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ARPES for f-electrons Issues and Prospects

ARPES for f-electrons Issues and Prospects. J. W. Allen University of Michigan. International Seminar on Strong Correlations and Angle-Resolved Photoemission Spectroscopy Dresden May 2, 2007. Funding: U.S. NSF

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ARPES for f-electrons Issues and Prospects

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  1. ARPES for f-electronsIssues and Prospects J. W. Allen University of Michigan International Seminar on Strong Correlations and Angle-Resolved Photoemission SpectroscopyDresden May 2, 2007 Funding: U.S. NSF and Advanced Light Source Doctoral Fellowship Program

  2. Collaborators S.-K Mo and Feng Wang University of Michigan J.D. Denlinger and G.-H. Gweon Advanced Light Source, LBNL Kai Rossnagel University of Kiel S. Suga and A. Sekiyama Osaka University H.-D Kim, J.-H. Park Pohang University, Pohang Synchrotron H. Höchst Synchrotron Radiation Center, Univ. of Wisconsin M. B. Maple University of California, San Diego Z. Fisk University of California, Irvine J. Sarrao Los Alamos National Laboratory A. D. Huxley, J. Flouquet CEA - Grenoble P. Metcalf Purdue University J. Marcus and C. Schlenker LEPES, CNRS, Grenoble J. He, R. Jin, D. Mandrus2 Oak Ridge Nat’l Lab and 2University of Tennessee A. B. Shick ASCR – Prague H. Yamagami Kyoto-Sangyo University D. Vollhardt, G. Keller, V. Eyert University of Augsburg K. Held Max-Planck Institute, Stuttgart V. I Anisimov Institute of Metal Physics, Ekaterinburg J. V. Alvarez University of Michigan A. Lichtenstein University of Hamburg L. Pourovskii Ecole Polytechnique, Paris B. Delley Paul-Scherrer Institute R. Monnier ETH-Zurich

  3. ARPES data acquisitionfor three dimensional materials

  4. Fermi Surface Mapping of a 3D metal Cu (100) h=83 eV “k”-space (repeated zones) [001] [100] [110] Constant energy measurement surface • Plane wave final state • Surface refraction included (inner potential = 8.8 eV)

  5. Yb Bi Pt  = 8000 mJ/mol K2 YbBiPt • 8 maps span full FS along <111> oriented cleave surface probed; bulk very near Yb 3+ • 3-fold symmetry & kZ-stacking observed in Fermi surface • First ARPES Fermi surface map of any Yb-compound • Small photon spot essential to get this data heaviest Fermions  ~ 8000 mJ/mol-K w/ Z. Fisk (UC Irvine)

  6. Kondo resonance in angle integrated Ce 4f spectra:early experiment and theory Fig. from Allen et al Adv. in Physics 1985 Spectra from photoemission and x-ray inverse photoemission (Xerox PARC) samples: (Maple, UCSD) Allen et al PRB 1983 CeAl small EK Spectral theory: Gunnarsson & Schönhammer PRL 1983 CeNi2 large EK “Kondo Volume Collapse” Ce  phase EK large  phase EK small Allen & Martin PRL ’82 Allen & Liu PRB ‘92

  7. hopping t repulsion U Hubbard model for Mott transition And. Imp. Bath elec ~kTK f1 f1 f2 f0 quasi-particle peak growing in gap as U/t decreases (“bootstrap Kondo”) Kondo physics—moment loss & Suhl-Abrikosov/Kondo resonance Mott-Hubbard metal-insulator transitionnew view from Dynamic Mean Field Theory(Vollhardt, Metzner, Kotliar, Georges  1990) DMFT: lattice  a self-consistent Anderson impurity model (exact in  dimensions) U/t small U/t large EF

  8. Experiment: SPring-8 BL 25SU (S. Suga) • h = 500-700 eV total E 90 meV • Cleaved single crystals from P. Metcalf, Purdue Mo et al, PRL (2003) Vollhardt and Kotliar, Physics Today (2004) McWhan et al1969 “Kondo peak” theory and experiment in M phase Previous work, 30 yearsNO M phase peak I phase GAP Surface layer more correlated than bulk Angle integrated bulk sensitive spectra for Mott transition in (V1-xCrx)2O3 x T Pressure

  9. surface-layer thickness = – (1012) cleavage plane 2.44Å  c = 14.0 Å side view  a = 4.95 Å top view Crystal structure and surface layer Vanadium Oxygen

  10. = 100 μm spot size Small spot also essential for large EF peak ! Optical micrograph—J.D. Denlinger EF peak much reduced with larger spotDifference for 300 eV to 500 eV range even larger With small spot can select probing point to avoid steps, edges, strain as much as possible Steps, edges have even lower coordination than smooth surface

  11. • Covalent bonded B6 • Ionic bonding: Eu2+ & B6(2-) Eu 4f More surface surface effects: EuB6 time  Time-dependent size of X-point electron pocket Time-dependent surface-shifted Eu 4f state  Time dependent relaxation of a polar surface  Surface slab calculation: (1) surface state in bulk gap (2) surface-shifted Eu 4f (1) (2) Time-dependence Model  t = 0 (Cleave) Statistically 50% Eu-terminated t < t* Clustering of mobile surface Eu atoms t > t* Residual gasadsorption w/ Z. Fisk (UC Davis), B. Delley (Paul-Scherrer Institut), R. Monnier (ETH-Zurich)

  12. Surface Bulk EuB6 --kill surface effects to see bulk Kill surface with pburst 1x10-9 torr Separating surface & bulk electronic structure FM < 15K • Surface: electron-rich Eu-termination  X-point electron pockets + higher binding energy-shifted Eu 4f state • Bulk: hole-like pockets just touch EF (p-type)  observe exchange splitting for T<TC  bulk Ferromagnetism in EuB6 likely from superexchange (like EuO) w/ Z. Fisk (UC Davis), B. Delley (Paul-Scherrer Institut), R. Monnier (ETH-Zurich)

  13. EuB6 bulk valence band exchange splittingnow observable

  14. Theory issues for non-low D f and d electron materials needing detailed Fermi surface data Compare to DMFT + LDA for FS and spectral function "Dual nature" picture for actinide f-electrons, e.g: U 5f3 = 5f2 + 1 in FS volume; Pu 5f5 = 5f4 + 1 in FS volume Zwicknagl and Fulde (PRB '02 UPt3, UPd2Al2) Wills et al (J. Elec. Spectros. Rel. Phenom. 04) and Joyce et al (Physica B 05) for Pu materials Distribution of f-weight around Fermi surface in relation to high mass sheets-- above and below TK "Two fluid" phenomenology for heavy fermion metals (S. Nakatsuji, D. Pines and Z. Fisk, PRL, PRB 04) In transport and NMR, single ion Kondo part and coherent lattice part, all at low energy. "Cold spots on FS?"

  15. M CeMIn5 (M=Co) Interplay & coexistence of AFM & SC 15 maps from 90eV to 125eV Fujimori et al PRB 2003

  16. CeMIn5 (M=Co) Three maps (T= 26K) span full kz BZ Compare to 2 kz-plane M point quasi 2d sheets of LDA Fermi surface P. Oppeneer, from PRB 69, 3310 (2004)

  17. Ce115, Ce218 Ce2RhIn8 CeCoIn5 92 eV 112 eV Single vs Double Ce layer • Ce 218: has ~2X more FS contours than for Ce115 . w/ M. B. Maple (UC San Diego), P. Oppeneer (Uppsala, Sweden)

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  36. UGe2 FM + SC w/ P Compare ARPES FS and spectral function (T= 30K, 92 eV photons) to LDA+ DMFT Both agreement and disagreement at detailed level w/ A. Huxley, J. Flouquet (Grenoble), A. Shick (Prague), A. Lichenstein

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  46. band 4 Z- hole pocket LDA for LaRu2Si2 and CeRu2Si2 compared La Ce

  47. LaRu2Si2 3D Fermi surface mapping Normal emission photon-dependence FS slice shows effects of kZ-broadening on a 3D big pillow-shaped FS topology with fcc-stacking. Full 3D character of FS observed by fine-angle maps at fixed photon energies & by fine photon-energy-step kZ-dependent slice at fixed angle. w/ J.L. Sarrao (LANL

  48. paradigm (dHvA) (Tautz et al,1995)  large Z-point hole FS f0 LaRu2Si2 LDA “band 4” hole Fermi surface no f- electron  reduced "pillow" hole FS counts  ½ Ce f- electron in Kondo CeRu2Si2 --at temperature below TK ½ extra f-electron here ( ½ f-electron in other multiply-connected complex FS piece) Fermi volume change at Kondo temperature:the f-electron in CeRu2Si2 Luttinger counting theorem  f-electrons counted in Fermi volume IF magnetic moments quenched (as in Kondo effect) Conjecture (Fulde & Zwicknagl, 1988) f-electrons excluded from FS above Kondo temperature TK Difficult to test with low-T dHvA.

  49. Same large hole FS for LaRu2Si2 and CeRu2Si2 for T 120K > 6TK f-electrons excluded from FS! XRu2Si2 review: J. D. Denlinger et al, JESRP 117, 8 (2001) samples J. Sarrao LANL Same conclusion from 2d angular correlation of positron annihilation studies-- (Monge et al, PRB, 2002) but didn't actually measure the "pillow"

  50. Z  m/me = 120 dHvA: m/me = 4, 2.5, 1.6, m/me = 13,20 Hole sheets (center = Z) Electron sheets (center = G) hn = 91 eV hn = 122 eV Fermi surface at high T — 4f weight at low mass , Z points for CeRu2Si2 LDA

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