Transcript Hidden Order and Kondo Effect in URu2Si2
Hidden Order and Kondo Effect in URu2Si2
Nat Phys 5:637 ‐ 641 U Ru Si 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.
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Hidden Order The CMT dark matter problem.
U Ru Si Entropy Loss at th e transition: 1/5 L og[2] URu 2 Si 2 : 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.
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“Adiabatic continuity” between HO & AFM phase
• Similar T 0 and T N • 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 10 8 6 4 T o 2 0 0 100 URu 2 Si 2 m z eff ~ 2.2 m B H // c H // a 200 T (K) 300 400 6
Pseudo-gap opens at Tc. URu 2 Si 2 ivity, D. A. Bonn et al. PRL (1988). measured through optical conduct 7.5 mev 7
Resistivity
keeps decreasing with decreasing T 500 400 300 T o ~ 17.5 K 200 100 T c ~ 1.2 K I // a I // c T.T.M. Palstra et al.(1985) W. Schlabitz et al.(1986) M.B. Maple et al.(1986) 0 1 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. 10
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.
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Dynamical Mean Field Picture A. Georges and G. Kotliar PRB 45, 6479 ( 1992).
G latt (
i w n
,
k
) D = [
i w n
+
m
+
t
1 - S
imp
(
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 Orbitally Resolved Spectral Functions Transfer of spectral weight. )
i
H
k
1 (
i
) Weiss Weiss field, collective hybridization function, quantifi es the degree of localization D
ab
= е
a V a a
*
V a b w
-
e a
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) .
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 ).
DOS when hidden order gap forms. Single particle gap~7 mev Just like T 0 , it should decrease with increasi K. Haule and G. Kotliar Nat Phys 5:637 ‐ ng magnetic field. [ prediction] 14
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: Moment free phase: tetragonal symmetry broken-> these terms nonzero J=5/2 15
URu2Si2 Valence histogram
f 2
.
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 • [0> -x or y - [0> (odd ) and [1> -y (x+iy) 4 [1> (even) (x-iy) 4 16
DMFT order parameter. Approximate X-Y symmetry X
01
1] =[0><
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!
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The two broken symmetry states
A toy model XY-Ising Magnetic moment: y -direction crystal field: z direction Hexadecapole: x -direction 18
HO & AFM in magnetic field
Notice that T 0 decreases with Increasing magnetic field but mangetic fie ld stabilizes hidden o rder. Mean field Only four fitting parameters: J eff 1 Exp. by E. Hassinger et.al. PRL 77, 115117 (20 08) , J eff 2 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) 20
Interpretation of Neutron scattering experiments
Goldstone mode AFM moment “Pseudo Goldstone” mode AFM moment K. Haule and G . Kotliar EPL 8 9 57006(2010) 21 hexadecapole Symmetry is approximate “Pseudo-Goldstone” mode Fluctuation of m - finite mass The exchange constants
J
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 cresing magnetic field. decreases with in 22
T>T 0
Fermi surface nesting, Reconstruction below Tc
T 24 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 ] 25 2 2 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 below T0 26 J’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 28 Off resonance Very good agreement, except at X point 29 LDA+DMFT - Si-terminated surface slab LDA+DMFT - bulk 30 Z X • No hole-pocket at the X-point. Z X • Hole pocket surface state appears at X-point! 31 32 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. 33 • DMFT tools can be used to understand (and in some cases it has already predicted) some properties of correlated materials • Kondo effect in URu 2 Si 2 is partially arrested bellow crystal field splitting energ y. • 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 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…… 35 Strong Correlations without high en ergy satellites in Ba Fe2As2 A. Kutepov K. Haule S. Savrasov and G. Kotliar to be submitted to PRL Protracted screening and multi ple hybridization Gaps in Ce115’s. K. Burch et.al . Origin of the particle-hole assymet ry between LaSrCuO4 and NdCuO4 C. Weber K Haule and G. Kotliar submitted to Nature Physics Quasiparticle multiplets in Plutoniu m and its Compounds. Hidden Order in URu2Si2, Kondo effe ct and hexadecapole order. 36URu
Si
Stress in ab plane
HO & AFM under stress
Lattice response
DMFT A(k,
) vs ARPES
Surface origin of pocket at X point
Surface Slab Calculation
Layer resolved spectra
Conclusions: URu2Si2
Conclusions: Somewhat Broader View