U
Ru
Si
Hidden Order and Kondo Effect in
URu2Si2
Nat Phys 5:637‐641
CIFAR Quantum Materials Program Meeting
Montreal 2010
Work in collaboration with Kristjan Haule
K. Haule and G. Kotliar EPL 89 57006(2010)
K. Haule and G. Kotliar Nat Phys 5:637‐641(2009)
1
URu2Si2: a typical problem in the theory of
correlated electron materials

A non-historical review of some important experimental
facts about URu2Si2.

URu2Si2 a good test of the LDA+ DMFT strategy.
New insights into a very old problem.

Comparison with some experiments
Outlook and Conclusions : key open questions and
some more general perspectives on strongly correlated
materials.

2
Hidden Order The CMT dark matter problem.
U
Ru
Si
Entropy Loss at th
e transition: 1/5 L
og[2]
URu2Si2: T. T. M. Palstra, A. A. Menovsky, J. van den Berg, A. J. Dirkmaat, P. H. Kes
, G. J. Nieuwenhuys and J. A. Mydosh Physical Review Letters 55, 2727 (1985)
3
Phase diagram T vs P based upon resistivity and calorimetric
experiments under pressure.
E. Hassinger et al. PRB 77, 115117(2008).
Very similar to Amitsuka’s T – P phase diagram
Consistency among experimental groups. First order phase transition.
4
“Adiabatic continuity” between HO & AFM
phase
•Similar T0 and TN
•Almost identical thermodynamic
quantities ( e.g. jump in Cv) and simil
ar
oscillation frequencies.
E. Hassinger et.al. PRL 77, 115117 (2008)
“Adiabatic “is a misnomer.
Need a better term.
5
Magnetic susceptibility
Extreme Anisotropy. Kondo?
12
c (10 -3 emu / mol)
10
URu2Si2
8
mzeff ~ 2.2 mB
6
H // c
4
To
H // a
2
0
0
100
200
300
400
T (K)
6
Pseudo-gap opens at Tc. URu2Si2 measured through optical conduct
ivity, D. A. Bonn et al. PRL (1988).
7.5 mev
7
Resistivity
keeps decreasing with decreasing T
500
r (mW cm )
400
I // a
300
T.T.M. Palstra et al.(1985)
W. Schlabitz et al.(1986)
M.B. Maple et al.(1986)
To ~ 17.5 K
200
100
01
Tc ~ 1.2 K
I // c
10
T (K)
100
1000
Heavy fermion at high T,low T HO + SC
8
Inelastic Neutron Scatterin
g
Neutron intensity present in
two regions, around
(1,0,0) and around (1.4, 0,
0)
And (.6, 0, 0)
Wiebe, C. et al. Nature Phys. 3, 96–100 (2007).
9
Hall effect as function of temperature in different external fields,
Y.S. Oh et al. PRL 98, 016401(2007).
•Fermi surface reconstruction in zero and small magnetic fields
•Very large fields metamagnetic transition to polarized Fermi liqui
d.
Some proposals for the hidden order in the literature
(disagreement aboutbasic aspects, Kondo physics valence etc)
•Lev. P. Gorkov: 1996:
-Three point spin correlators.
• Chandra and Coleman ., Nature’02
- Incommensurate Orbital Antiferromagnetism (ddw)
• Mineev & Zhitomirsky, PRB ’05
- SDW (with tiny moment, moment cancellation)
• Varma & Zhu, PRL’06
- Helical Order, Pomeranchuk instability of the Fermi surface time reversal
breaking)
• Elgazaar, & Oppeneer, Nature Materials’08
- DFT: antiferromagnetic order parameter, fluctuations.
• Santini and Amoretti PRL 04
-Quadrupolar ordering.
• Fazekas and Kiss PRB 07
-Octupolar ordering………………………………………………..
Haule and Kotliar : hexadecapolar order.
11
Dynamical Mean Field Picture
A. Georges and G. Kotliar PRB 45, 6479 (
1992).
G latt ( i w n , k ) [ D ] =
1
[ i w n + m + t ( k ) - S im p ( i w n ) [ D ] ]
DMFT picture. Atom in a medium obeying a self consisten
cy condition, Impurity Model.
Simplified reference frame for describing correlated solids
New concepts, more precise language to quantify the degree
of
itineracy.
Generalizations to cluster and to realistic modelling of materi
als
Many technical advances over the past decade.
12
Main DMFT Concepts in electronic structure.
Local Self Energies and Correlated Bands
G ( k , i )
Orbitally Resolved Spectral Functions
Transfer of spectral weight.

Weiss Weiss field, collective
ab
hybridization function, quantifi D ( w ) =
es the degree of localization
Valence Histograms. Describes the
Probability of finding the correlated
site in the solid in a given atomic state
J. H. Shim, K. Haule, and G. Kotliar, Nature London 446, 513 (2007).
1
i  H k   ( i  )
å
a
V
a
*
a
Va
b
w - ea
Functionals of density and
spectra, total energies: spectral
density functional.
Review: Realistic DMFT. Rev. Mod. Phys. G. Kotliar, S. Y. Savrasov, K. Haule,
V. S. Oudovenko, O. Parcollet, and C. A. Marianetti Rev. Mod. Phys. 78,865 (20
06).
13
Tunnelling: Orbitally resolved DOS
High temperature. Fano-shapes
first observed by S. Davis group
spd DOS small changes
only f DOS is gapped [no Kondo peak!!]
Kondo effect arrested by the splitting of th
e
two singlets (which is the consequence of
the bare small crystal field and the hexadec
apolar
order
).
Notice
BCS-like
coherence peaks in f
DOS when hidden order gap forms.
Single particle gap~7 mev
Just like T0, it should decrease with increasi
ng magnetic field. [ prediction]
K. Haule and G. Kotliar Nat Phys 5:637‐641(2009)
URu2Si2: DMFT allows two broken
translational symmetry states at low T
Density matrix for U 5f state
the J=5/2 subspace
J=5/2
Large moment phase:
J=5/2
Moment free phase:
tetragonal symmetry broken->
these terms nonzero
URu2Si2 Valence histogram
. fields two low
f2, “Kondo “ limit, Hunds. S=1, L=5, J=4. Crystal
lying singlets
J=4
Therefore there are two singlets relevant at low energies but the
y are not non Kramer doublets. Conspiracy between cubic cryst
al field splittings and tetragonal splittings bring these two states
close. This is why only URu2Si2 is different from thousands o
f U based heavy fermions.
Does not arise in one particle crystal field scheme. It is not forc
ed by symmetry.
.
•Under reflections x  -x or y  -y (x+iy)4  (x-iy)4
•[0>  - [0> (odd ) and [1> [1> (even)
DMFT order parameter.
Approximate X-Y symmetry
X01 =[0><
1]
Order parameter:
Different orientation gives different phases: “adiabatic continuity” explained!
Does not break the time reversal, nor C4 symmetry. It breaks inversion symmetry.
In the atomic limit:
Moment only in z-direction!
The two broken symmetry states
A toy model
Hexadecapole:
x-direction
Magnetic moment:
y-direction
crystal field: z direction
XY-Ising
18
HO & AFM in magnetic field
Notice that T0
decreases with
Increasing magnetic
field but mangetic fie
ld stabilizes hidden o
rder.
Mean field
Exp. by E. Hassinger et.al. PRL 77, 115117 (20
08)
Only four fitting parameters: Jeff1 , Jeff2
determined by exp. transition temperature
,
and pressure dependence .
19
Key experiment: Neutron scattering
The low energy resonance
A.Villaume, F. Bourdarot, E. Hassinger, S. Raymond, V. Taufour, D. Aoki, and J. Flouquet,
PRB 78, 012504 (2008)
Interpretation of Neutron
scattering experiments
Goldstone mode
AFM
moment
K. Haule and G
. Kotliar EPL 8
9 57006(2010)
“Pseudo Goldstone”
mode
AFM
moment
hexadecapole
Symmetry is approximate
“Pseudo-Goldstone” mode
Fluctuation of m - finite mass
The exchange constants J
21
are slightly different in the two phases (~6%)
Contrast this with the tunnelling gap, or the optical gap or the g
ap in the neutron scattering at (1.4,0,0) which decreases with in
cresing
magnetic field.
22
Fermi surface nesting,
Reconstruction below Tc
T<T0
T>T0
Nesting 0.6a* and 1.4a*
2 incommensurate peaks
(0.6,0,0), (1.4,0,0)
Fermi surface
reconstruction
Wiebe et.al. 2008
23
Visualizing the Formation of the Kondo Lattice and the Hidden Order in
URu2Si2 Pegor Aynajian, Eduardo H. da Silva Neto, Colin V. Parker, Yingkai Huang, A
bhay Pasupathy, John Mydosh, Ali Yazdani
arXiv:1003.5259 [pdf]
URu2Si2 Stress in ab plane
Large moment when stress in ab plane
No moment when stress in c plane
M Yokoyama, JPSJ 71, Supl 264 (2002).
Further Japanese work showed that NMR in unstrained samples did not broad
en
HO & AFM under stress
s sensitive to compression (strain), modeled by:
Very different effect of
in plane stress
and uniaxial stress
In plane stress favors AFM state
c-axis stress favors HO
M Yokoyama, JPSJ 71, Supl 264 (2002).
27
Lattice response
DMFT A(k,) vs ARPES
Off resonance
Very good agreement,
except at X point
Surface origin of pocket at X point
LDA+DMFT - Si-terminated surface slab
LDA+DMFT - bulk
Surface Slab Calculation
Z

X

• No hole-pocket at the X-point.
30
Z

X

• Hole pocket surface state appears at X-point!
Layer resolved
spectra
A very old puzzle, U diluted in ThRu2S
i2 is NOT a fermi liquid impurity!
Can we also explain the old dilution experiments of U on
ThRu2Si2 ? Reduce crystal field splitting.
Couple sigma_x and sigma_y to a bath of conduction electrons.
Earlier proposals (Dan Cox) for the two low lying singlets which were
degenerate due to symmetry, had difficulties due to the absence of Sh
otky peak in magnetic field.
Coupling of conduction electrons to two level system smells like and flows towar
ds the two channel Kondo form. [ A. Toth and G. Kotliar]. Logarithimic behavior
of
magnetic and hexadecapolar susceptibilities.
Conclusions: URu2Si2
•DMFT tools can be used to understand (and in some cases it has already
predicted) some properties of correlated materials
•Kondo effect in URu2Si2 is partially arrested bellow crystal field splitting energ
y.
Gives room to ordered states, either AFM state or orbital order.
•AFM state and hidden order can be unified by a complex
order parameter: “adiabatic continuity”
•Hidden order has hexadecapolar character
(does not break time reversal symmetry, nor rotation by
pi/4 symmetry)
•In the hidden order, fluctuations of the magnetic moment
as
a pseudo-Goldstone mode
•In AFM state there is a pseudo-Goldstone mode of hexa
decapolar symmetry
34
Conclusions: Somewhat Broader View
URu2Si2 has many things in common with many other strongly
correlated electron systems.
Hidden order
Pseudogap
Fermi Surface reconstruction
Non Fermi liquid behavior
Coherence Incoherence crossover
Unconventional Superconductivity
Multiple (pseudo) gaps
Itineracy and localization.
Good illustration of general concepts in the theory of strongly
correlated electron systems.
Requires care in interpretation in a material specific context.
Pushing the quantitative aspects of theory to its current limits.
On URu2Si2 the jury is out……
Protracted screening and multi
ple
hybridization
Gaps in Ce115’s.
J.H.Shim,
KHaule, G.Kotliar,Science
318, 1615 (2007)
Strong Correlations without high en
ergy satellites in Ba Fe2As2
A. Kutepov K. Haule S. Savrasov and
G. Kotliar to be submitted to PRL
Origin of the particle-hole assymet
ry between LaSrCuO4 and NdCuO4
K. Burch et.al.
Quasiparticle multiplets in Plutoniu
m
J.H.Shim, KHaule,
G.Kotliar,
Nature 446, 513 (2007).
and its
Compounds.
C. Weber K Haule and G. Kotliar
submitted to Nature Physics
Hidden Order in URu2Si2, Kondo effe
ct
and hexadecapole
KHaule ,andG. Kotliar,
Nature Physics 5, order.
796 - 799 (2009).