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Strongly Correlated Electron Systems: Hidden Order and Novel Phases

Strongly Correlated Electron Systems: Hidden Order and Novel Phases. J. A. Mydosh Institute of Physics II, University of Cologne Max Planck Institute for Chemical Physics of Solids, Dresden Kamerlingh Onnes Laboratory, Leiden University. Main Collaborators.

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Strongly Correlated Electron Systems: Hidden Order and Novel Phases

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  1. Strongly Correlated Electron Systems: Hidden Order and Novel Phases J. A. Mydosh Institute of Physics II, University of Cologne Max Planck Institute for Chemical Physics of Solids, Dresden Kamerlingh Onnes Laboratory, Leiden University

  2. Main Collaborators N. Harrison & M. Jaime NHMFL-LANL K. H. Kim Seoul National Univ. H. Amitsuka Hokkaido Univ. S. Süllow TU Braunschwieg C. Pfleiderer TU Munich Haung Ying Kai Amsterdam/Leiden

  3. Outline • What are SCES: Mott Insulators & Heavy Fermi Liq. • Theoretical Proposal: Novel Phases & QCP • Recent Phenomena & Elements of SCES • Introduction to URu2Si2 and Hidden Order (HO) • Pressure Tuning : Neutron Diffraction, NMR & Mag. • Theories, Models and Conjectures over HO • Destruction of HO with Field & Rh-Doping • Phase Diagram – Hall Effect • Nexus between Quantum Criticality and Novel Phase Formation • Summary & Speculations

  4. New / Recent Phenomena with SCES • • Unconventional or d – CDW / SDW • • (F)QHE (in 2DEG) • Polymeric and nanotube conduction • Superfluidity in supersolids 3He / 4He or H • S and M in organic conductors • Spin fluctuations in itinerant ferromagnets • Mott and charge transfer insulators (doped) • HTS (oxides) • CMR (spin, charge, orbital; structural orderings) • HF Liquids, NFL; QCP • Hidden Order & Dark Quantum Cond. Matter • Quantum Magnets / Quantum Spin Glasses • Bose Einstein condensation, Bose Glass

  5. Introduction 500 U 400 Ru 300 Si 200 100 0 1 10 100 1000 ThCr2Si2 bct - type ( I4/mmm ) URu2Si2 a = 4.127 (Å) c = 9.570 (Å) Coexistence of HO with SC T.T.M. Palstra et al.(1985) W. Schlabitz et al.(1986) M.B. Maple et al.(1986) I // a To ~ 17.5 K r (mWcm ) I // c Tc ~ 1.2 K T (K)

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

  7. 500 400 300 200 100 1 0 0 5 10 15 20 25 Q = (1,0,0) Intensity (arb.unit) Mason Fåk Honma T (K) Specific heat vs. magnetic Bragg-peak intensity URu2Si2 Smag ~ 0.2 R ln 2 C5f / T (mJ/K2mol) Tc To mord ~ 0.01 - 0.04 mB 0 xc ~ 100 Å xa ~ 300 Å Type-I AF

  8. Pseudo-gap in URu2Si2 measured through optical conductivity, D. A. Bonn et al. PRL (1988)

  9. Zone-center gap in URu2Si2 measured through neutron scattering, C. Broholm et al. PRL (1987) & PRB (1991) Similarity between optics and neutrons suggests magnetic excitations are strongly coupled to charge excitations

  10. Magnetization as function of temperature, C. Pfleiderer, JAM & M. Vojta, PRB Oct.(2006). ab-plane c-axis c-axis

  11. Neutron scattering under hydrostatic pressure H. Amitsuka, M. Sato, N. Metoki, M. Yokoyama, K. Kuwahara, T. Sakakibara, H. Morimoto, S. Kawarazaki, Y. Miyako, and JAM PRL 83 (1999) 5114

  12. 0.5 0.4 0.3 0.2 0.1 0 25 20 15 1 0.999 0.998 0.997 0.996 0.995 0 1 2 3 Neutron scattering under hydrostatic pressure Pc (a) URu Si 2 2 T = 1.4 K / U) B m ( 0 m this work Louis McElfresh Ido Schmidt Oomi Fisher (b) (K) r o , T + m T (c) C + T = 1.4 K T = 35 K a / a(P=0) Da/a ~ 0.2 % P (GPa)

  13. 0 1 2 3 104 resolution limit ~ 103 x(A) 102 P (GPa) Neutron scattering under hydrostatic pressure

  14. 1 0.8 0.6 0.4 0.2 0 1 0.8 1.5 2.3 0.6 2.7 2.8 0.4 0.2 0 0 0.5 1 1.5 Normalized Bragg-peak intensity URu2Si2 Q = (1,0,0) P ( GPa ) 0 0.26 0.61 1.0 1.3 I / IT=1.4K P < Pc MF Ising P ( GPa ) I / IT=1.4K 3D Ising MF Ising P > Pc T / Tm

  15. 0.3 < P (GPa) < 0.83 ; T < To Bint910 G evidence of a static AF order New resonance lines the AF order occurs partly in crystal ! Coexistence of previous line 29Si NMR under hydrostatic pressure K. Matsuda,Y. Kohori, T. Kohara, K. Kuwahara, H. Amitsuka PRL 87(2001)087203

  16. mord2 (0.02 mB)2 v   1 % mAF2 (0.25 mB)2 Magnetic properties of URu2Si2at ambient pressure IB = A mord2 = A v mAF2 Volume fraction of AF order: Hidden order : 99% NMR is consistent with µSR measurements under pressure. Axial strain: Distribution (c/a), variance > 10-3 then HO  (LM)AF. See, A.Yokoyama et al., PRB 72, 214419 (2005).

  17. Ambient pressure 15.9 kbars C. Pfleiderer, JAM and M. Vojta, PRB Oct.(2006)

  18. Dipolar order with small g values crystal fields Niewenhuys ’86 quant. spin fluctuation Sikkema et al. ’96 duality: loc./itin. Okuno, Miyake ’98 spin-orbital cancellation Yamagami ’99 fragile AF order Bernhoeft et al. ’02 S m=gmBS Non-dipolar order quadrupole Miyako et al. ’91 triple spin Barzykin, Gor’kov ’93 quadrupole (G4) Santini, Amoretti ’94 quadrupole (G5) H. A., Sakakibara ’94 structural distortion Barzykin, Gor’kov ’95 U dimer Kasuya ’97 d-wave SDW Ikeda, Ohhashi ’98 quadrupole (G5) Shimizu, Ohkawa ’99 bond order - OAF Chandra et al. ’01 unconventional SDW Virosztek, Maki, Dóra ’02 ? Hidden Order Unique Enough to Stimulate New Ideas:

  19. Very recent proposals Landau-Pomeranchuk Varma ’05 Valency transition Gor’kov ’04 Octupolar Kiss & Fazekas ’05 SDW Mineev & Zhitomir. ’05 Falicov-Kimble Zlatic ’05 Itinerant quadrupole Harrison et al. ’05 Itinerancy & HO Tripathi & (PC)2 ’05 Hexadeacpole Kuramoto et al. ’06 Hidden Order Unique Enough to Stimulate New Ideas:

  20. Destruction of HO with field: A specific heat study M. Jaime, K.H. Kim, S. McCall, G. Jorge, and JAM. PRL 89,287201(2002)

  21. Magnetocaloric Effect

  22. and Novel Phases

  23. c exhibits divergence for T > 6 K as for CeRu2Si2, Sr3Ru2O7 and UPt3 THEN SUDDENLY crossover splits for T < 6 K (T-stability crucial for discovery) H decreasing Transitions consistent with specific heat measurements [Jaime et al. PRL89, 287201(2002)] What happens as T is lowered? CAN FIELD-INDUCED QCP INSTIGATE NEW PHASES?

  24. Phase transitions observed as extremities in dr/dB and dr/dT confirmed in M, C and sound velocity vs Multiple phases nearby a QCP: H decreasing

  25. Metamagnetic transition Multiple new phases result from (1) multiple competing interactions and/or (2) close proximity of BM to Hidden Order phase Multiple phases nearby a QCP: H decreasing

  26. r=r0+ATn ~0.6KT 3 K Summary of Transport Results for URu2Si2 All the ”smoking guns” indicate Metamagnetic transition HQCP~37 T !! URu2Si2 : Another example of order created at quantum critical point ?? K.H.Kim, N.Harrison, M.Jaime, G.S.Boebinger and JAM. PRL91, ‘03

  27. Nexus between quantum critical point, phase II and BM observed as a function of Rh, indicating causality link Effects of Rh-doping in URu2Si2 K.H.Kim, N.Harrison, H.Amitsuka, G.A.Jorge, M.Jaime and JAM, PRL 93(2004) Phase diagram simplified on doping with Rh, yielding single field-induced phase (II) [without phase I (Hidden Order)] and clearer evidence for quantum critical point Quantum criticality occurs in absence of hidden order: so hidden order not responsible for quantum criticality (magnetization in pulsed fields and transport in dc fields)

  28. Evidence for quantum criticality occurs at at low and high magnetic fields, pointing to single quantum critical point concealed inside phase II, with scaling: T*  A-1/2  F Fits of A to (B-BM) support divergence in m* at quantum critical point: formation of phase II leads to suppression of fluctuations Phase II likely holds key to understanding magnetism, because it has 1/3rd of full saturated moment (neutrons should be able to detect large moment that is absent in Hidden Order phase): Ising moments imply broken translational symmetry likely Quantum criticality and Phase II  ~ 1  ~ 0.7

  29. Previous study in U(Ru1-xRhx)2Si2 K. H. Kim et al., PRL 93, 206402 (2004) HFL PFL II K. H. Kim et al., PRL 91, 256401 (2003) III What happens in Fermi surface volumes across a putative quantum critical point ?

  30. Hall Effect Results for URu2Si2 in Pulsed Magnet rxx for URu2Si2 rxy for URu2Si2 Curvature change? FS change

  31. B-dependent Hall resistivities of URu2Si2 & U(Ru0.96Rh0.04)2Si2 U(Ru0.96Rh0.04)2Si2 In each state, the slope of Hall resistivity, RH☞≡ρ/B , is constant Each state has different Fermi surface. It indicates that the orbital contribution is predominant in the Hall effect at low temperature. URu2Si2

  32. Discontinuous change of Fermi surface volume ΔRH~2.7×10-9m3/C ΔRH~0.6×10-9m3/C Δn~1 ± 0.3el/U ? Δn~1 ± 0.3 n~0.15 n~0.05 Sudden Reconstruction of Fermi Surface

  33. Hidden Order and Novel Phases • HO is createdwith T through a symmetry breaking/FS transition. Proposal: Itinerant quadrupole that also breaks transitional symmetry. • HO is transformed with pressure through lattice (c/a) strain & distortion as a subtle crossover to LM-IAF. • HO is destroyed with field through a myriad of novel phase transitions (1st order) via dramatic FS reconstructions (pocket depopulations from dH/vA). • HO is destroyed with Rh-doping through FS detuning as a crossover.

  34. A.V.Silhanek, N.Harrison, C.D.Batista, M.Jaime, A.Lacerda, H.Amitsuka and JAM, PRL 95(2005)

  35. X = 0.04 C/T X T2(K2)

  36. Low T ~ 2 K High T ~ 6 K

  37. Specific Heat, intermediate fields The anomaly in the specific heat associated with To is absent at H = 36 T !

  38. Specific Heat, high fields Schottky fit H (T) 40 42 D (meV) 1.58 2.03 S = 0.3 R ~ ½ R ln2

  39. 0  B < BC =35.8T 35.8T Hidden Order A new ordered phase above 36 T !! SC What happens to Cmag at high fields ? M. Jaime, K. H. Kim et al., PRL 89,287201 (2002)

  40. New physics: the magnetic phase diagram of heavy fermions (phenomenologically) inequivalent control parameters pressure = J chem. pressure ≠ disorder = J substitution • disorder and NFL behavior? • substitutional disorder?

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