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Insight into Hidden Order in Correlated Electron Systems: Experimental Phenomena and Spectroscopy Studies

Explore fundamental experimental phenomena and advanced spectroscopy studies related to hidden order in correlated electron systems, focusing on URu2Si2. Delve into unsolved questions, excitation spectrum, pressure-temperature phase diagram, and optical conductivity findings.

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Insight into Hidden Order in Correlated Electron Systems: Experimental Phenomena and Spectroscopy Studies

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  1. Lecture schedule October 3 – 7, 2011 • #1 Kondo effect • #2 Spin glasses • #3 Giant magnetoresistance • #4 Magnetoelectrics and multiferroics • #5 High temperature superconductivity • #6 Applications of superconductivity • #7 Heavy fermions • #8 Hidden order in URu2Si2 • #9 Modern experimental methods in correlated electron systems • #10 Quantum phase transitions Present basic experimental phenomena of the above topics

  2. Some Spectroscopy Studies of the HO State of URu2Si2 Introduction Inelastic neutron scattering (spin) Optical conductivity (charge) Ultrasonic velocity (thermo.) [and attenuation (transp.)] ARPES (charge) STM/STS (charge and spin) [But not PCS,  & QO] J. A. Mydosh Kamerlingh Onnes Laboratory, Leiden University, The Netherlands

  3. What is “Hidden Order” (HO)? [See, e.g. N. Shah, P. Chandra, P. Coleman and JAM, PRB 6I, 564(2000).] Now quite common usage of HO. Or as some theorists call it “Dark Quantum Matter” or as others call it “Novel Forms of Order” and “Novel Phases” {Reserve for high-field phases} or ‘‘Dark Order’’. A clear, from bulk thermodynamic and transport measurements, phase transition at T0 where the order parameter (OP) and elementary excitations (EE) are unknown, i.e., cannot be determined from microscopic experiments. Ψ is primary, unknown OP; m is antiferromagnetic, secondary OP

  4. Key Unsolved Problems/Questions of HO in URu2Si2 • Local, dual or itinerant? • OP’s primary / secondary? • Mediator of phase transition? • INS resonance mode causing HO: Q0 or Q1 ? • How to probe OP experimental? • Relation of HO to LMAF (Adiabatic Continuity)? • Symmetry breaking in HO vs. LMAF? • Spin – charge duality? • HF Liq.(hybridization) or Kondo Liq. at coherence T*? • Kondo effect in (Th1-xUx)Ru2Si2? • Generic  HO in other materials? Or is URu2Si2 unique? • Missing link experiments?(Hall effect under pressure, etc.) • Many theories/models -- which one is solution to HO?

  5. Spin:Inelastic neutron scattering - “resonances” at Qo=(1,0,0) and Q1=(1.4,0,0) • Broholm et al. PRL & PRB(1987 – 1991) • Wiebe et al. NP(2007) • Bourdarot et al. JPSJ(2010) ?(2011)? • Niklowitz et al. to be published(2011)

  6. Excitation spectrum of URu2Si2 at 1.5K along (H,0,0) gapping Cones of excitations persist to higher T>To and E~10meV. Well-correlated itinerant-like spin excitations at Q1(incomm). Strongly coupled spin and charge degrees of freedom.

  7. Resonance at E0 for magnetic response at Qo Longitudinal mode at 1.5K with continuum of Q-E scattering persisting to higher energies.

  8. Resonance at E1 for magnetic response at Q1 Longitudinal mode at 1.5K with continuum of Q-E scattering persisting to higher energies.

  9. T-dependence of Qo resonance Growth of intensity below To = 17.8K with Q-E continuum

  10. T-dependence of resonance gap E0 at Qo E0 represents a long lifetime (small decreasing half-width) collective mode rapidly reaching its final value 1.7 meV.

  11. Integrated intensity of dynamical spin susceptibilityWhat about at Q1 incommensurate resonance? Red line is a BCS-type gap fit giving T-dependence of HO-OP. No divergence of static spin susceptibility, i.e, HO non-magnetic.

  12. Low energy excitations scanned through HO transition Niklowitz et al.(unpublished,2011) Note peak at To for commensurate mode and step for incommen. mode

  13. Pressure – temperature phase diagram KL Collection of results by Niklowitz et al. PRL(2010).

  14. Pressure dependences of E0, E1 and bulk gap vaules HO LMAF Bragg peaks E0 disappears in LMAF phase, others persist. Note similar energy scales comparable to theoretical models.

  15. Charge: Optical Conductivity • Bonn et al. PRL(1988) • van der Marel et al. unpublished(2010 - 2011) • Lobo et al. unpublished(2010) • Timusk et al. cond-mat.(2011)

  16. HO-gap in URu2Si2 measured through optical conductivity, D. A. Bonn et al. PRL (1988). Preliminary data in a – a plane, gapping(~45cm-1) into HO phase. Strong phonons. Missing Drude peak and correlation gap

  17. Van der Marel et al., private communication, 2011

  18. Reflectivity to optical conductivity along a and c Clear but slow crossover (opening) of hybridization gap at 44K, persisting into HO gapping regime (not seen here).

  19. Extracting of scattering rate -1 as function of T & ωvia extended Drude model Note decrease of -1 into hyb. gap

  20. Optical conductivity along a and c-axes Opening of correlation gap ~15meV(125cm-1), clearer along a. Note low energy Drude peak and phonon modes.

  21. Optical conductivity 20 – 70K in hybridization gap region extrapolated to ω 0 via Drude peak analysis W(ω) is loss of spectra weight accumulation Note opening of hydridization gap below 50K

  22. Relaxation rate governing the frequency dependent scattering in hybribization gap region As T increases scattering becomes incoherent

  23. Lower frequency (E) optical conductivity above To Labo et al., private communication, 2010. Clear onset of hybridization gapping(~15 meV) below 50K. Drude peak forming at 2 meV(15 cm-1). Note phonons.

  24. Low T, low E optical conductivity probing HO HO gapping ~5meV with transfer of spectral wt. to just above gap and shifting of Drude peak to smaller E. Need lower E & T!

  25. Some conclusions • Drude peak narrows below coherent T*(≈ 70K) crossover into hybridization gapping (≈ 15meV) • Reflection peak (HO – gap) observed at lowest frequencies, (ω < 30cm-1 ). Need conversion into optical conductivity. New low ω technique/apparatus is necessary. • Gap (5meV) in the charge channel develops at the HO transition • Difference between a & c axes – gap anisotropy • Missing low frequency spectral suggests that a very narrow Drude peak exists • 47 meV phonon coupled to carriers plays (role in the scattering of the incoherent phase?)

  26. T – E dependences of optical conductivity Note lack of intensity(conductivity) above To – correlation gap. No clear sign of HO gap. Need lower T and E.

  27. Low E, high T

  28. Low E, low T

  29. Thermodynamics: Ultrasonics velocity (attenuation as transport prop.) Determination of elastic constants, cij • Lüthi et al. JLTP (1994) • Kuwahara et al. JPSJ (1997)

  30. Elastic constants (c = ρv2 ): c11, c33, c44; c66 Note c11 only longitudinal mode showing softening for T < 80K, min. 30K and HO shoulder.

  31. Analysis of elastic constant cij behavior of URu2Si2 Need new interpretation here: softening due to slow opening of hybridization gap. No CDW?

  32. Charge: ARPES • J. Denlinger et al. JES&RP(2001) • A. Santander-Syro et al. NP(2009) • R. Yoshida et al. PRB(2010) • Kawasaki et al. PRB(2011) • G. Dakovski et al. PRB(to be published, 2011) • XXX et al. ??? (2012)

  33. Among the many difficulties of ARPES: URu2Si2 is 3D thus depending upon the energy tuning one scans an arc through the BZ (or changing detector angle). Note in bct the high symmetry directions Γ, Z; X

  34. Denlinger et al.(2001) – pioneering work • Synchrotron scans  14 - 230 eV with ΔE > 50 meV at T > 20K. • Good resolution and DFT comparisons of 4d (Ru); 5d (U) lower bands. Poor agreement with “old” LDA bands near EF. • But Fermi surface mapping. • Insufficient resolution for near FS and qp studies. • Surface states/bands difficulties! • X hole pocket observed in FS, not confirmed!!! • Local 5f2 model! • Awaiting new results at SCES-2011.

  35. Comparisons ARPES vs (old) LDA Fermi energy intensity maps off(85ev) / on(112eV)-resonance, 5f enhancement X-point descrepancy: distinct hole pocket; LDA : small elec. pocket, also  pts. vs large contours DFT-LDA calculations bold=hole; fine=electron

  36. Santander Syro et al. (2009) – T dependences • Temperature scan into HO state • He lamp low energy (21 eV), high resolution ARPES • Surface states, poor vacuum • Two k space directions: [100] and [110] • Band of heavy quasi-particles drops below EFupon entering the HO state • Large restructuring of FS in HO • Many difficulties with data and analyses • Reproducible?

  37. Integrated photoemission spectra along <110>Note quasiparticle peak that moves below To: Dispersing band of heavy QP, new electron pocket in HO state Surface state Surface state

  38. Heavy qp band hybridized with light hole conduction band along <110> at 13 K ARPES intensity EDC Averging of 2nd derivatives along E and k MDC

  39. Heavy qp band hybridized with light hole conduction band along <100> at 15 K ARPES intensity EDC

  40. Yoshida et al.(2010) – Laser Arpes • Low energy (7 eV) Laser ARPES, high resolution (2 meV), good vacuum technique • Narrow, dispersive band in HO only, few meV from FS • Yet non-FS crossing • Destroyed with Rh doping on Ru sites • Another hole-like dispersive crossing band and surface states at ~35 meV • “Periodicity modification“: HO doubling of unit-cell, band backfolding, predicted by Oppeneer et al. • Low energy ARPES is only sensitive to d-bands, cannot detect 5f-U bands. Seeing broad (partially hybridized) 4d-Ru bands which appear in HO state

  41. Laser ARPES intensity at 7K for [110] and [100] Hole-like dispersion Surface state

  42. Temperature evolution of ARPES intensity integrated over different k cuts

  43. Kawasaki et al.(2011) Soft X-ray ARPES • Energy 760 eV with resolution 140 meV • Vary energy or detector angle to scan BZ • Spanning vast k-space, all of high symmetry BZ • Bands below 0.6 eV are Ru-4d states, agreeing with previous ARPES • Band above 0.6 eV to EF disagree with previous ARPES, e.g.,surface band at  not observed here. No hole band at X. • All U-based 5f bands are itinerant!!! • Quasiparticle bands clearly observed at Z(large hole FS and at (large electron FS) with some nesting • APRES bands consistent with LDA of Oppeneer et al.

  44. BZ with orange and blue scanning planes. Spectral image comparison with LDA band structure Measured spectral weight along hi-sym. Bands 4, 5; 6 cross EF Calculated BS Agreement with LDA of Oppeneer

  45. Photoemission intensity with FS crossings and LDA comparison Intensity around EF Indicated band crossings Calculated band crossings: 6, 5; 4 with C, B; A, and 4; 5 with D; E

  46. Fermi surface images compared with LDA Estimated Fermi surfaces with nesting vectors Integrated intensity Band structure FS’’s

  47. Dakovski et al.(2011) Time Resolved ARPES • Pump (1.55 eV)– Probe (29.5 eV) method. First for SCES • Tune ARPES on URu2Si2 to focus on “hot spots” (maximium gap) in k-space, i.e., below Z in <110> plane as determined from band structure • Excite quasiparticles via pump, probe their fs decay • Measurements above To rapid fs decay within hybridization gap • Measurements below To qp excited above HO gap have longer fs decay times • Momentum (k) dependent interactions at hot spots causing HO gapping • Energy resolution: tr-ARPES ≈100meV; ARPES ≈10meV

  48. Femto second spectroscopy at hot spot in HO(12 K)

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