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Hidden Order and Kondo Effect in URu2Si2

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.

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Hidden Order and Kondo Effect in URu2Si2

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  1. 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  EPL89 57006(2010) K. Haule and G. Kotliar Nat Phys 5:637‐641(2009) 1

  2. 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

  3. U Ru Si Hidden Order The CMT dark matter problem. Entropy Loss at the transition: 1/5 Log[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

  4. 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

  5. “Adiabatic continuity” between HO & AFM phase • Similar T0 and TN • Almost identical thermodynamic • quantities ( e.g. jump in Cv) and similar • oscillation frequencies. “Adiabatic “is a misnomer. Need a better term. E. Hassinger et.al. PRL 77, 115117 (2008) 5

  6. 12 10 8 6 4 2 0 0 100 200 300 400 Magnetic susceptibility Extreme Anisotropy. Kondo? URu2Si2 mzeff ~ 2.2 mB c (10 -3 emu / mol) H // c To H // a T (K) 6

  7. Pseudo-gap opens at Tc. URu2Si2 measured through optical conductivity, D. A. Bonn et al. PRL (1988). 7.5 mev 7

  8. 500 400 300 200 100 0 1 10 100 1000 Resistivity keeps decreasing with decreasing T I // a r (mWcm ) Tc ~ 1.2 K I // c T (K) To ~ 17.5 K T.T.M. Palstra et al.(1985) W. Schlabitz et al.(1986) M.B. Maple et al.(1986) Heavy fermion at high T,low T HO + SC 8

  9. Inelastic Neutron Scattering 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

  10. 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 liquid. 10

  11. 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

  12. Dynamical Mean Field Picture A. Georges and G. Kotliar PRB 45, 6479 (1992). DMFT picture. Atom in a medium obeying a self consistency 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 materials Many technical advances over the past decade. 12

  13. Main DMFT Concepts in electronic structure. Local Self Energies and Correlated Bands Orbitally Resolved Spectral Functions Transfer of spectral weight. Weiss Weiss field, collective hybridization function, quantifies 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). 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 (2006). 13

  14. 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 the two singlets (which is the consequence of the bare small crystal field and the hexadecapolar order ). Single particle gap~7 mev Just like T0, it should decrease with increasing magnetic field. [ prediction] Notice BCS-like coherence peaks in f DOS when hidden order gap forms. K. Haule and G. Kotliar Nat Phys 5:637‐641(2009) 14

  15. 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 15

  16. URu2Si2 Valence histogram. f2, “Kondo “ limit, Hunds. S=1, L=5, J=4. Crystal fields two low lying singlets Therefore there are two singlets relevant at low energies but they are not non Kramer doublets. Conspiracy between cubic crystal field splittings and tetragonal splittings bring these two states close. This is why only URu2Si2 is different from thousands of U based heavy fermions. Does not arise in one particle crystal field scheme. It is not forced by symmetry. . J=4 • Under reflections x  -x or y  -y (x+iy)4  (x-iy)4 • [0>  - [0> (odd ) and [1> [1> (even) 16

  17. 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! 17

  18. The two broken symmetry states A toy model Hexadecapole: x-direction Magnetic moment: y-direction crystal field: z direction XY-Ising 18

  19. HO & AFM in magnetic field Notice that T0 decreases with Increasing magnetic field but mangetic field stabilizes hidden order. Exp. by E. Hassinger et.al. PRL 77, 115117 (2008) Mean field Only four fitting parameters: Jeff1 , Jeff2 determined by exp. transition temperature, and pressure dependence . 19

  20. 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

  21. Interpretation of Neutron scattering experiments K. Haule and G. Kotliar  EPL89 57006(2010) “Pseudo Goldstone” mode Goldstone mode AFM moment AFM moment Symmetry is approximate “Pseudo-Goldstone” mode Fluctuation of m - finite mass hexadecapole The exchange constants J are slightly different in the two phases (~6%) 21

  22. Contrast this with the tunnelling gap, or the optical gap or the gap in the neutron scattering at (1.4,0,0) which decreases with incresing magnetic field. 22

  23. 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

  24. 24

  25. 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, Abhay Pasupathy, John Mydosh, Ali Yazdani arXiv:1003.5259 [pdf] 25

  26. 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 broaden below T0 26

  27. HO & AFM under stress 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 27 M Yokoyama, JPSJ 71, Supl 264 (2002).

  28. Lattice response 28

  29. DMFT A(k,w) vs ARPES Off resonance Very good agreement, except at X point 29

  30. Surface origin of pocket at X point LDA+DMFT - Si-terminated surface slab LDA+DMFT - bulk Surface Slab Calculation Z  X  Z  X  • No hole-pocket at the X-point. • Hole pocket surface state appears at X-point! 30

  31. Layer resolved spectra 31

  32. A very old puzzle, U diluted in ThRu2Si2 is NOT a fermi liquid impurity! 32

  33. 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 Shotky peak in magnetic field. Coupling of conduction electrons to two level system smells like and flows towards the two channel Kondo form. [ A. Toth and G. Kotliar]. Logarithimic behavior of magnetic and hexadecapolar susceptibilities. 33

  34. 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 energy. • 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 hexadecapolar symmetry 34

  35. 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…… 35

  36. Protracted screening and multiple hybridization Gaps in Ce115’s. Strong Correlations without high energy satellites in Ba Fe2As2 J.H.Shim, KHaule, G.Kotliar,Science 318, 1615 (2007)‏ A. Kutepov K. Haule S. Savrasov and G. Kotliar to be submitted to PRL K. Burch et.al. Quasiparticle multiplets in Plutonium and its Compounds. Origin of the particle-hole assymetry between LaSrCuO4 and NdCuO4 J.H.Shim, KHaule, G.Kotliar, Nature 446, 513 (2007). C. Weber K Haule and G. Kotliar submitted to Nature Physics Hidden Order in URu2Si2, Kondo effect and hexadecapole order. KHaule ,andG. Kotliar, Nature Physics 5, 796 - 799 (2009). 36

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