Pressure induced quantum phase
transitions in d- and f-electron systems
Vladimir A. Sidorov
Institute for High Pressure Physics of Russian
Academy of Sciences
Troitsk - Moscow
Workshop “Heavy Fermions and Quantum Phase Transitions”, November 10-12, 2012, IOP CAS, Beijing
Outline
Three compounds CePt2In7, CeCoSi and CoS2 which exhibit quantum
phase transition under pressure will be discussed in the presentation.
• CePt2In7 - a very close analog of CeRhIn5 , where 4f-electrons of Ce play
the main role in magnetism, QPT and superconductivity.
• CeCoSi - a layered antiferromagnet in which Co 3d-electrons become
important at high pressure along with Ce 4f-electrons.
• CoS2 - a ferromagnet and nearly a half-metal with a high degree of spin
polarization. Co 3d-electrons are responsible for magnetism and QPT.
• A brief review of the experimental technique used in high pressure
experiments will be presented.
Collaboration:
Los Alamos National Laboratory, USA
E. Bauer, P. Tobash, M.Torrez, R.Baumbach,
H. Lee, Xin Lu, F. Ronning, J.D. Thompson
Sungkyunkwan University, Korea
Tuson Park
Institute for High Pressure Physics RAS, Russia
S.M. Stishov, A.E. Petrova, V.N. Krasnorussky,
A.N. Utyuzh
Ames Laboratory, USA
W. M. Yuhasz, T. A. Lograsso
High pressure apparatus and methods
Toroid-type anvil pressure cell
6 GPa at 27 ton, 8 GPa at 34 ton
T = 1.2 – 300 K, no magnetic field
The electrical resistivity, magnetic ac-susceptibility
and ac-calorimetry measurements can be organized
in a single experiment
Before high pressure
After 6 GPa
Cylinder-piston (up to 2.2 GPa) and indenter-type (up to 3.2 GPa) cells also were used
for some experiments down to 0.1 K and in the magnetic field up to 9 Tesla.
CePt2In7 - pressure induced heavy-fermion superconductivity near QCP
Our first measurements on CePt2In7 polycrystals reveal that it is a close analog of
famous CeRhIn5. Pressure above 3 GPa
suppresses magnetism and a broad dome
of the heavy-fermion superconductivity
appears around quantum critical point.
Indium contamination prevents from detailed
resistivity measurements in zero magnetic
field. The main method was ac-calorimetry.
Now In-free single crystals of CePt2In7
became available and we present the
new data obtained at high pressure.
We constructed P-T diagram based on
resistivity and ac-specific heat of single
crystals of CePt2In7 and determined
some parameters of this heavy-fermion
superconductor near QCP.
Resistivity of CePt2In7 single crystals at high pressure
60
25
20
10
CePt2In7
0
0
50
100
150
200
250
300
350
T(K)
ab (-cm)
P(GPa)
0
0.67
1.54
2.19
2.47
2.66
2.97
3.08
3.29
3.51
3.85
4.33
5.30
CePt2In7
15
10
5
0
0
1
2
3
4
5
T(K)
6
7
8
9
10
0(-cm)
2.5 K
5
0
-5
(T) = 0 + ATn
4
10
TC
5
3
P(GPa)
2.66
2.97
3.08
2
1
0
0
0
1
2
3
4
T(K)
25
20
15
n
30
20
TN
5
6
7
8
n
40
CePt2In7
A (-cm/K )
ab (-cm)
50
10
 (-cm)
P(GPa)
0
0.67
1.54
2.19
2.47
2.66
2.97
3.08
3.29
3.51
3.85
4.33
5.30
10
5
0
0
1
2
3
4
5
6
P(GPa)
The kink on (T) dependence at TN shift first to higher temperatures
And then above ~ 1.5 GPa it shifts to lower temperatures. At 2.47 GPa
a signature of a very broad superconducting transition appears at ~2K.
At higher pressures it becomes sharp. At 5.3 GPa one can see the
onset of a very broad superconducting transition at ~1.7K.. Fits of the
low temperature reistivity by the relation (T) = 0 + ATn give the
values of A, 0 and n, which are anomalous near 3.2 GPa. Remarkably,
the exponent n is close to 0.5 at this pressure. Similar sublinear
behavior of the resistivity was found in CeRhIn5 (T. Park et al., Nature
456(2008) 366).
The upper critical field of CePt2In7 superconductor
20
0,003
R()
0,002
0,001
0,000
0,0
0
0.2
0.5
1
1.5
2
3
4
5
6
7
8
9
0,5
CePt2In7
CePt2In7
15
3.1 GPa
0.5 mA
J//ab, H//c
0H (T)
H (T)
-12.4 T/K
10
3.1 GPa
5
J // ab, H//c
TC onset
TC (50% RN)
TC (5% RN)
1,0
1,5
T(K)
2,0
2,5
3,0
0
0,0
0,5
1,0
1,5
2,0
2,5
T(K)
Resistivity measurements in the indenter cell down to 0.3 K and up to 9 Tesla at 3.1 GPa allow
to estimate Hc2(0) and the initial slope dHc2/dT at Tc. The initial slope -12.4 T/K is close to that
-15 T/K observed by Muramatsu et al. (J. Phys. Soc. Japan, 70 (2001) 3362) for CeRhIn5 heavyfermion superconductor near pressure-tuned QCP and in the same orientation of the magnetic
field. The estimated Hc2(0) ~15 Tesla is lower, than that (~20 Tesla), estimated by WerthamerHelfand-Hohenberg formula for orbital pair-breaking. So the upper critical field may be limited by
Pauli paramagnetic pair breaking as was suggested for CeRhIn5 by T. Park and J.D. Thompson
(New J. Phys. 11 (2009) 055062).
Specific heat of CePt2In7 single crystals at high pressure
0,6
0,3
CePt2In7 + GW 60/40
0,3
0,2
0,1
0,2
3.29 GPa
2
2
C/T (J/K )
0,4
CePt2In7
C/T (J/K )
P(GPa)
0.67
1.54
2.19
2.47
2.66
2.97
3.08
3.29
3.51
3.85
4.33
5.3
0,5
0,1
0~ 0.5-0.8 J/mole-K
2
0,0
0,0
0
1
2
3
4
5
6
7
8
9
20
25
30
35
2
0,15
0,10
1
2
3
4
5
CePt2In7
0,30
1,5
15
0,25
1,0
0,5
2
C/T (J/K )
0,20
0
2
P(GPa)
0
1.54
2.19
2.66
2.97
3.08
3.29
3.85
4.33
C/T (J/mole-K )
CePt2In7
0,25
2
15
T (K )
0,35
0,30
C/T (J/K )
10
2
T(K)
0,35
5
10
 (-cm)
0
10
0,20
0,15
5
0,10
0,05
0,05
0,00
0
1
2
3
4
5
T(K)
6
7
8
9
0,0
10
3.29 GPa
0,00
0
0
1
2
3
4
5
T(K)
The specific heat measurements correlates well with the resistivity measurements. The Neel temperature
increases first and then rapidly decreases at high pressure. Above 3.08 GPa the resistive and bulk transitions
to the superconducting state take place at the same temperature. But at 2.97 GPa where the resistance of
CePt2In7 becomes zero below 2 K, the upturn of the specific heat preceding a peak at the superconducting
transition takes place at 1.4 K. This is very similar to CeRhIn5 (T. Park and J.D. Thompson, New J. Phys. 11
(2009) 055062). Superconductivity in CePt2In7 emerges from the heave electron normal state, which is due to
strong magnetic fluctuations near QCP.
Close analogy between CePt2In7 and CeRhIn5
P-T diagram
Colossal scattering
near QCP
Entropy
7
CePt2In7
TN, peak C
TN, kink 
TC onset 
TC  = 0
TC peak C
4
AFM
3
2
1
entropy at TN
entropy at TC
SC
1
0
0
1
2
3
P(GPa)
4
5
6
8
7
6
5
4
3
2
0
10
(P)/(5 GPa)
2
CePt2In7
100
CePt2In7
Temperature (K)
T(K)
5
3
Entropy (J/mole-K)
6
AFM
SC
0
0
1
2
3
4
P(GPa)
T. Park and J.D. Thompson, New J. Phys. 11 (2009) 055062
5
1
0
1
2
3
4
5
Pressure (GPa)
T. Park et al., Nature
456 (2008) 366
CeCoSi: multiple transitions and quantum criticality at high pressure
Literature data:
First synthesis and report of crystal
AFM transition at 9.2 K (μeff = 2.8 μB, X-ray absorption spectroscopy:
structure: Bodak et al., Zhurnal Struct. Θp =- 53 K), DOS calculations:
O. Isnard et al., J. Synchrotron
Khimii, 11 (1970) 305
B. Chevalier and S.F. Matar,
Rad., 6 (1999) 701
Phys. Rev. B, 70 (2004) 174408
Specific heat measurements
B. Chevalier et al., Physica
B, 378-380 (2006) 795
Single crystals are not available.
All experiments were performed
on polycrystalline samples.
Properties of arc-melted CeCoSi
Single phase material, tetragonal P4/nmm, a = 0.4046 nm, c = 0.6969 nm
7.0x10
-5
6.0x10
-5
5.0x10
-5
4.0x10
-5
3.0x10
-5
2.0x10
-5
1.0x10
-5
1500
MT124
CeCoSi
800 C 2 wks
60000
40000
0
50
100
150
200
250
300
2
P= -93K
eff= 3.18 B
20000
0
C/T (mJ/mol-K)
1/ (gm/emu)
 (emu/gm)
80000
350
T(K)
CeCoSi / MT124
annealed 800C/2wk
H=0.1T
2/14/11
0.0
0
50
100
150
200
250
300
1000
500
0
350
0
100
T(K)
200
300
400
500
2
T (K)
20
CeCoSi MT124, annealed 2 wk at 800 C
CeCoSi MT124, annealed 2 wk at 800 C
350
60
200
 ( cm)
 ( cm)
250
d/dT ( cm/K)
RRR = 42
300
150
100
40
20
10
5
0
50
0
2
4
6
8
10
12
0
T(K)
0
15
0
50
100
150
T(K)
200
250
300
0
5
10 15 20 25 30 35 40 45 50 55 60
T(K)
Resistivity: pressures up to ~1 GPa. Transformation of the
AFM transition related with Ce-sublattice.
CeCoSi MT124, annealed 2 wk at 800 C sample 1
CeCoSi MT124, annealed 2 wk at 800 C
300
250
d/dT ( cm/K)
20
P(GPa)
0
0.31
0.69
0.91
1.21
15
10
5
0
P
150
0
10
20
30
40
50
60
70
T(K)
P(GPa)
0
0.31
0.69
0.91
1.21
100
50
CeCoSi MT124, annealed 2 wk at 800 C sample 1
20
0
0
10
20
30
T(K)
40
50
d/dT ( cm/K)
 ( cm)
200
P(GPa)
0
0.31
0.69
0.91
1.21
15
10
5
0
2
4
6
8
T(K)
10
12
14
Resistivity: pressures up to ~2 GPa. New SDW-like transition.
CeCoSi MT124, annealed 2 wk at 800 C sample 1
CeCoSi MT124, annealed 2 wk at 800 C sample 1
16
300
P(GPa)
1.47
1.71
1.83
1.89
1.92
2.02
 ( cm)
200
P(GPa)
1.47
1.71
1.83
1.89
1.92
2.02
14
12
d/dT ( cm/K)
250
P
150
100
10
8
6
4
2
50
0
0
0
10
20
30
T(K)
40
50
-2
0
10
20
30
40
T(K)
50
60
70
Resistivity: pressures ~3-4 GPa. Valence transition.
CeCoSi MT124, annealed 2 wk at 800 C
CeCoSi MT124, annealed 2 wk at 800 C
sample 1
4.5
350
P(GPa)
0
2.77
3.25
3.63
3.63
3.95
3.95
4.67
5.41
5.77
 ( cm)
250
200
150
Valence transition region
4.0
P(GPa)
3.0
3.25
3.63
3.95
3.5
d/dT ( cm/K)
300
100
3.0
2.5
2.0
1.5
1.0
50
0.5
0
0
50
100
150
T(K)
200
250
300
0.0
0
50
100
150
T(K)
200
250
300
Resistivity: P-T diagram
Tn (K)
Tm (K)
Tv (K) cooling
Tv(K) warming
T(K) broad peak1 of drho/dT
T(K) broad peak2 of drho/dT
40
CeCoSi
dTV /dP ~ 400 K/GPa
30
15
III
10
I
5
II
IV
0
1
(T) = 0+ ATn
n
A (-cm/K )
20
QCP
10
CEP
0
0
1
2
3
4
0.1
0.01
1E-3
1E-4
3.0
P(GPa)
0.40
2.5
0.35
n
CeCoSi
0.30
2.0
1.5
0.25
1.0
n
A ( cm/K )
T (K)
CeCoSi
20
0 ( cm)
50
0
0.20
1
2
3
4
5
6
P(GPa)
0.15
0.10
Resistivity measurements at 2 GPa down to 0.1 K
Show no signature of superconducrivity near QCP
0.05
0.00
0
1
2
3
P(GPa)
4
5
6
AC-calorimetry and strain gauge: Possible structural
transformation at P ~ 1 GPa. Valence transition at 4.5 GPa.
13.1
55
CeCoSi
CeCoSi
50
13.0
300 K
45
Rheater ()
R (m) 300 K
12.9
40
35
L/L0 ~1.8%
12.8
L/L0 ~0.7%
12.7
30
25
12.6
20
0
1
2
3
P(GPa) LT
4
5
6
0
1
2
3
P(GPa)
4
5
6
AC-calorimetry: data.
CeCoSi + GW60/40
20
5
CeCoSi
15
 (arb. units)
2
C/T (J/K )
4
3
P(GPa)
0.35
0.65
1.02
1.16
1.24
2
1
0
5
0
0
10
20
30
40
50
T(K)
CeCoSi + GW60/40
4
3
2
P(GPa)
1.51
1.71
1.82
2.0
2.04
2.14
2.56
3.0
3.62
5.0
2
1
0
0
10
20
30
T(K)
0
1
2
3
4
5
P(GPa)
5
C/T (J/K )
10
40
50
The temperature of AFM transition related with Ce-sublattice
does not change much at high pressure, but it splits into two
transitions at modest pressure. At ~1.2 GPa the new magnetic
transition appear at ~35 K probably related with Co-sublattice
and Ce-related transition becomes very broad and is shifted to
~14 K. These big changes in magnetism of CeCoSi are most
probably related with a structural transformation at 1.2 GPa.
Magnetism is quencehed at ~2 Gpa in the manner of a QCP.
The A coefficient of the T2 term in resistivity and the electronic
specific heat coefficient  diverges at 2 GPa. But the enhanced
specific heat at 2-3 GPa shows the importance of critical
magnetic fluctuations in this pressure range.
AC-calorimetry: P-T diagram.
P-T diagram of CeCoSi by calorimetry
40
300
CeCoSi
CeCoSi
250
SDW ?
30
peaks of  and A
sharp drop of 
structural
reconstruction
20
n
broad C(T) anomaly
with small entropy
short rande
correlations ?
T(K)
T(K)
 = 0 + AT
Tn(K) peak1
Tn(K) peak2
Tsrc(K) broad peak
Tm(K)
Tv(K)
Tv(K) rho
200
150
100
10
50
broad C(T)
anomaly
AFM
0
0
0
1
2
P(GPa)
1
2
3
4
5
P(GPa)
Very complex P-T diagram was found in CeCoSi - structural and valence transitions,
two different magnetic transitions, quantum critical point for magnetism and critical
end point for valence transition.
The structural, valence and magnetic instabilities are probably originate from the
effects of hybridization and interplay of Ce 4f and Co 3d-electrons.
First-order-like quantum phase transition in the itinerant ferromagnet CoS2
Below TC = 122 K CoS2 becomes a ferromagnet
with high degree of spin polarization.
C. Utfeld et al., PRL 103 (2009) 226403
Magnetic measurements under pressure reveal metamagnetism and a transformation
of a second-order transition to a wekly first-order one at P ~ 0.3-0.4 GPa.
T. Goto et al., PRB 56 (1997) 14019
Resistivity measurements of CoS2 are controversial:
in a liquid pressure medium TC decreases faster at high pressure than
in a solid medium and the resistive anomaly becomes sharper, whereas
it broadens and disappear in a solid pressure medium.
S. Yomo, J. Phys. Soc. Japan, 47 (1979) 1486
Resistivity and magnetic ac-susceptibility of CoS2 at high pressure
V.A. Sidorov et al., Phys. Rev. B, 83 (2011) 060412(R)
120
150
a)
110
105
100
10
5
50
a)
0
100
110
2.5
115
120
0
125
ac (a.u.)
ac(a.u.)
100
150
1.0
0.5
b)
6
4
2
115
120
125
Temperature (K)
Compressed helium pressure cell
(pressure up to 0.9 Gpa)
20
30
0
200
P(GPa)
0
1.22
2.34
3.39
3.88
4.24
4.54
4.78
4.92
8
1.5
110
50
b)
10
2.0
0.0
0
10
 ( cm)
 ( cm)
 ( cm)
115
0
0
50
100
150
200
Temperature (K)
Compressed liquid toroid-type
anvil pressure cell (P up to 6 GPa)
Specific heat and magnetic entropy of CoS2 at high pressure
2
1.22 GPa
4
2
0,3
0,2
0,1
0,0
0
1
2
3
P(GPa)
3
2
TC CoS2
4
5
TG GW60/40
1
3
0
50
100
150
T(K)
200
250
300
CoS2
0
2.34
1
3.88
4.24
70
80
3.39
90
100
110
120
130
5
0
0
4.24
3.88
3.39
2.34
-5
1.22 GPa
-10
0
1.22 GPa
a
2
0
60
Phase shift (deg)
CoS2
5
C/T (J/K )
Smag / Rln2
0,4
6
4
Cmag/T (J/K )
S. Ogawa, J.Phys.Soc.
Japan, 41 (1976) 462.
7
60
b
70
80
90
100
T(K)
110
120
130
P-T diagram and nature of the quantum phase transition in CoS2
0.08
CoS2
100
20
105
0 (-cm)
n
110
0.0
0
A (-cm/K )
115
40
17.5 mJ/mole-K
1.28 K
0
120
60
2
0.06
1
2
3
4
5
6
1.0
1
0.5
1.0
1.5
Pressure (GPa)
2
3
2.0
4
Pressure (GPa)
5
6
0.5
loading
unloading
0.0
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0
1
2
3
4
5
6
0.02
0.01
0.00
3.0
7
2.5
n
80
0.07
0.05
125
0
CoS2
2
C/T (J/K )
120
[7]
[10]
[15]
[16]
Tc(K)
Transition temperature Tc (K)
140
2.0
1.5
1.0
P(GPa)
Three systems with quantum phase transitions were considered
in this presentation:
CePt2In7 – a very close analog of CeRhIn5. The evolution of magnetic
entropy through the quantum critical point where one can see the smooth
flow of the spin entropy from the magnetic to the superconducting channel
gives evidence of the magnetic origin of superconductivity.
CeCoSi exhibits a diversity of ground states. The magnetic entropy decreases
strongly on approaching the critical pressure (2 GPa) at which quantum critical
phenomena usually associated with a QCP are observed. However the residual
magnetic anomaly with progressively decreasing magnetic entropy is still visible up
to much higher pressures (3 GPa) where the critical end point of the valence
transition takes place at low tenperature. These complex phenomena are probably
related with the development of magnetism in two different (Ce and Co) magnetic
sublattices.
CoS2 exhibits a first-order like quantum phase transition from the ferromagnetic to
the paramagnetic state. No quantum critical phenomena are observed and the
magnetic entropy decreases to the negligibly small values on approaching the critical
pressure. These observations indicate on the progressively increasing itinerancy and
the delocalization of the magnetic moment in CoS2.
Thank you for your attention !
Appendix
Basics of AC calorimetry in the ideal case
• If the heater is exited by oscillating power P(t)=P0(1-sint)
then the oscillations of the sample temperature are related
with the sample heat capacity (Sullivan and Siedel, 1968) by
TAC = P0/C[1 + (1)-2 + (2)2]-1/2 = (P0/C)F()
where
1 = C/K1 describes the thermal coupling to the bath and 2
describes the thermal coupling sample-heater
if (1)2 >> 1 and (2)2 << 1 then TAC = P0/C and F()≈1
F() has maximum value [1+2(2/ 1)]-1/2 at the optimal
frequency 0=(12)-1/2, which is the best for AC calorimetry
measurement. Frequency dependence of the product TAC
is to be determined to find 0. It may vary with temperature
(and pressure).
AC calorimetry of Glycerol-water 60/40 at high pressure
4
1.2
Glycerol-Water 60/40 at 10 kbar
1.1
9 Hz
15 Hz
31 Hz
51 Hz
102 Hz
205 Hz
835 Hz
1670 Hz
1.0
3
0.7
T(K)
0.6
298
156
75.5
51
25
16.2
9.1
3.95
1.1
0.5
0.4
0.3
0.2
0.1
2
-1
fR / fR max
0.8
(fR) (sec/V)
0.9
1
10 kbar
0
1
10
100
1000
10000
f (Hz)
• Frequency dependence of AC
calorimetry signal at P=10 kbar
Glycerol-water 60/40
0
50
100
150
200
250
300
T(K)
• The inverse of temperature
oscillations (~C) vs T at P=10kbar