mi]
1
s
mini
104
10
5
(s)
<
300 mK, the
down and deviate from the
Note that the fraction of remnant
measuring time
1
102
10
t
Figure 6.24:
1
1
magnetization
decreasing temperature.
beginning
of the
decays
purely logarithmic
that leaves the
time
sample
in
6.4 Vortex creep measurements
~i—i
i
i
i
89
1—i
inj
i
i 111 r
|
1—i
i
i i
iii|
1—i
i
i
mi|
1—i
i
I
mi|
Region (III)
1.000
0.990
-
CO
0.980
0.970
-
S17R11O4 (C49)
Hllc
0.960 I
10°
'
'
1
'
""I
1
1
1
1
mil
1
1
1
1
102
10
mil
1
1
1
mil
1
1
1
1
111
105
104
l(p
.(s)
7'(mK)
Figure
28.5
-1.894-10
38.4
At
ß
M(0)
4
9018
0.5624
1.0006
-2.452-10-2
4
3372
0.4367
1.0020
44.0
-2.703-10"2
4
I960
0.4114
1.0028
50.0
-3.262-10-2
4
830
0.3277
1.0064
6.25: In
range could
[M(~)-M(0)]
Region (111)
-
with 28.5 mK< T
quite satisfactorily
<
50mK, the
be fitted to stretched
parameters stated above. Note however, the deviation
decays
in the
temperature
exponentials (solid lines)
at
long
times.
with the
6.
90
Experimental Results
on
Sr2Ru04
37010-3
^ 2-10"3
CD
r—(
CD
Sr2Ru04 (C49)
F10°
H//c
0 i&
I
i
i
200
0
I
I
i
L.
600
400
T
j
i_
1000
800
(mK)
decay
laws
3 10
ro
-3
2-10~J
-
ro
o-3
1
F10
•
0
I—KXV-1
100
1000
2"(mK)
Figure
6.26:
in linear and
Normalized creep rates of SriRuCF
gions (I)
Figure
to
semi-logarithmic plot.
(IV) correspond
6.23.
Figure
The field
was
(C49)
as
a
function of temperature
applied parallel
to the c-axis.
Re¬
to the different creep behaviours described in the text and in
6.24 and
Figure
6 25. The lines
are
guides
to the eyes.
6.4
Vortex creep measurements
seen
and
91
The four different creep
regimes
are
from
they
plotted
Figure 6.26,
semi-logarithmic
In the transition
fitting
regime
to the
slope
are
regime (50
< T <
deviate
decays
in the
logarithmic decays
do not follow the
only
high-temperature regime,
for 10<.< 100
decreasing
are
expected dependence
gion (II). Indeed,
104
in this temperature
is
s
of
with
thermally
interesting
by
region,
with
increasing
a
we
decided to
use
the
exponentials
to note,
that
similar behaviour (i.e.
a
local maximum at lower
for the field
region (III)
decreasing strength
with
they
activated creep. A broad minimum
increasing again
the fraction of the remnant
narrow
but
decreasing temperature,
temperatures)
a
as
in
re¬
magnetization
Around 60 mK the creep
decreasing temperature.
local maximum. In the very
the form of stretched
followed
the
regime.
is observed around around 300mK, before the creep rates start
It is
on
s
the results in the transition
the creep rates
region (I),
rates reach a
from the
and extract the initial creep rate:
Note that this choice affects
in
strongly
\dM/dlnt\ depends
Therefore, the slope
dependence.
9 In/
decays
be
function of temperature, both in linear
300 mK), the
^
that
as can
range. However, in order to be able to compare the data in this transition
at short times
In
as a
reflected in the creep rates
scale.
time
purely logarithmic
chosen
where
naturally
vortex
creep
occurs
under
the temperature is reduced.
minimum at
high temperatures
has also been observed in
layered
high conductivity planes:
in
(BEDT-TTF)2Cu(NCS)2 |124], jnTl2Ba2CaCu208 andinBi2Sr2CaCu2Ox [125,126].
In
superconductors
a
detailed
study
of vortex creep in
identified with the
with the
and
one
crossover
crossover
by
we
3D.
pancake
we come to one
Below 20 mK,
to
enter
to
the
Bi2Sr2CaCu2(\ [126], the maximum in creep
from 0D to ID
from ID
would not expect
Finally,
applied perpendicular
However, Sr2Ru04 is
and the
not a
following
minimum
layered superconductor
vortices to form in this material.
of the
major results
the "zero
three orders of magnitude
pinning regime,
rates was
of this thesis:
creep" regime:
to zero
within
our
the creep rates have
dropped
sensitivity (|31nM/31nr| «2-10-6).
6.
92
The latter is limited
the
mainly by
Experimental Results
of the
reproducibility
on
S12RUO4
creep of
background
the NbTi field coils.
The temperature
presented together
linear
plot,
for
observations
1. Two
Figure
comparison.
6.27 in
In both
a
and in
semi-logarithmic plot,
samples
can
be
and for both field
clearly distinguished:
of the order of 0.1%; and
by
a
Figure
low levels within
2. For the low-77
our
rates
sample (C81),
the
drop of
in linear scales.
plotted
represent
a crossover,
by
with "zero
than two orders of
more
regimes
as can
arc
separated by
gradually
with
be
seen
creep",
rather than
being
connected to
high quality sample
sharp drop
high quality
a
true
higher
where the
rates may
phase
same
be considered
transition. The
does not set in
high quality sample
low-77, sample, indicating larger pinning.
expect the opposite
to
abruptly
but
decreasing temperature.
3. At all temperatures, the creep rates in the
than those of the
separ¬
magnitude,
rather
a
Figure 6.28,
from
Therefore, the drop in creep
mechanism in the
pinning
increases
a
with creep
creep rates is broadened and shifted to much
temperatures, around 150mK,
novel
6.28 in
sensitivity.
the two
sample (C49),
high-temperature regime
A
of creep rates around 50 mK for both field directions. However in the
to
are
orientations, the following
low-temperature regime
a
strong reduction of creep
undetectabely
data is
samples
be made:
can
regimes
rates
ated
in
of all the measured creep rates for both
dependence
to be true.
Sample (C49)
shows
a
are
At first
much smaller
sight
shoulder in the
one
would
out-of-phase
component of the ac-susceptibility (see Figure 6.2) indicating the presence of im¬
purities
in the
dominated
sample
the
4. In the
extrinsic
by
If the vortex creep in the
pinning
would show stronger
observed,
at
sample.
we
conclude that
at
crystalline defects,
pinning (i.e.
some
with
pinning
be effective
of finite creep, the temperature
in the two field directions. For fields in the
tinuously
increasing temperature.
one
of the
already
In contrast,
would expect that this
same sort
at
dependence
flb-plane,
was
rates). Since the opposite is
lower creep
intrinsic
low-temperature regime might
regime
high-temperature regime
than observed
higher temperatures.
of the rates is different
the creep rates increase
as
we
have
already
con¬
discussed
6.4 Vortex creep measurements
93
1000
Figure
6.27: Normalized creep rates of
logarithmic plot.
and the closed
77
=
St'iRuC^
as a
function of temperature in
The open svmbols represent data of
symbols
1.4 K. The lines
before, the creep
are
those of
guides
rates
sample (C81)
with
a
sample (C49)
higher
with Tc
a
—
semi-
1.03 K,
transition temperature of
to the eves.
for fields
along
the c-axis show
a
pronounced
minimum at
77«300mK.
Considering
teresting
to
the
to
ones
the structural
similarity
to
high-temperature superconductors,
compare the observed temperature
of
high—77 superconductors.
dependence
In the
latter,
as
ductors, quantum tunneling of vortices has been observed
Mota
et
al.
and tend to
ment
[127, 128]. In these systems, the creep
a
finite,
non-zero
rates
of the creep rates in Sr2RuC>4,
well
as
in
organic
at millikelvin
|31nM/31nf |
value of the order of 1%. values which
with the theoretical values of quantum creep
it is in¬
theory by
Blatter
et
supercon¬
temperatures by
saturate
for T
good
are
in
al.
[129].
->
0
agree-
94
Experimental Results
6.
T
15-10-
;
I
Sr2Ru04
-
-
c
L0104
T
—I
i
|
—i
i—
—
on
Sr2Ru04
1
Hlc
o
(C49)
•
(C81)
-
-
-
ro
ro
-
510
-4
~
_
cf
.
**~-»^-^*
/#
o
-
-
p
üf
i
i
i
i
1
II
1
1000
500
0
T(mK)
Figure
6.28: Normalized creep rates of SriRuCL
plot, for
the field
sample (C49)
applied
with Tc
=
in the
r/7-plane.
The open
1.03 K, and the closed
transition temperature of Tc
—
as a
1.4 K. The lines
function of temperature in
symbols represent data
symbols
are
guides
those of
parallel
to the
by
277^715 jk
el P»
h
ancl the theoretical quantum creep
rate
dissipation,
the effective action
c-axis, it is given by LI29]:
is defined
9 lna/
V
7
as:
h
T-v0
Jr
on
a
linear
the of
higher
to the eyes.
In the limit of low and intermediate fields and strong
derived quantum creep rate is determined
(C81) with
a
5|lf.
the
theoretically
For fields
applied
Vortex creep measurements
6.4
normal state
resistivity
95
pn
YBa2Cu307
Bi2Sr2CaCu2Ov
O.lSußcm'
10
30pflcm
1520
penetration depth
À
pQcm
1400
Â1
720
length
coherence
Sr2Ru04
12-18Â
20-40Â
50-350
anisotropy 1/e
23-26*
5-7
depairing
6-106A/cm2
3
current
critical current
«
A/cm2
l O4
1400-2000 Ä
À
•
J
08 A/cm2
3-108A/cm2
3-106A/cm2
106A/cm2
id jo
2lu"3
6-10-3
3-10-3
effective action
2.0-106
160
sf-=
5-10-6
6-10"3*
0.05*
4-10^*
0.017*
ratio
theoretical quantum
»-4-«20
creep rate
experimental quantum
creep rate
Table 6.2: Values of the physical quantities used
For
1
comparison values of
values taken
:
from
YBCO and BSCCO
Mao et al.
l:
value taken
front Kealc\
7
value taken
from
7
value taken from Mota
where p„ is the
et
in-plane
calculate the quantum creep
also shown.
[46].
[124,130].
normal state
critical current and
valid for
anisotropic superconductors independent
crystal
the
resistivity, 2)
in-plane
and the
of SroRuOâ,.
[48].
al.
;),
rate
[47].
al.
Mao et al.
et
are
to
orientation. The
m-plane
depairing
the
value of the
current
in-plane
coherence
depairing current.
of the
angle
is defined
length, /*<
the
This lormulais
between the
applied
field
by:
On
12
with X the
(e^/p„).
determining
the action and
Observable quantum creep rates
anisotropy 1/e, large
S^
çA2
in-plane penetration depth.
The main parameter
ratio
vTS k1
normal state
depends only weakly
on
the
resistivity
are
thereby
expected
also the
in
\fj0/jc
rate is the
with
high
length ç7 Note,
that
superconductors
pn and short coherence
pinning potential through
tunneling
96
6.
Experimental
To estimate the theoretical quantum creep rate for
Table 6.2, where
we
have also
which is
a
Taking into
are
by
Figure 6.29,
our
we
S12R11O4 lies below the limit of
have
group obtained
plotted
on
In
YBCO, the creep
m
Sr2Ru04.
rates
rates saturate
As
can
be
seen
in the two materials is
for T
—>
0 and tend to
5
high—77-
lower
together
YBCO. First of all, the creep rates of the
much stronger than those observed
=
•
For
10~6,
super¬
[124,130],
sensitivity.
the creep rates of Sr2Ru04
temperature dependence of the creep
-
our
S/^RuCÀf
the values of
\dlnM/dint |
usually
account that the measured values are
the quantum creep rate of
data
theoretical quantum creep rate
on
comparison.
thousand times smaller than the quantum creep rates found in
conductors.
In
a
we use
values of YBCO and BSCCO for
given
S12R11O4, the calculations lead to
Sr2Ru04,
Results
a
with
some
high-77
from
older
material
Figure 6.29,
completely
the
different:
value of about
4%.
-
In
Sr2Ru04, the creep
regime
with "zero
undergo
a
"transition" to
a
low temperature
creep".
We conclude that the vortex
tunneling.
rates
dynamics
we
found in Sr2Ru04 is not affected
by quantum
6.4 Vortex creep measurements
i
i u
97
1—i—i
i
1—i—irr i
|""|-|"|"|"|
1—i—i
111
i
i
r
111|
10-
YBa2Cu408
—m——
Sr2RuO4(rc=1.03K)
P
10
-3
r2Ru04(rc=1.4K)
ro
io-
10-5
r
-O
io-6
Q
j
i
i
111111
10
_l
I
of temperature.
for
rates
i
The open circles
tunneling (data
temperature dependencies.
we
are
also
i
i
I
'
plotted
i
i
i
il
10000
(mK)
applied
for the lovv-7;.
taken from
r
1000
of St^RiiCV for the field
(C81). For comparison,
its quantum
i
100
T
Figure 6.29: Creep
i
data
[128]).
on
in the
cib-planc
sample (C49).
as a
function
the closed circles
YBa^Cu+Os powder, which exhib¬
Note the difference between the two
6.
98
Experimental Results
on
Sr2RuÖ4
1.000
0.999
^
t/5
A
0.998
B
J
0.997
$
0.996
0.995
0.994
103
102
10
105
104
t(s)
Figure 6.30: Relaxation
of the maximum
shows the field
is in the
of the
cycling
magneti7ation of S12R11O4 (C81),
field H,mn. at the
dependence
fully critical
remnant
of the remnant
Relaxation measurements
We also
investigated
namics.
Hmn is
to
which the
magnetization.
as a
At
=
Hmax
function of
the influence of the maximum
the field
sample
temperature T
function
700mK. The insert
=
200 Oe the
sample
state.
6.4.3
not
same
as a
was
applied during
cycled,
cycling
cycling
field Hmcn
field
on
the vortex
dy¬
the measurement but it is the initial field up
before the relaxation measurements at
zero
field
were
started.
In
the
-
Figure 6.30
same
and
Figure 6.31,
wo
plotted
vortex
decays
of Sr2Ru04
(C81)
temperature for different cycling fields:
Figure
6.30 shows relaxation measurements taken
at
T
—
700 mK in the
high-temperature regime
-
Figure 6.31 presents decays
vortex
creep
rates occurs.
taken
at
T
=
70 mK
just
below the
drop
in
taken at
6.4
99
Vortex creep measurements
i—ri
n—r—TT-rmqi
i
i
1—i
1111]
i
i
1—i
mi|
i
11
1—rr
ii|
T=70mK
1.0000
600 Oe
350 Oe
O
i—i
II
76 Oe
0.9990
0.1%
50 Oe
0.9980
35 Oe
hfft
I 1 Mill
4++4W—1
1.0000
Sr2Ru04(C81)
O
0.9998
600 Oe
350 Oe
0.9996
76 Oe
50 Oe
35 Oe
_i
i
i
i
i nil
i
l
II
iml
I
1
1
I
i
111
\
1
.
I.
I
i
liiI
11
Inil
i
1_J_
105
104
I03
10
I
Ks)
Figure 6.31: Relaxation
cycling
in the
scale.
field Hmcix.
fully critical
at
the
state,
of the
same
see
remnant
magnetization
temperature T
Figure
=
as
a
function of the maximum
70 mK. At Hmcn
6.17. kovver
graph:
same
--
200 Oe the
data in
a more
sample
is
expanded
6.
100
The field
dependence
that in the
At 7"
of the
of
—
700 mK in
decays
curves
Figure 6.30.
is observed
Hnun
at
(H„un
state. There is no
=
—
as a
logarithmic
40 Oe the
on
S12R11O4
is very distinct from
same
completely
strongly
significant change
=
field. As
cycling
shape
can
be
nor
seen
in the
350 Oe), the
critical
sample
decays
from the insert
state.
is
already
in the
field
be
this temperature, the
seen
from
The time
Figure 6.31.
magnetization
fully
the
which leaves the
critical state is realized
logarithmic time-dependence.
flattening.
shape
The lower the maximum
6.17. In the undercritical
initial creep starts
critical
dependence
is
practically
in
sample
our
for all fields.
dependent.
fraction of remnant
fully
that started from the undercritical
different situation is encountered in the
can
strength
is still in the undercritical state. For the two
difference between
fully
in the
for all fields. Moreover, the fraction of vortices that leave the
7-70 mK. As
Figure
high-lemperature regime
sample
200 Oe and Hmn
significant
time interval is the
are
no
function of
state, and those that start from the
A
in the
decays
Results
low-temperature regime.
Figure 6.30,
other
of the
Experimental
regime,
--
and the
cycling field,
sample
277+
in
our
200 Oe,
^
of the
strength
the
as can
decays
larger
measuring
be
at
is the
time.
seen
At
from
for fields H < H\ the decays follow the classical
For fields II
At 77
at
low-temperature regime,
>
277", they become
600 Oe. the first 100
flat. After the first hundred seconds, the relaxation
recovers
s
more
of the
rounded and the
decay
are
again, resulting
in
practically
a so
called
avalanche.
These observations suggest that the unconventional
perature regime strengthens with increasing fields
pinning
found in the low tem¬
6.5
Summary
101
Summary
6.5
investigated
We have
vortex
field, and performed
netic
in
dynamics
S12R11O4
as a
function of temperature and mag¬
of the lower critical field.
measurements
Vortex creep measurements in S12R11O4 lead to the distinction of two temperature
regimes
1. A
with distinct flux line
high-temperature regime
sample (C49)
and
2. A
relatively
where
an
we
so
phenomenon
sample (C49),
logarithmic decays
with
where
that
no
they
visible
decay
few hours after the start of the
a
low-T, sample, the
sample
in
regimes
two
a so
transition temperature of 1.4 K, the
and shifted to
continuously
an
higher temperatures,
are
with
dependence
The critical current
ous
drop
of lovv-7^
104
s
-
on
a
could be detected. The vortices
sample. Therefore,
it should be noted that in the low-
decay measurement,
vortices
some
separated by
a
rather
sharp drop
However, in sample (C81) with
of
a
of creep rates is very much broadened
the creep rates for fields in the
with temperature. Whereas, for fields
unusual time
exception
around 150 mK.
high-temperature regime,
In the
with the
of creep rates:
called avalanche.
creep rates around 50 mK for both field directions.
higher
-
drop
do not manage to escape the
creep". However,
""zero
manage to escape and leave the
For the
unusual
low creep rates of the order of 0.1%.
strongly pinned
call this
an
acceleration of the vortex creep is observed around
low-temperature regime,
remain
77
dynamics, separated by
pronounced
along
a£>-plane
increase
the c-axis, the creep rates show
minimum at T
pu
300mK.
the other hand remains finite and does not show any anomal¬
temperature dependence.
In the
low-temperature regime
field is observed: At
time
dependence
in the
high
fields the
unusual
decays
dependence
deviate
of field.
the
decays
are
of the
strongly from
and the initial creep decreases with
high-temperature regime,
independent
an
decays
the classical
increasing cycling
logarithmic
the
on
cycling
logarithmic
field. Whereas,
in time and their
strength
is
6.
102
of
Si"2Ru04. is very distinct from
observed in the
dynamics,
We have shown that the vortex
pinning
mechanism
pinning
mechanism activated
increase with
seems to
low
Sr2Ru04
thermally activated flux
low-temperature regime
at
on
low-temperature regime
the well known Kim-Anderson
creep. The strong reduction of creep rates in the
additional, strong
Experimental Results
is
sign
a
for
an
temperatures. The strength of this
increasing cycling
field and with
decreasing
temperature. Recently. Sigrist and Agterberg have interpreted this drastic reduction in the
vortex creep rate as
due
the presence of domain walls
to
holding fractionally quantized
vortices [2|.
A similar behaviour has been observed in the
FJo 972sTbn 0275Bcn,
and
in creep rates is very
towards
is
no
a
sharp
experimental
temperature, where
see
evidence for
superconducting
chapter.
second
a
superconducting
theory,
accompanied by
a
but did not show any measurable feature at
transition to the "zero
the
creep" regime
high quality sample
true
phase
"vortex
Sigrist
transition. It
phase"
and
with
kink in the lower critical field.
drop
be due to
of creep
a
in
as
proposed by Sigrist
state
shall
Sr2Ru04 does
S12RUO4
A
cannot
more
and
see
in
is caused
detailed discussion is
are
low-temperature
type of vortices.
in the next
chapter,
given
treated
to
Uo9725Thoo275Bei3>
not occur at the onset of the time
Agterberg [2],
and UPti,
a
StoRuO.^ [2).
by
sets
domain walls
then
one
has
to
in
in
chapter
together.
only
carrying
reversal sym¬
much below
Tc. If
fractional vortices,
conclude that domain walls in
carry fractional vortices at all temperatures, but
Uo9725Thoo275Bei3
rather than to
"transition" of domain wall states, associated with the
as we
creep"
a crossover
a
where the
in creep rates in
drop
structures and/or a new
metry breaking phase observed by uSR experiments. It
the observation of "zero
strong deviation from
''vortex transition" towards
a
superconducting
UPtj and,
rates
Moreover, since the
type of strong pinning
Agterberg proposed
In contrast to
the
might
a
low-temperatures,
is very broad, it may be connected to
a new
multiband nature of the
occurs.
So far there
UPt3 and Uq 9725Tho 027sBei3
Our measurements of the lower critical field in Sr2Ru04 gave
BCS
transition
transition in Sr2Ru04 around the
in creep rates. In
drop
transition is
phase
of UPt3 [1]
In these systems, the transition
which breaks time reversal symmetry.
observe the
we
in the next
and coincides with the second
low-temperature phase
other
the second
will
as we
low-temperature phases
only
at the
lowest
8. where the three systems,
[7].
S12R11O4,
Experimental
7
results
thoriated
on
UBei3
7.1
Introduction
Antecedent to the present work,
single crystal of UPF.
tinguished.
pinning
investigated vortex dynamics
peaks
two
in the
specific
was so
strong that flux creep of the first 104
temperature T(
a
7
pinning
observed
that increased
rate
The
zero
rapidly
as
to
of
which the
low-temperature
superconductors
time reversal symmetry
should manifest itself
creep
w
one
B-phase
\3-5], According
through
measurements
should shed
critical concentration
of nature of the
experiments
regime,
are
some
regime.
expected
light
This is
Steglich
group
give
a
even more
see
regime
by Sigrist
pinning
important,
are
the
only
transitions
and
and
on
an
an
known
occur
of
with broken
Agterberg,
the latter
inhibition of vortex
thoriated
ones
UBen in the
in
UPfii. Our
low-temperature phase
since the present
in the
interpretation
UBej? has been challenged by
also page 43.
103
attributed to
vortices [2].
results similar to the
of thoriated
[102],
was
superconducting phase
the nature of the
on
[1]. In the
the initial vortex creep
superconducting
the model
to
zero
of UPt3
creep measurements
vortex
low-temperature phase
of the
to
lead to
anomalous strong
an
[2]. Following their theory,
critical concentration
to
dis¬
down to
carrying fractional
here two consecutive
is believed
clearly
of FJPI3, vortex
regime:
UPF and thoriated UBei? in the critical concentration
examples
high quality
temperature approached the transition
the
domain walls
a
B-phase
dropped
different vortex
a
initial creep rate in the
mechanism due
s
in
heat could be
Mota. Amann and coworkers found out that in the
finite with
intrinsic
group
for which the
high temperature phase, they
was
our
recent
104
7.
To
further
gain
field-cooled
This
insight
Experimental
into the nature of the
results
on
pinning mechanism,
thoriated
we
also
UBcl3
performed
experiments.
chapter
is
organized
as
follows: In the first section
a
description
of the two
Uo.9725Thoo275Bci3 single crystals, which have been investigated during this thesis, is
given.
In the
short section
vortex
are
same
presenting
ac-susceptibility
our measurements
creep measurements both
presented.
The results
crystal
section
on
In addition,
Uo 9725Tho
"El Bucno"
by
we
0275
as a
measurements are
shown.
Then follows
of the lower critical field. In the third section,
function of temperature and maximum
compare zero-field-cool eel and field-cooled
Be
n
w
ill be
a
compared
Mota, Amann and coworkers
to
those obtained
[131].
on
cycling
field
experiments.
the
UPt3 single
7.2
Description
of the
105
Uq,9725 Thg,0275 Be i j samples
i-.J
i
1
i
>
1
-
#
4
.
2.0
t
-
"5
S
1.5
*
U
-
1.0
9725TI10 275BC13
-
_
-
1
1
1
200
77
Figure
All
Fos Alamos National
We
analyzed
preliminary
crystal.
So,
we
(mK)
IVr^Thooj/riBen.
in this section have been
taken
on
sample
a
of the
same
It
soon
single crystals
with
a
became evident thai this
another
sample (also
sample I,
sample
a
was
a
first,
Uo 9725Tho 02756013 single
contaminated with Al
single crystal)
At
of the
same
(about 10%).
batch where
we
did
of Al.
I
The first
sample
missing.
The dimensions
64.2 mg. The
has
roughly
magnetic
are
field
the form of
a
rectangular parallelepiped with
3.62 mmx3.29
was
in
Figure 7.2,
is
7<
1 =s
mmx
applied along
The transition temperature, obtained from
picted
in the group of I. L. Smith at
thorium concentration of 2.75%.
measurements were done on
investigated
Sample
prepared
Laboratory [132].
two
not observe any trace
-
800
Sample Description
samples presented
some
heat data of
1
600
[1331.
batch
7.2
Specific
7.1:
1
1
400
its
1.41
mm
largest
and the
a
width
ATC\
edge
sample weights
dimension.
ac-susceptibility
530 mK and has
one
«
measurements,
130 mK.
as
Specific
de¬
heat
106
Experimental
7.
1
1
1
t
I
-"1
t
•
I
I
results
"
~
1
thoriated
on
UBe^
'|
i
0
• 0
-
0
000 0
• » 0 MH
/
-
-
S
^9725Th()275Bej3
0
0
-
I
sample
0
-
0
-
-
0
.
-
0
-
-
0
•-••••• mm
1
i
i
i
i
i
i
1
i
1000
500
0
1500
77 mK)
Figure
in-phase component %'
7.2: The
measured with
an
ac-amplitude HlU
The
susceptibility
x!
at
the lowest temperature. One
is
most
probably
œ
«
As
can
be
seen
a
from
as
a
Sample
H'dts
the minimal value of the
<
2mOc.
susceptibility
second transition at about 1.2 K which
width of 77;
Figure
big
as
was
2
~
r;
on a
sample
of the
l50mK and show
same
a
batch
second
[133]
jump
at
40 mK.
7.2. another transition is observed at about 1.2 K. This
107 of the total
impurities
superconducting
in the
sample,
which
transition. It is due
originate
from the
grown in.
II
The second
and the
a
width of ATL[
presence of aluminum
crucible where it
-
distinguishes
the residual dc-field
Figure 7.1, performed
561 mK with
transition is about
to the
using
in
of Uo 9725Tho 027sBen
due to aluminum contamination.
350 mK with
77t2
ac-susceptibility
33mOe
=
has been renormalized
measurements, shown in
give 771
of the
sample has
mass
the form of
is 8 mg. The
a
magnetic
parallelepiped.
field
was
The dimensions
applied
to the
are
2.3
sample along
mm x
its
0.9
largest
dimension.
The results of
conducting
ac-susceptibility
measurements are
depicted
transition temperature has been found at T,
ATC\ «67mK.
\
^
in
Figure 7.4.
the super¬
523 mK and has
a
width
mm x
1.0
mm
7.2
Description
of the
107
U0.9725 Tho.0275Be t3 samples
"
Z'lU
1
1
1
1
1
-
U9 72?Th0 27sBoi3
sample
-
II
HO"6
-
7"c2
0
-
-
J[
A
*•*
y
-
Tel
IKE6
-
0.00
1
1
0.20
0.40
1
<
0.60
T (K)
Figure
7.3:
sample
II
as a
coefficient
expansion
Thermal
function of temperature, taken
«
by
-
C'Cll/dT
Uo9725Tho027s-Be-n
of
N. Oeschlcr in the group of F.
Steg-
lich, Max-Planck-lnstitut, Dresden.
Thermal
of F.
Steglich
7.3.
ure
much
expansion
at
The two transitions
than in the
point
specific heat
^
presented
The results
it is
clearly visible,
important
on
with the
sample
The results
one
we
f
1
obtained
~
as
II in the group
depicted
are
the transtion at
temperature 7^
Tci
~
one
in
Fig¬
523 mK is
in the spe¬
given by
thermal
by ac-susceptibility
300mK is
slightly
lower
measurements, however, it has to be noted that it is also
85 mK.
in this
chapter
has been taken
the Al-contaminated
to note,
on
The upper transition temperature
The lower transition
much broader ATr2
All the data
are
measurments coincides
measurements.
performed
90mK) in the thermal expansion than the
~
measurements.
expansion
have been
Max-Planck-lnstitut. Dresden.
sharper (ATci
cific heat
sample.
measurements
that
they
are
sample
are
on
the second,
given
in accordance with the
in
higher quality
Appendix
A. At this
high quality sample.
108
7.
^
Experimental
on
thoriated UBe/j
Ir-
0.0
i
"79725 "-'-1
x
results
-0.5
O275BO13
sample
H
II
1
1
h
0.02
x
0.01
%
0.00
4—
» »
W
WW
WWW
500
T
Figure
7.4: The
in-phase y'
and
the
H'JS
< 2
mOe. The
susceptibility y'
(mK)
out-of-phase y" component
U09725TI100275Ben measured with
field
1500
1000
an
susceptibility
at the lowest
ac-amplitude Hac
---
around 1.2 K has been observed. The lines
serve as
guides
ac-susceptibility
of
33 mOe in the residual dc-
has been renormahzed
temperature. This time,
of the
using
no trace
to
the
the minimal value of
of another transition
eves.
1.3 DC-Masnetization and the lower critical field
4.0
t"
1
1
1
1
1
1
109
i
i
"
i
i
i
r
i
|
T= lOOmK
u.9725 Ln.0275J:5e13
-
r=200mK
-
T=300mK
2.0
r
p^.
"
"v~
r
=
400mK
T
=
480mK
—
,
''*'•..
~
'v.
*
-
-
•*
'•.
's.
0
v
•X
C3
_
TT—"*~-«^—^
Jx
_Ni>
\
'.
*,.
N
S.
-2.0
~~
:
i
S
s
''*••.,_
'•','n.
\t
\
—
"\
*\
""••--.
\
-
-
-4.0
-
-
1
1
1
1
1
0
1
1
1
1
1
100
1
!
1
I
1
200
300
//(Oe)
Figure
7.3
Magnetization
dc-magnetization
single crystal
at
above and below the second
the lower critical field at
T(2.
of the
have been
performed
magnetization
pinning.
~
applied
shown in
on
curves
show
shown in
a
a
Fig¬
pronounced
the
T
=
ir-
400mK
magnetization
magnetization
transition results from
7.6.
U.9725Th 0275BC13
curve at
higher fields,
field. The difference of
Figure
the
curves are
For instance, the
100 0c and at
superconducting
as
different temperatures.
Typical magnetization
All the
evidence for strong
independent
at
and the lower critical field
very shallow minimum around H
becomes almost
9725Tb 027s;Bcp
measurements
7.5 for different temperatures.
a
of U
different temperatures.
reversibilty, giving
has
curves
DC-Magnetization
Isothermal
ure
7.5:
curves
drastic increase of
110
7.
Experimental
results
on
thoriated
UBe!3
50
50
o
O
40
-
30
(0
3-105
HO5 2-105
T2 (mK2)
0
o
o
&3
20
10
cl
U.9725Th.0275^e13
0
0
200
100
300
T
Figure
7.6:
data is
plotted
with
demagnetization factor of D
a
Temperature dependence of
as a
function of
77A
the lower critical field. In the
Figure
of its
7.6
slope
as a
slope,
of the
magnetization-curves
function of 7^ and
T2.
One
coincident with the second
has been observed
by Rauchschwalbe
We fitted the data to two T~-laws
\
et
as
clearly visible.
is
are
to the
same
The data is scaled
data with
The values of
easily recognize
in the
al. and
fits
insert, the
a
T2-law.
the field where the first deviation from
occurs.
can
jump
specific
reported
the
Hc\
are
plotted
pronounced
in
increase
heat at T(2. This behaviour
earlier
[99].
[116] with different 77ri and Tc. And thus obtained
the value of the lower critical field
at zero
accordance with Rauchschwalbe
al.
et
HL
0.15. The lines
The lower critical field has been obtained
the initial
500
(mK)
The kink in
=
400
temperature: If \ (0)
[99],
—
49 Oe. This value is in
7.4
Vortex creep measurements
t
i
111
i
t
r
|
1
1
1
1
1
^—w
1.0
r
^
_
-
.9725
)Th.0275Be13
c3
0.5
£
-
T>Tc2
CD
n
i
400
0
800
"max
Figure
T
=
7.7:
7.4.1
remnant
~
400 Oe. The line
serves as
1200
(Ve)
magnetization
on
the maximum
400 mK, above the lower transition temperature. The
state at H
7.4
Dependence of the
I
i
i
sample
cycling field,
is in the
fully
for
critical
to the ey es.
guide
Vortex creep measurements
Remnant
The temperature
Magnetization
dependence
function of temperature and field
as a
of the remnant
magnetization
is very distinct in the low-
temperature and in tho high-temperature phase:
For T > TC2
In the
as
high-temperature phase,
described
where
we
Hmn, for
by
-
remnant
magnetization follows
the Bean model (see section 6.4.1).
plotted
T
tho
the remnant
magnetization
400mK. It increases
as
a
as a
This
can
be
the classical behaviour
seen
from
function of the maximum
function of
Figure
cycling
IImcn until Hmnx reaches
7.7.
field
the value
.12
277*
CZ5
+->
'&
H
cd
x>
fi
Figure
3
2
0
0
t
J
1
I
1
I
r
L
t
i
7.
1
1
1
1
Tco
L
j
i
on
thoriated UBe 13
i
field at dif¬
1500
L
250 mK
200 mK
100 mK
r
Experimental results
1
1
T<
1
cycling
U.9725rTh.0275Be13
a
maximum
1000
function of the
#max (°e)
as a
500
7.8: Remuant magnetization
in
the
high-temperatme phase,
to the ev es.
independent
of Hmn.
figure.
These
277*, the
[119, 120]. The
for fields H >
the Bean model
shown in the previous
dependence picdicted by
suides
deviate from the field
dependence
ferent temperatures, below the second transition temperature. Note the difference to the
field
curves
sen e as
sample
becomes
is in the fulh critical state, i.e.
If the
magnetization M,em
400 Oe.
lines
rj
remnant
7.4
113
Vortex creep measurements
For T <
Tc2
2.0
2
X>
200
300
T
Figure
7.9: Values of the
crystal
as a
ues
higher
Figure 7.87 The line
serves as
is very distinct from that
we
temperatures T
of field. For
through
a
than the
magnetization M,ein of the
plotted
<
to
the
U
Muin{H,n(,A
we
dependence
the Bean model,
dependence
plotted
of the remnant
as can
of the remnant
fields H!}hn. the remnant
maximum and then decreases
have
takes its maximum
the val¬
valuefsee
again
be
seen
from
Figure
function
first increases, goes
increasing
field.
Lowering
the temperature from 200 mK to 100 mK. the maximum of Mrcm is shifted towards
field values
H,mn. This indicates
a
novel field-induced
"memory
7.8.
for different
not saturate as a
magnetization M,cm
with further
magnetization
magnetization
Tc2. In the low-temperature phase. M,em does
increasing
9725Tb027.sBei3 single
eves.
the field
expected by
the field
where
one
etude
low-temperature phase,
In the latter
(mK)
function of temperature. For temperatures below 77,
of A/,m at fields
In the
remnant
400
effect" in vortex
higher
pinning.
114
7.
It results in
the
sample
In
Tc2.
we
a
different critical state at 77
has been
Figure 7.9,
have
cycled before
we
plotted
shows
depending
as a
Figure
significant change
on
thoriated
UBe^
the maximum field to which
decay.
higher
than the
7.9 reflects the temperature
continuously increasing
at the lower
on
function of temperature. For temperatures below
the values of Mrm at fields
The critical current is
no
0
the start of the
plotted Mum
takes its maximum value.
current.
—
Experimental results
with
one
where
dependence
Mrem(H,mx)
of the critical
decreasing temperature
transition temperature
Tc2.
and
7.4
Vortex creep measurements
7.4.2
115
Relaxation measurements
Isothermal relaxation measurements
on
temperature range 7 niK\ 7"
a
Figure
a
7.10 shows
7^. in
^
as a
function of
Uo972sThoo;?75Bci3 have been performed in the
time window from 1
sample
value
has been
to a field
cycled
(see Figure 7.8).
s
to
104
—
103
relaxation measurements of the remnant
typical
function of temperature. For temperatures below 7^.
the
temperature
The field
larger
plotted
we
the
s.
magnetization
decays
as
taken after
than the one, where Miem takes its maximum
of the relaxation measurements will be
dependence
discussed in Section 7.4.3.
For T
In the
T
=
>
Tc2
rather strong vortex creep is observed
high-temperature phase,
400mK). which follows
almost
an
logarithmic
cays of vortices have been observed in conventional
high-77 cuprates.
activated
time
superconductors,
the vortices
the
over
pinning potential
in
organics
at
de¬
dependence. Logarithmic
This is the classical Kim-Anderson flux creep,
jumps of
(about 30%
and in
governed by thermally
barriers
[122,123],
see
also
page 82.
For T <
Tc2
For temperatures below
7^, the decays
time behaviour. The initial
decay
creep is observed. After
some
accelerates, resulting in
a
reduced below
the
is
waiting
7,2, these avalanches
creep is observed in
our
time
strongly
at
w
T
<^
from this classical
deviating
reduced,
so
occur at
recovers
and
longer waiting
772. the vortices remain
indow.
so
no vortex
and the vortex creep
As the temperature is
longer
logarithmic
that for short-times,
time, the relaxation
called avalanche.
so
low-temperature phase,
start
more
and
more
times. Far inside
strongly pinned
that
no
Experimental results
7.
116
thoriated
UBc^
100 mK
F>15()mK
200 mK
1.0
^
250 mK
\^
\K
%
\> \v
f
on
^,
V
300 mK
0.9
\
325 mK
^
-
350 mK
0.8
380 mK
-
U9725Tho275Bel3
-
400 mK
-
i
i
i mi
101
i
i
i
i
i
inn
i
i
i
1
inn
1
1 1 III!
1
i
i
i nm
i
i
i
io5
io4
103
10-
I
as)
Figure
7.10: Relaxation of the
crystal
at
remnant
different temperatures.
taken after the
sample
has been
magnetization
of the
FF^Tfhf^sBen single
For temperatures below Tt2.
cycled
its maximum value (see Fi cure 7.8).
to a
held
larger
than the
we
one.
plotted
where
the
decays
M,em takes
7.4
117
Vortex creep measurements
3.985
^
3.980
AM(t)
CZ3
-t—l
'5
3
3.975
U.Q725Th.0275Be13
3.970
3.965
ni
1
10°
1..
I
1
1
1
ml
1
1
1
1
ml
1
1
I
I
Mill
IO3
H)2
IO1
1
I
I
I
I I III
IO5
IO4
as)
Figure
7.11:
AMjMiem
Illustration of
marked. The
are
our
the
decay analysis,
decay
was
taken
at
two
quantities d\nM/d\nt
200 mK, with
a
maximum
cycling
and
field
H,mn=1500 0c.
As the
the
-
decays immediately
time
logarithmic
stretched
below the second transition show
dependence,
exponentials,
as
a
strong deviation from
tried to fit them to other time-laws:
we
observed for
example
in
SroRuCU, cf. Sec¬
tion 6.4.2.
-
power laws,
But this
characterize the
the initial
rates
-
observed for
procedure did
compare the data
-
as
on
not
give
example
any
in
CeCii2Si2 by the Mota group [ 108].
satisfactory
results. On the other hand,
Uo 9725Tho rcrsBeu with that
decay s of Uo Q725TI10
logarithmic slope
\d In M Id In/
02
of 37
oBe^ by
vs.
/.
on
SP2RUO4 and FJPts,
two
which
we
so we
time, which takes into
gives
us
the initial creep
logarithmic time dependence AMlMiem
account
the avalanche.
choose to
parameters (see also Figure 7.11):
.
the deviation from the
wanted to
at a
fixed
118
Experimental results
7.
on
thoriated UBeu
0.15
?c2
U.9725Th.()275Be13
S
0.10
GO
O
i—i
II
0.05
r,cl
-
<
0.00
t
il
-4-J
I...
0
M»J
I*
7.12: Deviation of the
from the
decays
function of temperature. The deviation
ition temperature 77
=
350mK, but
For temperatures below 77,
has been
cycled
to a
field
very
logarithmic
one,
I
I
1
I
L
500
=
104s
as a
below the second trans¬
above and much below the transition.
the values of the
than the
I
time-law at t
pronounced [ust
negligible
plotted
we
larger
is
I
400
(mK)
T
Figure
I
_1
300
200
100
where
taken after the
decays
sample
its maximum value
M,em takes
(see
Figure 7.8).
This choice
the transition Tc2
temperatures,
viation
cay
=
occurs
very
arbitrary,
350 mK. It does
as can
AM/Miem
In the
ure.
seems
(t
be
—
seen
1Ü4 s)
from
not
from the
longer
times (/
>
7.12.
In this
logarithmic
a
103s).
mainly
influence the data
Figure
high-temperature phase,
at
but it affects
the relaxation data around
much
at
graph,
time-law
AM/M,em
ature
(t
—
region.
IO4 s)
is
zero.
sample.
much lower
plotted
the de¬
function of temperat¬
a
The deviation is very
pronounced immediately
The
phase of U()9725Thoo27.sBei3, vortices
manage to leave the
a
have
or
small deviation from
At very low temperatures T
practically
we
as
below the second transition 250 < T y Ti2. which is due to
in that temperature
higher
reason
remain
being,
so
<
purely logarithmic
de¬
non-logarithmic decays
200mK,
on
the other hand,
that far inside the low
strongly pinned,
that
temper¬
they do
not
119
7.4 Vortex creep measurements
1
1
1
1
1
^^
-
N^
-
^^
\
-
2
Afrera
at t
Is
=
-
Tc2
-
-
a
-
\t
-
U.9725Th.0275Be13
-
W
-
1
\T
,
Mremat
-
i"cl
-
><
*
r= 104s
-
-
i
i
i
i
i
100
200
300
400
500
0
0
T
Figure
7.13: Remnant
perature. Diamonds
tilled circles for
that leaves the
T < 200mK,
we
plotted
Mum
we
sample
of
different times,
our
The shadowed
decay
area
Deep inside
as a
function of tem¬
measurement
(f
~
1 s), and
indicates the amount of flux
the
low-temperature phase, for
M,tm
at
fields
larger
than the one, where
seen
from
a
M,cm{Hmcn)
takes its
(see Fisurc 7.8).
can
also be
show values of the remnant
function of temperature.
the
at two
flux creep is observed in litis time scale. For temperatures below 77,
This behaviour
where
s.
in this time window.
the values of
maximum value
IO4
at t
taken
(mK)
at the start
for MIL,„
are
sample
no
magnetization,
600
high-temperature phase.
magnetization,
The shadowed
between the start of
7'
>
our
7'(2-
a
different
area
decay
point
of view in
taken at
two
Figure 7.13,
different times,
as
indicates the amount of flux that leaves
measurement (t
considerable
amount
«
Is) and
t
=
IO4
of vortices leave the
s.
In the
specimen
7.
120
50
~i
1
1
results
on
thoriated FiBe^
r
1
1
1
1
1
Experimental
0.03
U.9725Th 0275-130,13
0.02 TT
M
ro
o
G
tf
r—-">,
CO
0.01
()»-»
0.00
»4
2-105
1-UP
0
3-l(P
T2 (mK2)
Figure
7.14: Lower critical field ff
fits to the data obtained
lines
are
rates
—d]nM/dhit (closed
(closed circles, left scale)
\
as a
function of T~, the
described in section 7.3. Normalized initial creep
as
diamonds,
tight scale)
of the L7)725Th
02756013 single crystal,
the line is smide to the eves).
in
IO4
s.
Whereas, deep inside the low-temperature phase, for T
is observed in
our
From
an
indication for
an
untisal strong
pinning
Figure
7.12 and
of
Figure 7.13, it
gradually
temperature phase it is
case
no
flux creep
mechanism which
below the second transition temperature and inhibits flux motion
anism increases
the
200 mK,
time scale.
This lack of creep is
sets in
<
Si^RuO.},
so
we
with
becomes also clear, that the novel
decreasing temperature
strong, that
refer to this
out
vortex
below Tl2.
creep is reduced to
phenomenon
as "zero
of the
pinning
mech¬
Far inside the low-
practically
creep".
sample.
zero.
As for
7.4
121
Vortex creep measurements
The initial creep rates
are
plotted in Figure
with the lower critical field data. At T
Tc2.
—
creep rates. Note, that the transition in creep
critical field. The rates
(|91nM/91n/|
group at
pound
interesting
an
earlier stage
exhibits
lincar-in-T
For
of Uo
is
thoriated
sample,
from T
the
vortex
sensitivity
of the
reproducibility
the
a
~
creep
pinning
or to
UPt3 LI |. In Figure
with that of UPti
as a
7.16.
we
plotted
by
the Mota group
persists
performed
to
on
=
thermally
similar
the creep rates of
of both
a
well defined
see
also page 82.
sample.
YBa2Cii30g [128].
high-Tc superconductors,
down to T
function of temperature. The two
low-temperature phase
creep"
[122,123J,
5 mK, As
or
can
be
profound.
mechanism described above induces
group has
com¬
with the
observed in the thoriated
one wo
quantum creep (observed in high-77
our
our
This is the classical temperat¬
Tc.
activated creep
transition like the
together
UBen follow
for the creep behaviour observed in
the strong
linear in T).
In the
4.4. the pure
creep rates of pure UBen,
The creep rates of
thermally
Figure
in
by
that does not violate time reversal sym¬
T(2. This behaviour is fundamentally different
The
to zero within our
phase diagram
5 mK up to T
=
independent quantum
As mentioned before,
-
magnitude
the difference between the three types of behaviour is
graph,
-
plotted
972sTho r^sBe^.
representative
from the
tal of
to
have also added data taken
we
where temperature
rates
have
of Kim-Anderson
comparison,
rates at
we
indication for
no
curve
11]. According
dependence
dependence
The
transition in the initial
coincides with the break in the lower
sensitivity is limited mainly by
Our
single superconducting phase,
a
vortex creep rates
There is
sharp
a
together
compare these results to those of pure UBei3 obtained
to
metry. In Figure 7.15,
ure
function of temperature
observe
rates
three orders of
drop by
10"~6).
•
we
as a
creep of the NbTi coils.
background
It is
2
~
7.14
a
drop
seen
In the
of creep
activated creep
(creep
organic superconductors).
experiments
on a
single
crys¬
Uo 9725Tho0275Bei3 together
curves
look rather similar:
multiphase superconductors
"zero
is observed.
drop
of creep
transition to
a
rates
of both materials coincides with the second
superconducting phase
with broken time reversal sym¬
metry.
Moreover,
novel
pinning
as
observed in
Figure 7.15, there
mechanism in the
is
no
high-temperature phase
experimental
of
evidence for this
Uo.9725TI10 027sBci3>
nor m
122
the
t—"H
CO
ro
0.03
0.02
0.01
0.00
-
7.15:
and 77.
are
sight,
as
well
as
400
7.
Experimental results
600
T(mK)
as
on
thoriated
UBc13
crys¬
1000
single
observed in the
high-7"c superconductor
in creep rates
creep data of the
sample.
Uo 9725Tho 027sBen,
the critical temperature of the UBen
uncon¬
Uo 9725Tho 0275Ben
UBej}. This is another indication for the fact that the
of
increasing temperature,
On the other hand, the creep rates
with
of
of both sys¬
but rather intrinsic to the
low-temperature phase
activated creep.
high-temperature phase
high-temperature phase
0275^et3-
sample-dependent feature,
thermally
linearly
7.16. Indeed, in the
in the
UPh and Uo 972STI10
Figure
dependence
from in
the temperature
seen
indication for
the creep rates increase almost
be
transition
comparison quantum
marked,
has been added. The transition temperatures of
For
a
Normalized creep rates of the thoriated and the pure UBen
sample.
The pure FTBep, does not show
Figure
tals.
thoriated
1
YBaiCmOg [128]
7)
of
and/or
mechanism found in the
material-dependent
pinning
superconduting phase
a
ventional
is not
At first
as can
low-temperature phase of
differs,
nature of the
tems
an
Uo 9725Tho 0275Boi3,
which is
7.4
123
Vortex creep measurements
6-10---3
440-3
y
ro
ro
2-10
T
Figure
7.16: Normalized creep
(circles) from [1].
bigger,
Uo
9725
and
Ty
the data of UPh in
Uo 9725Tho 0275Bet3 (closed diamonds) and UPt3
Fo972sThQ0275Ben
expanded
are an
(right scale).
scale
order of
magnitude
The left scale is for
9725
Tho 0275Ben,
and T~ those of FPU,
high-temperature superconducting phase
dependence [131].
However,
comparing
that this difference is duo to the
Figure
7.17
we
time-law of the UPt3
very similar to the
sample
is due to the
vicinity
the second transition
in
Tc2.
near
the two
of the
curves
two
as a
do not show such
in
—
104s)/A7re,„
of AMIMmn (t
of the
Figure
two
AM j M n„n U
temperature.
could argue,
from the
-
104s)
7.12. But
again,
one
in the
logarithmic
UPt3 single crystal is
the maximum observed in the
could argue, that this difference
transition temperatures in FJPF.
—
one
function of temperature.
U00725TI10 02756013, except for
see
Figure 7.16,
temperature
a
critical temperatures in UPfiv
present the deviation AM(t
dependence
one
Uo.972sTho 027.sBei3
vicinity
single crystal
The temperature
thoriated
(mK)
Tho 0275BC13. TL\ and TLz mark the transition temperatures of Uo
of UPt3 in the
In
of
As the creep rates in
plotted
we
rates
-j>
104 s) of the UPF, single crystal
However, similar to
tends to
zero
below
124
Experimental results
7.
thoriated
on
UBeu
-
9
UPt3 single crystal
O
UPt3 single crystal Hlc
-
UPt3 powder
-
0.30
p
H II
c
-
B
-
"~
0.20
t/)
D
o
S
-
*
D
0.10
<
g
D
C]
O
0.00
i
i
i
i
1
i
i
100
0
A
i
i
ri
i
i
i
200
as a
7.17: Deviation of the
lt is
ure
interesting
to the ones
7.17. The
are
obtained
powder
logarithmic
decay
by
our
to
grains
with
magnetization
the
in the first
decay.
IO4
s.
on
on
AM
i
1
i
i
i
i
i
600
500
(mK)
powder sample.
group
l^tpfti
400
in FPU from the
the results
consists of
contribution
of vortices that
for the
to compare
the relaxation of the remnant
no
p
logarithmic
function of temperature. The closed and open circles
Bucno''. the open squares
crystals
decays
Oi
i
300
T
Figure
^
the
arc
time-law at
for the
IO4
s
"El
The data is taken from [13 li¬
Uo972sTho 02756013 and UPt3 single
also
plotted
average diameter of about 7
in the
=
single crystal
powdered UPt^ [131]
an
t
showed
powdered sample
Miem (t
=
IO4 s) presents
urn.
in
Fig¬
Since
practically
in fact the fraction
First it should be noted that the
decay
at all tem¬
peratures is orders of magnitude larger in the powdered sample than in the single crystal.
Moreover, in the powdered sample
ature
independent
and saturates for T
pinning mechanism,
not
at
observed in the
low temperatures,
-+
0
at
rather
high
single crystals
of
AM/Mlcm (/
=
IO4 s) is temper¬
values of about 10%. The strong
UPtj and U09725TI10 0275BC13, is
present in the UPtj powder sample.
The novel
tures
pinning
12] which inhibit
mechanism could be due to the presence of "fence-like"' struc¬
vortex
motion and which
are
activated below the second transition
7.4
125
Vortex creep measurements
temperature. The observations
on
UPF
small for these fences to form and/or
powder suggest,
efficiently
that the
powder grains
inhibit vortex motion.
are
too
126
7.4.3
Relaxation measurements
In this
section,
vortex
creep. In
at
the
the
same
we
>
Figure
ling
Figure
7.18 and
Figure
7.18 shows
decays
is very distinct from that in the
of
Flo 9725Tho 0275Bei3 taken
high-temperature phase,
decays
are
be
There is
seen
no
logarithmic
field H,mn
on
the
low-temperature phase.
the field
at T
~=
400mK for different cyc¬
dependence
of the
from
remnant
Figure
significant
7.19. the
-
that started from the undercritical
300 Oe:
or
from the
fully
creep
[122.1231.
that
magnetization
difference
following
in time for all fields,
thermally activated flux
2. The fraction of
=
field
relaxation measurements taken
plotted
we
cycling
UBei3
decays
is charac¬
by:
Anderson
77
7.20.
cycling
thoriated
Tc2
1. The
can
function of
on
temperatures for different fields H,mx, The field dependence of the decays in
fields. In the
terized
as a
will discuss the influence of the maximum
high-temperature phase
For T
As
Experimental results
7.
decays
sample enters
nor
critical
shape,
in the
state
the
state
77
>
500 Oe.
same
for all fields.
critical state at 277*
in the
or
also page 82.
is the
fully
nor
H y 200 Oe;
sec
the classical Kim-
strength
from the
-
«
500 Oe.
between
decays,
partially
critical state
1.4
127
Vortex creep measurements
i
i
rnnj
i
i
i
i
ni|
i
i
i
i 1 ! i 1
1
|
1
1
1
I
1 M
1
|
11
ill)
1.00
U.9725'Th 0275^e13
NcV
vV
\V
\
II
**i
0.90
5-,
_ -
-
o3
X^V
1200 Oe
s
T
=
^
700 Oc
500 Oe
300 Oe
0.80
400mK
\ ^v.
w
200 Oe
^
^x^v
100 Oe
\
0.70
i
u)°
i
102
10l
ni
i
i
i
i
i i
ni
i
i
i
i
IO4
IO3
im
1(
,(s)
Figure
7.18: Relaxation of the remnant
crystal for different cycling fields H„hn
magnetization
taken at the
of the
same
U972iTh.027sBen single
temperature T
=
400mK,
above the second transition.
—i—i—
'
i
1
i
!
Mrem
—T
|
!
at t
1
1
ls
==
1.0
-
/
M
j*—
G
G
/
a
•
Mrcm
at/
104s
==
0.5
-
T
n
i
i
i
i
i
0
i
>
i
Tc2
i
i
500
l
l
r
1000
#max (Oe)
Figure
7.19: Remnant magnetization at T
function of field. Diamonds
and filled circles for
that leaves the
MHI>,
sample
for A/,t„,
are
at t
-
10;
s.
at
-
400
the
m
start
K. taken at two different times,
of
The shadow ed
in this time window.
our
decay
area
measurement
(t
~
as a
1
s).
indicates the amount of flux
128
7.
For T <
be
seen
and the
results
thoriated UBei3
on
Tc2
completely
A
Experimental
from
different situation is encountered in the
Figure
strength of
7.20,
the
at T
100 mK, and T
-~
decays
~
respectively,
200 mK
strongly field dependent.
are
As
low-temperature phase.
The
both the
following
can
shape
features
are
observed:
is obscrv cd
creep"
1. "zero
2. At all fields, the
shape
3. The
field
decays
and the
only
if the
sample
has been
deviate from the classical
of the
strength
decays
in the
cycled
to
logarithmic
high enough
fields.
law.
low-temperature phase
strongly
are
dependent.
4. For the
same
field, the amount of flux that leaves the
in
sample
measuring time,
our
is smaller the lower the temperature.
5. At the
temperature, the lower the maximum cycling field, the larger is the
same
fraction of remnant
large
How
field
ure
strength
7.22,
we
function of
a
field. In the
cycling
At T
200 mK.
Hmax
Miem(Hmtn)
œ
oi
Miein(H,nax)
the deviation from the
plotted
function of
around
which leaves the
sample
same
observed in
logarithmic
graph,
we
time-law
measuring time.
our
creep"?
7.8?
Is this
In
Fig¬
AM/Miem (104s)
as a
Figure
magnetization
also show the remnant
as
field.
AM/M,un
(t
-
-
IO4
s)
function officiel shows
as a
500 Oe. This field value coincides with the
occurs.
in
held Hmd\ be in order to observe "zero
cycling
related to the maximum
cycling
—
the
must
magnetization
The strong
the field above this value.
pinning
AM/Mnm
(t
mechanism
~
IO4 s)
sets
one
a
small maximum
where the maximum of
in above 500 Oe. With
decreases. "Zero
creep"
increasing
is observed for
fields Hmn >800Oe.
At T
—
lOOmK, the
of "zero
onset
fields, the values of AMjMnm (t
This is
an
observation
already
decreasing temperatures.
ventional
pinning
~
IO4 s)
creep" is
are
much lower than the
made before, that the
Moreover, the field
mechanism,
shifted towards lower fields.
is
strength
ones at
pinning strength
T
—
For all
200mK.
increases with
necessary to activate the
lower if the temperature
is
reduced.
At T
=
uncon¬
lOOmK,
7.4
129
Vortex creep measurements
T
I
I'"l'"l"l't'l'|
1—I
I '"I "II l'l|
1—I'I'll'l'll'l
1—I
I
I
llll|
1—I
I I IUTT
1—TT
1500 Oe
1.00
1000 Oe
800 Oc
00
.9725
Lll0275t5e13
<u
r=200mK
0.90
-f++#|—I
+H
I
lllllll—I
1
lllllll—r-H
1000 Oe
700 Oe
1.00
500 Oe
C/}
400 Oe
Ü
300 Oe
O
200 Oe
r= lOOmK
0.90
100 Oc
j
i i
i
10°
mil
i
i
i
101
7.20:
crystal
for different
cycling
the second transition.
i
i
i
i
IO2
Relaxation of the
Figure
i
mil
remnant
fields
mil
i
103
at two
i i
mil
IO4
magnetization
H,mx taken
i
of the U
i
i
i i
mil
J_L
io5
9735Th 0275^13 single
different temperatures, both below
130
7.
t
1
p
1
~i
Experimental
M rem
.-s
1
1
1
1
at f
=
results
1
1
on
thoriated
UBej3
r
1S
2
G
G
a
r=200mK
1
-
0
j
i
i
_i
i_
0
i
i
i
i
500
i
i_
j
1000
L
1500
#mav (Oe)
Figure
7.21: Remnant
magnetization
function of held. Diamonds
and filled circles for
that leaves the
"zero
creep"
M,em{tlnun)
is
Mnw
sample
are
at t
in this
at T
foivU,(,„
—
IO4
time
s.
at
much
higher
200 mK. taken
the
start
of
Fhe shadowed
our
at two
decay
area
different times,
measurement
(t
«
as a
1 s),
indicates the amount of flux
window.
already observed for fields
occurs at
—
fields.
as
low
as
500 Oe. However, the maximum of
1.4
131
Vortex creep measurements
n
i
i
r
t
1
r
i
1
4.0
r
0.05
3.0
2.0
C/3
-S
o
U.9725Th.0275BcF
1.0
<1
T= lOOmK
0.00
t
500
0
fr
ii
i—4
i
1
1500
1000
T
I
I
I
p
0
L
i
i
r
-3.0
0.05
2.0
§
GO
o
-1.0
<
0.00
0
0
500
1000
1500
#max (Oe)
Figure
7.22: Deviation of the
law at
t
--
IO4
s
open diamonds)
decays
in
Unq725Thon27sBen from the logarithmic time-
(left scale, closed diamonds), and
as a
function of
From these observations
we
maximum
cycling
infer that the
remnant
magnetization (right scale,
field.
pinning strength
increases the
more
the
temperature is reduced below 7,2. and the higher the maximum field in which the sample
has been
cycled
before the start of the
decay.
132
7.
It is
the UPt3
interesting
Experimental results
to compare these results to the ones obtained
single crystal
"El Bueno". Fet
by
thoriated
UBei3
the Mota group
the main feature of the
recapitulate
us
on
on
decays
in
UPti:
-
The fraction of the remnant
decreases with
-
-
For low
With
increasing cycling
cycling
fields, the
by
a
logarithmic
These features
are
from the
logarithmic
itatively
the
tho
clearly visible
at
77
For instance, at T
than 277"
^
300 Oe.
But
still in the undercritical
model, it
was
center of the
ated. It may
in
leaking
8.
a
given
time interval
of the
beginning
a
stretched
decay gets
more
exponential.
and
dom¬
more
Figure 7.23,
in
/'Mnm
(t
=
IO4 s)
ones
where
of FlPh
of
the "zero
creep" regime
even
450 mK, the
as a
regime,
vortex
only
vortices
a
no
function of field.
sense
increasing
fields.
Qual¬
that
In
vor¬
con¬
UPt^ is already established
in
at
close to the second transition temperat¬
larger
creep is
very
the deviation
7.22 in the
Figure
fully critical
for fields
already
plotted
we
narrow
state is reached for
fields
than lOOOe. when the
strongly
region
Following
reduced.
of
a
few
[[]. In this picture, the field has
tens
to
larger
sample
is
the Bean
of gm at the
penetrate right
sur¬
to the
Uo 9725^1002756013 sample before the strong pinning mechanism is activ¬
as
well be that
Uo9725Tho027sBep,.
chapter
—
concluded that
face of UPI3 is
within
low fields and then decreases for
Uo9725Thoo275Bep%,
.
decays
be well fitted with
can
very low fields in the undercritical state,
ure
hieb
law.
time-law AM
large
w
field.
look rather similar to the
graphs
creep is rather
trast to
decays
increasing cycling fields,
inated
tex
magnetization
higher
We will
fields
come
are
necessary to activate the
back to this aspect
m
the
pinning
mechanism
general discussion of
7.4
Vortex creep measurements
0.6
i
i
i
1
!
|
i
-
0.4
200
0
A
/
?
1
I
>
UPt3
1
0.2
-
100
-'1
4
i
r=350mK
>
0
r
f
*--,
200
0
1
„„
k
1
1
1
1
0
1
600
400
1
3000
'
1
1
•
A
V
-
î
-
1
0.4'
t-
-
UPt3
0.2
7
1
-
46
c3
450mFs
=
500
T
-
/0s
oif
S+T-
.__
1
200
0
+ __,___
.
400
+{
r
0
600
f/max (Oc)
Figure
7.23: Deviation of the decav
arithmic time-law
(right scale,
from [131].
at t
-
IO4
open diamonds)
s
s
in the UPu
single crystal
"El Bueno" from the
(left scale, closed diamonds), and
as a
function of maximum
cycling
remnant
log¬
magnetization
field. Fhe data is taken
134
Experimental results
7.
0.3
-i
1
1
on
UBe[3
40
r
^>
-<y
^y
thoriated
.
30
0.2
i
20
CO
5
UPt3 powder
ai
-
10
T
ii
=
350mK
0
0.0
100
0
200
#max (Oe)
Figure
7.24: Deviation of the
time-law at t
IO4
—
in the UPb,
decays
powder sample
(left scale, closed diamonds), and
s
scale, open diamonds)
as a
function of maximum
remnant
cycling
from the
logarithmic
magnetization (right
field. The data is taken from
11311.
let
Finally,
sample.
In
we
the
104s)
—
transition. As
ing
no
as
seen
the first
I04s
100Oe.
on
s.
the
remnant
function of
a
logarithmic
104
contribution
(t
=•
ones
to
obtained
the
at T
decay
lu4 s) represents
dependence
low-temperature phase
=
UPI3 powder
with the deviation
350mK below the second
has been observed in the
the total fraction of vortices
is
completely
9725 Tho
In contrast to the latter, the fraction of vortices that leave the
increases with
increasing
field and
finally
high-temperature phase
tion of vortices
of
saturates at
decaying
again
an
Vq 9725TI10 02"5Bei3. Indeed, in the latter
in the first
IO4
s
saturates at
high fields,
indication for the fact, that the novel
see
powder
decay¬
different to the
of the UPt^ and Uo
the other hand, this behaviour is rather similar to the
This is
the
on
magnetization together
cycling field,
The observed field
before in the
single crystals.
area).
plotted
we
quantity AM/Mnm
in the first
have
compare these results with the
Figure 7.24,
AM/Mrem(t
sample,
us
fields
one
ones
02756013
sample
higher
in
than
observed in the
we saw
that the frac¬
Figure 7.19 (shaded
pinning
mechanism is not
1.4
active in the
is
probably
powder sample.
too small
urn).
We attribute this observation to the size of the
for the "fence-like"
inhibit vortex motion (the
7
135
Vortex creep measurements
powder
[2] pinning
consists of
grains
structures to
with
an
grains
form and/or
which
efficiently
average diameter of about
136
Experimental results
7.
1.2
t
1
r
i
on
1
thoriated
r
^_
^0
UBei3
*W
•O
ZFC
0.8
-•—#.
03
o
^
0.4
U,9725Th.0275Be13
T
>
Tcy
0
0
400
800
1200
77max (Oe)
Figure
7.25:
at T
400 mK: remnant magnetization taken at
=
Diamonds
M,e„,
at t
this time
are
=
w
Comparison
for Mnm
104
between field-cooled (FC) and zero-field-cooled
at
the start of
The shaded
s.
area
arbitrary
7.4.4
corresponds
Field-cooled
We have
applied
to
versus
is
closed
IO4*,,
to
the
desired
as a
function of
sample
at a
different times
measurement (r
amount
as a
~
open
s), and circles for
symbols
symbols and light shaded
at the
1
function of field.
of flux that leaves the
represented by
sample
in
and dark shaded
area.
In both cases,
SQUID.
zero-field-cooled relaxation measurements
performed preliminary field-cooled
temperatures,
to the
unit
by
decay
indicates the
indovv. The field-cooled data
area; the zero-fickUcooled data
one
our
two
(ZFC) mode
cycling
fields.
relaxation measurements at two different
In the field-cooled mode,
a
field Himn is
temperature above Tc. Subsequently, the sample is cooled down
measuring temperature, keeping
the field
HnMX
constant. When the
sample
1.4
Vortex creep measurements
t
3.0
1
_j
r
,
!
j_
1
-|
1
r
1
-
2.0
5-1
03
1.0
0
1
j
L
1500
1000
500
0
j
AU (Oe)
Figure
at
T
=
200 mK: remnant
Diamonds
Mum
Comparison
7.26:
at t
-
are
for Mnm
104
s.
between field-cooled (FC) and zero-field-cooled
magnetization
taken
at the start ol our
Fhe shaded
area
one
the zero-field-cooled data
arbitrary
unit
corresponds
decay
indicates the
this time window, "fhe field-cooled data is
area:
at two
different times
measurement (/
amount
as a
«
\(f<l\>
at
represented by
the
SQFID.
function of field.
1 s), and circles for
of flux that leaves the
open
sample
in
symbols and dark shaded
by closed symbols and light shaded
to
(ZFC) mode
area.
In both cases,
138
7.
attained thermal
equilibrium (this
the field is reduced
temperature),
experiments.
The remnant
After
of
decay
a
and the
given
For T 7
Figure
s,
the
of the
as a
sample
flux is recorded.
as sum
in the
to zero
on
UBe!3
the desired
way than for zero-field-cooled
function of time in
field is recorded.
zero
is warmed up above its transition temperature
The remnant
decayed plus
same
thoriated
on
depending
take up to six hours,
magnetization
typically IO4
expelled
is
decay
can
results
Experimental
magnetization M,em
expelled
the
at
the start of the
flux.
TC2
7.25 shows data at T
qualitative
400 mK, i.e. in the
—
high-temperature phase.
There is
no
difference between the results obtained in zero-field-cooled and field-cooled
mode.
For T <
In the
Tc2
low-temperature phase
field-cooled mode
-
respect
as
At 200mK "zero
at 7~
to
creep"
=
200 mK,
-
at
high
fields,
Moreover, the field
as
ts not
it is
at
of
dependence
not saturate at
increasing
is
fields. The
not
increases
"memory effect"
covered in the
cooling
the
in
is field-cooled
On the contrary, the
decay
is
as
experiments.
fields
7.87
as
one
In zero-field-cooled
would be
Instead it goes
expected
through
from
a max¬
fields. In field-cooled mode, the
continuously
and
seems to
saturate at
observed in zero-field-cooled mode
present when the sample has been field-cooled.
From these observations
this
high
imum and decreases with
high
sample
Mnm is considerably altered if
Figure
magnetization
considerably altered
is
low fields.
the Bean model (see also
remnant
dynamics
observed, if the
compares zero-field- and field-cooled
mode. Miem does
ortex
zero-field-cooled:
in fields up to the value of 1000Oe.
strong
v
we
infer that the
low-temperature phase
sample.
point definitely.
of
Further field-cooled
new
pinning
mechanism which
Uo9725Thoo275Ben
experiments
are
is
no1
we
dis¬
active when field-
desirable in order to clear up
1.5
Summary
139
Summary
7.5
We have
investigated
the results in UP7,
ous to
dynamics
vortex
we
ders of
magnitude, exactly
For T 7
In the
-
a
a
Flo 9725TI10 02756013 single crystal. Analog¬
observe two different
clearly
Uo 9725TI10 0275Be B separated by
in
sharp drop
of vortex creep in
regimes
of initial creep rates,
by
than three
more
coincident with the lower transition temperature 77r2
=
or¬
350 mK.
Tc2
high-temperature phase,
Strong
classical
thermally
creep shows rather classical features:
which follow
decays
vortex
vortex
an
almost
logarithmic
activated flux creep described
which is also observed in conventional,
as
well
by
time
i.e. the
Kim and Anderson
[122,123]
organic
supercon¬
high—77.
as
dependence,
and
ductors.
-
-
The field
No
dependence of the
remnant
magnetization
as
described
by
the Bean model.
difference between the results obtained in zero-field-cooled and
significant
field-cooled mode.
For T < T,. ->
The vortex
dynamics
in the
low-temperature phase
of Uo
hand, exhibits several unconventional characteristics,
not
9725
Tho
0275
Be 13,
on
the other-
observed in classical supercon¬
ductors:
-
Far inside the
low-temperature phase (for
The vortices remain
measuring
-
so
no vortex
and leave the
<
A strong
imum
they
no vortex
cannot
creep is observed.
escape the
T(2. the initial decay is strongly reduced,
creep is observed. After this time,
sample in
a so
dependence
cycling
some
so
sample
in
our
of both the
field is observed.
occur at
shape
longer
and the
and
strength
that for short-
vortices manage to escape
called avalanche. As the temperature is
reduced below 7'c2- these avalanches
-
that
Tc2).
time.
At all temperatures 7'
times,
strongly pinned,
T <7
more
longer
times.
of the
decays
on
and
more
the
max¬
140
7.
"Zero
-
creep"
The remnant
-
is
only
observed if the
magnetization
shows
Experimental results
sample
has been
unusual field
an
In field-cooled mode, vortex creep remains
-
creep" regime
is observed if the
The unusual field
-
increases
Our observations
trinsic to the
seems
low-temperature phase
dynamics
pinning strength
nor
than the
of this
high
even at
high fields
fields. No "zero
is not observed in field-cooled mode: M,em
an
fields.
high
pinning mechanism,
anomalous strong
of Uo 9725^0 027sBen.
in¬
It is not observed in the
in pure UBen. It manifests itself in
a
completely
different
high—77 superconductors.
The
type of mechanism increases gradually with decreasing
tem¬
one
now
to very
UBci3
dependence.
strong,
to saturate at
indication for
are an
high-temperature phase,
vortex
and
thoriated
is field-cooled.
sample
dependence oiMlcm
continuously
cycled
on
observed in classical,
or
in
perature, and also with increasins maenetic field. Far inside the low-temperature phase
(for
Tc2). it is
T 77
measuring
strong that the vortices do
phenomenon
sample.
can
be
explained,
These "fences" appear below
if
where the three systems
ics of
been
ers,
that "fence-like" structures
challenged by
of the
more
nature
detailed discussion is
dynamics
the
chapter 4.3).
Based
propose that the unusual strong
pinning
of Uo
9725 Tho 0275 Ben
phase
that violates time reversal symmetry.
is of the
same
Steglich
We observe
low-temperature superconducting phase
dynamics.
treated
low-temperature phase
on
of
previous
low-temperature superconducting phase of UPF by
we
are
given
in
chapter 8,
together.
in pure UBen with the
investigation by
of the
the latter (see
vortex
[2]
Tt2 and their strength increases with decreasing
in view of the recent
UBen concerning
and pure
our
that the latter do not manage to escape from
compare the vortex
interpretation
difference between the
in the
to
Uo9725Thoo27sBei3
UBej3 has
in
mechanism is, that it does not
SnRuO.;. l'o 1P25TI10 027sBen and UPt3
interesting
since the present
pinning
one assumes
so
temperature and increasing cycling field. A
It is also
sample
manage to escape the
current
exist which prevent the passage of vortices
the
not
time. Another property of the described
affect the critical
This
so
Uo
a
dynam¬
group
LI 02],
of thoriated
fundamental
9725 Tho 0275 Ben
results of "zero
creep"
Mota, Ainann and cowork¬
found in the
physical origin, namely
a
low-temperature phase
second
superconducting
8
and Conclusion
Summary
In this thesis,
features
some
discuss
we
are
low-temperature
very
vortex
specific
"zero
conventional
pinning
defects,
analogy
new
ductors with
a
interesting
topological)
mains of different
The
up to
now
have
a
only
known
is
physics
to
such
examples
At zero-held,
expected
by
form
can
in unconventional supercon¬
yields
many
separated by
interpreted
as
LI 4]. In those
which show
phase
being
two
due
to
< x <
more
transitions
fractional
are
0.045)
than
one su¬
with broken time
we
observed
magnitude
are
observed, of
the addition of
systems,
than three orders of
141
do¬
domain walls. A
holding
U] _xThxBen (with 0.019
superconducting phase
more
degrees of
motion [2],
consecutive
a
more
into vortices with frac¬
decay
such domain walls
superconductors
leads to
rates
vortex
and
two
order parameter at the lower transition
states
repulsion
on
topological
of
degenerate superconducting phases,
domain wall
a
of
versal symmetry [3-5J. This has been
of initial creep
extraordinary variety
an
be
stable defects. In
one
call this
very distinct from the
pinning,
vortex
strong,
so
we
a
property of the material, but it is intrinsic
not a
which shows
to vortex-vortex
low-temperature
ally sharp drop
type of
a new
heavy fermion systems UPt3
the
The latter is
pinning.
time scale of several hours, therefore
a
considerable effect
perconducting phase.
which the
in
UPf3. Although
have found in all three materials
order parameter, since (his
approaching
tional flux quanta. Due
we
with unusual strong
degenerate superconducting
conventional vortex
can
each system,
and
question.
vortex
multicomponent
freedom to form
vortices
in
superfluid 3He.
to
and
is
Sr/jRuO.^ thoriated UBen
due to defects. It is
superconducting phase
In
zero
creep". This
phenomenon
the
to
regime
creep
that vortex creep is reduced to
to
creep in
vortex
a
re¬
second
an unusu¬
to zero
within
142
our
8.
sensitivity (|31nAf/31n/|
exactly
A
with the second
ever, in
10
6).
superconducting
S1-2R11O4
do
wo
not
transition at
is
reduction of creep rates coincides
Tc2.
certainly
most
also realized in
observe "zero
creep" immediately
S12R11O4,
below the
A strong reduction of creep rates similar to the
transition.
and
Uo9725Tho0275Ben,
main walls
abrupt
This
revealed the breakdown of time reversal symmetry below
ing
one
•
multicomponent order parameter
experiments
uSR
2
?a
and Conclusion
Summary
in
sets
only
much below
fractional vortices,
carrying
as
Tc. If
"zero
proposed by Sigrist
77 16]. How¬
superconduct¬
observed in UPp;
one
is caused
creep"
and
where
by
Agterberg [2],
do¬
then
has to conclude that domain walls in Si-2Ru04 cannot carry fractional vortices at all
Uo 9725Tho0275Ben,
lowest [7],
at the
temperatures, but only
we
observe
a
indicates that it may be connected
Sigrist
and
Agterberg suggest
"transition" of domain wall
state in
broad
to a crossover
drop
to the
sharp
in creep
drop
rather than to
in creep
transition in UPt3 and
a true
might
rates
in
rates
Si*2Ru04. This
phase
transition.
be associated with
due to the multiband nature of the
a
superconducting
Sf2Ru04 [2|.
Although
"zero
relatively
that the
states
Contrary
vortex
creep" regime
dynamics
shows many characteristics
specific
is observed in all the three systems with the
to each
following
material,
common
a
fea¬
tures:
-
-
Vortices remain
strongly pinned
Several hours after the start of the
the
sample
in
a so
these avalanches
-
so
For the
that
no
decay,
creep is observed in the first few hours.
some
vortices manage to escape and leave
called avalanche. As the temperature is
occur
at
longer
and
longer waiting
and
more
reduced
times.
field, the amount of flux that leaves the
same
more
sample during
the avalanche
is smaller, the lower the temperature.
-
At the
sample
-
The
same
in
temperature, the fraction of
our
measuring
pinning strength
increasing cycling
time is smaller, the
seems to
field.
remnant
increase
larger
gradually
magnetization
which leaves the
the maximum
cycling
with
field.
decreasing temperature
and
8.
Summary
and Conclusion
Although
-
143
vortex creep goes to zero, the critical current remains finite.
did not observe any anomalous temperature
we
Some of those
and
by Sigrist
domain walls
phenomena
Agterberg [2]
occupied
The described
superconducting
described in Section 2.3.
observation of
our
itself.
Pinning by
of the critical current. The latter
is
This is in accordance with
crystal.
zero
Since vortices
originating
performed by
at
T~ in the
the first
extrinsic
governed by
our
our
at
the
superconducting
the
peak
does not
With
increasing amplitude,
ures
depend
on
superconducting
transition
of the
the A- and
our
of
onset
T
~
dissipation
480mK. The
that it
might
up in the
able to
w
on
hich has
slope
the other hand
interpretation
field but rather
on
its
position
and width of the first
of the
amplitude Hac
peak
of the
between 1.6 mOe and
to
the
applied
and fractional vortices
of
dependence
approximately
to be
seems
towards lower temperatures for
According
move
to the
slow
ly.
the
meas¬
33mOe).
peak
of the
\\c.
50 mK/7,000 Oe for H
independent
at T~
between
phase boundary
of
77flr and it
is not trivial. It
was
reducing
strongly pinned,
so
The
occurs
at
concluded,
below the second transition the domain walls
field. On further
are more
at
temperature of the peak's maximum with field
of the second
B-phase f 1]. Immediately
peak
amplitude:
be related to the motion of domain walls and/or fractional vortices
adjust
may then
a
second
is about 300 times smaller than
measuring system
does not follow the field
B-phases
a
meas¬
is shifted towards lower temperat¬
peak
practically independent
It is clear that the strong reduction in
(~ 50mK/30mOe)
due to defects of the
given by ac-susceptibilty
peak
measuring
In contrast, the
field (at least in the range of
uring
This
the maximum of the
are
pinning,
magnitude
transition. Between 16 Hz and 160Hz, the second
frequency
and its width increases.
approaching
from the nature of the
UPh single crystal. They revealed
on a
group
each other,
observations.
out-of-phase component x" LU-
peak
repel
domain walls does not influence the
Further support for the formation of domain walls is
urements
in the framework of the model
creep.
mechanism is intrinsic,
pinning
state
readily explained
of the critical current.
with fractional vortices act like "fences" for other
explain
vortices. This would
be
can
dependence
Moreover,
building
might be
the temperature, the domain walls
that the maximum in
y"
ls
pushed
higher H„L amplitudes.
theory [2).
the enclosed vortices
Since domain
w
alls
can
be
can
press the domain walls which
pinned at impurities
and lattice defects.
8.
144
they
do not
too
move
the vortices find
a
easily. Eventually, they
way
Summary
sample.
reach the surface of the
Thus, the observed avalanches
to move out.
and Conclusion
In that case,
be attributed to
can
a
slow domain wall motion.
Motion of domain walls is also
[134]
group
performed
on a
UPh
(with
torus
series of consecutive
a
supported by
a
hole of
magnetization cycles, using
around H
0, which is
=
trinsic noise" from their
ature
started
phase,
This observation
measurements
increasing
was
Ty
,
argued
InAs-Hall-probe
a
to
avalanching" in
was zero
and increased further with
during
was
the field
in the
simulations
cycles.
are
perature that leads
a
to a
randomly
time reversal sxmmetry
provide
such
smaller number but in
is due to the fact that the
the
zero
leading
to a
field-cooled
magnetic
preferred
case
on
qualitative
a
at
above the
domain walls
"in¬
bulk, away
might move
region
positions, leading
superconducting
the
violating
bias. Therefore,
bigger
due to
This has been confirmed
formed
an
should
oc¬
to deviations
These observations agree well with the results of numerical
believed to nucleate
field could
meter, thus
field
high temper¬
state, unless there
transition tem¬
is bias for
type of domain. In time reversal symmetry breaking superconducting phases,
ult in
a
[2].
Domains
magnetic
array.
decreasing temperature.
placed
cycle,
different external fields for different domain wall
between consecutive
diameter). They
high temperatures. They extracted
and showed, that it
that,
in
under the pressure of the vortices. "Avalanches" in the center
slightly
at
at
"instability
also made when the magnetometer
from the hole. These authors
cur
observed at
not
an
of the Rosenbaum
experiments
approximately 150,um
Below 777 their magnetization loops exhibited
region
recent
a
by
Uo9725Thoo275Ben.
field-cooling
domains than in the
field may
"polarize"
domain type.
larger
The
zero
the
the
sample
external
would
res¬
field-cooled process. This
superconducting
pinning
an
one
order para¬
should then be stronger in
number of domain walls.
field-cooled relaxation measurements which
Whereas in the
high-temperature phase,
we
per¬
there is
no
difference between the results obtained in zero-field-cooled and field-cooled
mode, the intrinsic pinning mechanism found in the low-temperature phase in zero-fieldcooled mode, is not activated in field-cooled relaxation
"zero
creep"
contrary
in the
vortex
low-temperature phase
creep remains strong
even
if the
at
high
experiments.
sample
fields.
We do not observe
has been field-cooled. On the
8.
Summary
and Conclusion
145
A similar observation has been made
UBen. They investigated flux pinning in
0.6
proximately
cooling
mm
and also
in diameter).
the difference between the
at 77
=
0. At
cooled mode, but
effect in
an
difference is due to
an
is the
quantity
an
local
same
"excess
when the magnetometer
procedures only,
observe such
this
a
torus of pure
a
enhanced
a
hole of ap¬
Bi-Hall-probe, they
cycling
UBo]
was
one
in field-cooled and zero-field-
flux" in
trapped
placed
over
a
zero
field-cooled
difference between
the hole.
down to 320mK.
^
measured
Hnun and the
field
decreasing temperature. They detected
mode which increases with
both
Uo 97TT10 o^Ben (with
at the maximum
Tc2. they observed
near
of
samples. Using
magnetization
high temperatures
a torus
They performed magnetization cycles after zero-field-
their
field-cooling
the Rosenbaum group [1351 in thoriated
by
did not
They
They argued,
that this
of vortices in zero-field-cooled mode relative to
pinning
the field-cooled mode.
What remains nuclear at this moment, is the observed field
cays. From
which
the
are
our
-
field is turned off.
following
sample, strong
"zero
remained strong,
grains
are
was
Whereas this
S1-2R11O4,
observed in the
for domain walls
explanation
Uo9725Thoo275Bep,,
the "zero
the barriers
are
to
second transition temperature
fields
higher
pinning
applied
to
the
powder sample.
form and/or
that of Sr:Ru04.
high
fields.
TL
.
But
sample,
in
even
we
Probably
powder
the
is
only
the
case
Uo 972.5Tho 0275Ben
and
phase
decay
apply
of UPt3 is
to
already
es¬
for temperatures close to the
observe "zero
arc
In fact,
strength.
Uo 9725TI10 027sBen and S1-2R11O4,
before
low
at
inhibit vortex motion.
In contrast to
the low temperature
m
when
On the contrary, vortex creep
efficiently
than the critical field of the Bean model
mechanism in
decays
works well in UPh. where the strong vortex
creep" regime
sample
UPfis powder. In the powder
observed for every field
tablished at very low fields, in the undercritical state,
field has to be
leave the
few tens of pm at the surface, it docs not
a
nor
to
can
resulted from the motion of vortices at the
the lowest temperature and for
observed for vortiees from
of
-
of the de¬
concluded that those vortices
measurements on
exponential decays
even at
too small
law
was
that the observed strong
argued
was
supported by
was
stretched
creep" regime
It
UPF, [1], it
impeded by
exponential
stretched
surface. This argument
no
measurements on
close to the surface and not
magnetic
fields
group's
dependence
creep".
a
rather
high
We conclude that
necessary to activate the novel
Uo 9725TI10 02^sBep, and in Sr2Ru04.
146
Summary
8.
Our observation of "zero
walls in the
low-temperature phase
So far.
the lowest temperatures.
tional vortices has
magnetic
creep"
a
vortices in NbSeo [136]
peratures needed
to
or
apply
of UPb, and
U09725TI100275BC13 and in St-2Ru04
successfully applied
have been
YBa2Cii307_d- [137]. Unfortunately,
this
sort
of
techniques
to
to
the
at
frac¬
occupied by
scanning tunneling (STM)
In the last ten years,
microscopy (MFM)
force
indirect evidence for the presence of domain
an
direct observation of domain walls
boon made.
not
is
and Conclusion
or
image (standard)
low tem¬
relatively
UPt;,, thoriated UBen- and Si*2Ru04
(the interesting temperature range lies below 0.5 K). and problems with surface prepara¬
tion, could
for
some
delay
the search for domain walls and/or fractional vortices
of UPt^.
Uo
we
have found
9725 Tho
distinct from the standard
dynamics
pinning
than the
mechanism is
027sBen«
ing temperature.
This
so
strong that
period,
no
vortex
superconducting
MFM
drop
low-temperature
completely
a
different vortex
high-77 superconductors.
creep is observed in
a
The novel
time scale of several
a
small "avalanche". We
increasing cycling
field and with decreas¬
resulting
in
dependent,
Our observations
and
can
but rather intrinsic
be
explained
in the
Agterberg [2].
Flo972sThoo27sBen.
the novel
pinning regime
coincides
which violates time reversal symmetry in both
vortex
creep in
S1-2R11O4 docs
not set
in
right
transition temperature where the breakdown of time reversal
symmetry has been observed [6], but it
material, the
in
recovers
by Sigrist
respective low-temperature phase
below the
or
states.
systems [3-5]. In contrast, the reduction of
states
or
temperature. It is very
at the lowest
mechanism is not material
superconducting
of UPti, and
mechanism in the
delects. It results in
increases with
framework of the theoretical model
case
pinning
SriRiKTFj.
tho relaxation
pinning
to these unconventional
In the
novel
and in
pinning by
pinning strength
observe that the
a
observed in classical,
one
hours. After this time
with the
STM
time.
Summarizing,
phase
by
in creep rates
might
attributable to the multiband
occurs
only
at
much lower temperatures. In this
be associated with
nature
of the
a
"transition" of domain wall
superconducting
state
in
S12R11O4 [2].
Appendix
We used the
A
Experimental
following definitions
and conventions:
the maximum
resp.
Mrem:
a
throughout
|91nM/31n/|:
the initial
ziM/M,„„(l04s):
to
field for
a
magnetization curve,
magnetization, given
this work
arbitrary
refer
cycling
decay.
the remnant
one
Data
unit
arbitrary
corresponds
logarithmic
Chapter
in <F0 at the
SQUID
units have been used,
to
104<7>o.
creep rate, for the definition
6 and 7.
the deviation from the logarithmic time-Jaw at
147
IO4
s.
148
Appendix
1. The Sr2Ru04
Table l.a:
7(mK)
8
single crystals
Sample Sr2Ru04 (C81)
EI
mux
(Oe)
MH,m Aly)
348
1463506
with H A
71tu|
7/n(Oe)
2-10""6
19.3
(7In37
^
c
15
22
18.4
351
145930
^2-10~6
18.0
35
50
352
146082
O-10^6
60
350
146144
^
2-10^6
65
70
18.3
18.6
20
699
35
5478
50
13170
76
38561
112
90496
151
132144
200
145400
350
146225
450
146633
600
147136
4 59
j
0-6
80
350
145275
5 61
1
(T6
90
351
145363
8.04
IO"6
100
353
145436
3 61
io~s
110
360
145906
4.20
io-s
120
351
145653
3.59
uys
130
351
144837
6.24
io-s
150
374
145219
1.14
HT"
18.7
200
351
143896
2 00
10
4
17.1
18.8
18.1
A.
Experimental Data
Appendix
A.
Experimental
Table l.a continued:
'f(mK)
149
Data
Sample SnRu04 (C81)
with 77 JL
|31nM/31iu|
77„m(Oe)
Mrcm(yP0)
250
351
140991
2.75
10
300
350
137131
4.30
10
350
351
132611
4.15
10
400
350
128771
3.99
10
500
353
119782
4.41
10
600
350
105898
5.00
10
700
40
13226
65
42424
350
98834
5.63
10
86582
6.23
10
800
200
65
27352
300
65
17755
Table Lb:
Sample Sr2Ru04 (C49)
Hcl (Oe)
with H Ac
\dhiMA\nf\
r(mK)
//,„,„ (Oc)
Mrcm(®o)
6.6
65
4100
6.7
68
4090
<27(76
6.8
68
4107
<
7.2
79
4097
< 2
2-
Hc[(Oe)
IO'"6
10~6
15
14.5
c
6.1
6.1
68
4100
<r
2
•
10^6
17.4
6.1
19.8
6.1
23.2
6.1
26
68
4111
<2- 10^6
28
6.1
-IO"5
6.1
10"5
6.1
35
69
4082
40
68
4102
8.5-
45
68
4100
1.1
2.54
-KU4
150
Appendix
Table Lb continued:
Sample SriRu04 (C49)
with H Ac
|31n37/71nf|
Hmax (Oe)
M,an((P0)
50
68
4097
2.9- 10
75
68
4062
4.1-IO-4
100
73
4044
4.8-ur4
6.0
200
69
3871
6.7-10^4
5.8
T(mK)
4
5 6
250
300
^i(Oe)
68
3630
lAAir4
5 4
350
5.1
370
5.0
400
70
3195
8.8
IO"4
•
4.9
4.2
500
600
3 5
50
69
2615
1,14-10^
345
2726
9.8-itr4
2.8
700
800
3
201
10
1141
46
1776
1.41- 10"
900
41
1378
1.48-10-''
920
30
1267
42
1227
1 62
41
1101
1.87-
42
1106
1.85
970
42
884
3 07 7
0^
1000
41
458
3.56 7
(T^
950
1.9
'
LO
0.8
7(7^
IO"'
7(7^
A.
Experimental Data
Appendix
Table l.c:
A.
151
Experimental Data
Sample Sr2Ru04 (C49)
77
||
c
\d\nM/dhit\
Aèdecax/Miem
iK)
Umax (Oe)
Mnm((E,)
8
299
9694
O
16
299
9682
^2-10^6
20
299
9683
<.
29
299
9683
1.23-10-*
0.018
4
0.023
•
2-
10
6
H(](Oe)
22
IO"6
38
300
9681
5.09 70
44
300
9674
1.16-10~3
0.024
50
298
9660
2.76-KT''
0.027
60
299
9616
2.78-10"
70
299
9566
2
86-IO"^
0.028
75
301
9551
2.49-10^
0.028
100
299
9380
2.44-itr'1
0.024
125
299
9190
2.02- 10
150
299
9016
L65-10
200
299
8654
1.33-10"
300
260
7855
1.20-10-^
400
39
473
0.012
75
5185
0.013
260
6953
1.34-IO-*
0.014
500
209
5993
1.80-10-'
0.017
600
178
5034
2.25-
IO"*
0.027
700
139
3984
3.1-10"'
0.029
800
100
2961
4.07-IO-3
0.039
'
*
'
^
0.027
0.018
0.015
0.011
24
0.01 I
19
10
Appendix
152
Table l.tl:
Sample Sr2Ru04 (C82)
J'(mK)
Himx(OC)
Mn,m(%)
15
280
23764
33
280
23978
70
301
23978
600
252
15269
1200
102
5199
2. The
Table 2.a:
7\mK)
77 A
c
dlnMAmt
Uo.9725TIi().o275Bei3 single crystals
Uo972sThon275ßen sample I (with 107c of Al impurities).
dlnMAlnt
Umax (Oe)
M,cm (<*>„)
7.6
339
123571
<2-
50
1360
256978
o-io~6
2043
249120
v.
2
2086
246310
^
2-IO"6
340
80533
681
353687
340
190222
0.316
681
305860
0.014
350
340
152254
1,181
450
202
42483
2.459
500
201
600
68
100
200
A.
•
IO"6
HT6
0.025
7
2IO"6
1.291
2370
1 ^23
Experimental
Data
Appendix
Table 2.b:
T(mK)
A.
153
Experimental Data
Uo972sThoo275Bei3 sample II. only
zero-field cooled data
d\nM/d]nt\
AM/M,em (IO4 s)
HmC!X(Oc)
Mum{0o)
1003
30584
72
io-6
1202
28302
<2
HT6
101
1377
0.0122
200
6075
7.4-IO-3
305
13895
402
22932
2.3
502
30495
1.0-io-3
704
34557
4.0- 10
1006
29985
<2
10-6
3.1-IO"4
1197
28909
<2
io-6
2.8-IO-4
1197
27668
5.67-ur5
100
2375
3.9-IO-3
97
2740
3.7-
200
9328
299
18895
400
27456
0.027
500
31881
0.033
605
31216
0.026
702
29792
8.5-
796
29344
3.5-IO-3
1000
27122
2.4- 10-3
1002
27120
2.1-10-3
1201
25897
2.7- 10-3
1301
25 180
1.4- 10-3
1500
23802
0.0168
•
•
io-5
4
7-IO-4
6.03
9.33
IO"3
IO-3
KU3
IO-3
1.2-10-3
Appendix
154
Table 2.b continued:
A.
Uq 972sT1iq 027560n sample II, only zero-field cooled data
AlnM'd\nt]
AM/M,em (IO4 s)
Hnm(Oc)
M,c„,(®o)
70
1267
201
12657
406
24888
7.5- 10-3
605
26417
0.0465
803
24865
0.0208
1008
24390
0.0105
1101
23900
0.0107
1197
23136
5.19-10 ~3
1312
22918
1008
20137
1
1112
20265
1.24-
325
1101
17349
3
350
1011
15291
360
1197
13932
2.17-10"2
0.0109
370
1204
13205
2.78-10-2
9.1-10-3
380
1001
12297
0.0194
1212
12135
0.0164
100
5976
2.9-Itr2
0.0134
200
8811
3.0-itr2
0.0227
400
9806
3
0-10-2
0.0204
503
10627
3.0-10"2
0.0150
700
10408
2.8L10-2
9.5-10-3
799
10493
2.86-
itr2
9.5-10-3
1198
10446
2
84-ur2
9.5- 10-3
r(mK)
250
300
400
450
Experimental
5.1
6.LIO-4
•
10-3
9.63-10-3
62-10-*
0 0312
IO-3
0.0336
02-itr3
0.0530
0.1094
504
3 01
700
2.96
•
or2
itr2
Data
Appendix
A.
Expeiimental
Table 2.c:
7(mK)
200
400
Data
Uo972sThoo27sBen sample II, only field cooled
dlnM/dlnt\
AM/Miem(104s)
Hmn (Oe)
MnmCEA
101
18851
3,79-10
101
18707
3 92-10
201
29702
8 67-10
500
31471
0.046
1019
32512
0.070
100
8130
0 0261
0.234
306
9317
0 0307
0.273
515
9428
0 0285
0.267
996
9438
0 0323
0.283
'
data
0 046
*
0.045
*
0.092
^
i
t
i
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#
S
Acknowledgements
It is
not
great pleasure
a
only
completion.
especially
ics. Moreover. I
to my
Prof. Ana Cclia Mota. She
supervisor,
I
profited
a
lot from her
knowledge
extraordinary experience
enjoyed
teaching
very much
Finally,
physics community
I
am
and
the
me
the
in
opportunity
and
introducing
to
essential
to
its
physics,
low-temperature phys¬
low-temperature
also indebted to her for
giving
were
in condensed matter
benefited from her
classes with her.
tional
gratitude
initiated this thesis, but her continuous advice and support
successful
and I
to express my
superconductivity
me
to
the interna¬
present my results
at so many
international conferences.
I would very much like
to
thank Prof. Maurice Rice and Prof. Manfred
their interest in my work, and their
a
great honour for
to Prof.
me,
that
they agreed
1 express my
about thoriated
in
answering
profited enormously
to Prof. Frank
Sleglich
UBen and his sincere interest in
Some of the
numerous
am
from
questions.
It
for
was
also very thankful
our
discussions and
physics.
gratitude
go to Niels Oeschler for
my
co-referee this thesis. I
to
Gianni Blatter for his support. I
his lectures in theoretical
letting
me use
measurements
Maurizio Leonard!. Andreas
ure
patience
Sigrist
Baumgartner
so
many
our vortex
his thermal
presented
for
enlightening
creep studies.
expansion
working with them.
169
von
Special
measurements in
in this thesis have been taken
and Marc
discussions
Waldkirch. It
by
was a
thanks
my thesis.
my students
great pleas¬
Acknowlcdgemen ts
170
I
acknowledge
many fruitful discussions with the
people
from the theoretical de¬
partment Daniel Agterberg, Rolf Heeb. Karin Le Hur. Mike Zithomirsky, and
Carsten
Honerkamp,
Many
who
patiently taught
me
the
theory of
Andreev
most
of all
scattering.
thanks go to Hans Ruedi Aeschbach for his competent technical support, and
for their
lo Marisa van der Mark and Doris Arnstadt
repeated
assistance in administrative
work.
I
am
grateful
very
to
Prof. Yoshiteru Maeno and Dr. Jim Smith for
samples investigated in
this thesis, and to Roland Wessicken, Peter
Schönfeld for
the
I
ing
orienting
Edouard
Lamboray
opportunity
to
thank my
and Prof. Antonfn Van cura for correct¬
colleagues
De Morais-Smith, Andreas Fuhrer. Matthew
and friends at the ETH Cristiane
Dodgson. Jorge Gavilano,
Kaufmann. René Monnier, Marco Niederöst, Ivo Stalder. Orlando
Wälti. I would
owe a
and Dr. Bernd
manuscript.
I seize the
serving
the
Sr2Ru04 samples.
gratefully acknowledge
this
Waegli,
providing
a
especially
like to
acknowledge
good working atmosphere
debt of
gratitude
Throughout
Thomas Ihn,
Evelyne
Wagner, Christophe
my office mate Marco Saalfrank for pre¬
until the very end, and Andreas Amann to whom I
for his many encouragements and advices.
all these years at ETH. I could
friends and members of my
family.
1
am
firmly rely
deeply grateful
to
on a
bunch of
Malek Bou
really good
Diab; Thorn,
Jean, Louisette and Marguerite Dumont; Franziska Pfister: Ulrike Stege; Tobias Vancura;
Nathalie Weiler; and Ariane Wir/. I would like to thank my father Paul Dumont for his
support, and Edouard Lamboray for his patience and love during the whole time of my
studies.
Curriculum Vitae
April
1979
1985
1992
2nd, 1973
-
-
-
born in
Luxembourg City.
1985
Primary
1992
Secondary
1997
Study
November 1997
school in
of
Walferdange, Luxembourg.
school in
Physics
Diploma thesis
at
on
Luxembourg City.
the ETH Zürich.
"Unconventional Vortex
ics in Sr2Ru04" carried out under the
Dynam¬
supervision
of Prof. Dr. A.C. Mota, ETH Zürich.
1997
-
2000
Teaching
and research assistant in the group of Prof.
Dr. A.C. Mota. ETH Zürich.
171
Seite Leer /
Blank ieaf
Publications
1.
"Transition into
ning
in
a
low temperature
superconducting phase
of unconventional pin¬
Sr2Ru04"
A.C. Mota. E. Dumont. A. Amann, Y Maeno
Physica
2.
B 259-261. 934 (1999).
"Strong
vortex
pinning
m
the
low-temperature
superconducting phase
of
(Ui_vThOBen"
A.C. Mota. E. Dumont. J.L. Smith
J. of Low
Temp. Phys. 177.
3. "Unconventional
Uo
0725
Tho
027s
strong
1477 (1999).
pinning
in
the
low
temperature
Ben"
E. Dumont, A.C. Mota and J.L. Smith
Physica
4.
B 284-288. 525 (2000).
"Unconventional strong pinning in
multiphase superconductors*'
A.C. Mota, E. Dumont. J.L. Smith and Y Maeno
Physica
C 332. 272
(2000).
Presentations
I. "Ultrasensitive
Magnetic
Nanophysics Seminar.
5.4.1999 (oral
Measurements at mK"
ETH Zurich
presentation)
173
phase
of
174
Publications
2. "Observation of unconventional strong
Uo
9725
pinning
in the low temperature
phase
of
Tho 0275Ben"
XXII International Conference
8.6.1999
on
Low
Temperature Physics (Helsinki)
(poster)
3. "Unconventional
pinning
strong
in
the
low
temperature
phase
of
Uo 9725Tho 0275B°n"
International
29.9.1999
Workshop
Concepts
on
in Electron
Correlation
(Hvar, Croatia)
(oral presentation)
4. "Anomalous strong
pinning
in the low temperature vortex
18th Conference of the Condensed Matter Division of the
phase
of SP2R11O4"
European Physical
Soci¬
ety (Montreux)
15.3.2000
(poster)
5. "Anomalous strong
American
the low temperature vortex
phase
of Sr2Ru04"
Physical Society, March Meeting (Minneapolis)
23.3.2000 (oral
6. "Vortex
pinning in
presentation)
Dynamics
Sr2Ru04", Seminar
27.3.2000 (oral
in the unconventional
at
Argonne
presentation)
National
superconductors UPt^, (U,Th)Bei3
Laboratory (USA)
and