Heavy Fermion systems

Transcription

1 Heavy Fermion systems Satellite structures in core-level and valence-band spectra Kondo peak Kondo insulator Band structure and Fermi surface d-electron heavy Fermion and Kondo insulators

2 Heavy Fermion systems Satellite structures in core-level and valence-band spectra

3 Double peak structure in photoemission spectra of Ce compounds with 4f4 1 configuration Ce intermetallics Ce monopnictides 4f 1 4f 0 Photoemission BIS on-resonance off-resonance 4f-derived emission 4d-4f resonant photoemission Intensity ratio f 1 f 2 f 1 f 0 µ J.W. Allen et al., PRB 83 A. Franciosi et al., PRB 81

4 Cluster-model analysis of Ce 4f-derived photoemission spectra from 4f4 1 ground state Ground state Final state Cluster model ~ 1 ev many-electron energy f 1 f 0 f 1 L photoemission N N-1 ~2V Binding energy µ A. Fujimori, PRB 83

5 Cluster-model analysis of Ce core-level photoemission spectra from 4f4 1 ground state Ground state Final state cf 1 cf 2 L Binding energy 3d 5/2 3d 7/2 many-electron energy photoemission f 1 J. C. Fuggle et al., PRB 83 A. Fujimori, PRB 83

6 Cluster-model analysis of Ce core-level photoemission spectra from hybridized state Ground state Ψ I = c I0 4f 0 > + c I1 4f 1 L> Final state Ψ F = c F0 c4f 0 > + c F1 c4f 1 L> + c F2 c4f 2 L 2 > many-electron energy cf 0 cf 1 L cf 2 L 2 photoemission Binding energy f 0 f 0 f 0 peak intensity ~ 1 - n f f 1 L A. Fujimori, PRB 83

7 Cluster-model analysis of Ce core-level photoemission spectra from hybridized state Ce 3d XPS of CeO 2 cf 0 f 0 many-electron energy cf 1 L cf 2 L 2 photoemission Binding energy f 0 f 1 L A. Fujimori, PRB 83

8 Cluster-model analysis of Ce core-level photoemission spectra from hybridized state cf 0 f 0 many-electron energy cf 1 L cf 2 L 2 photoemission Binding energy f 0 f 1 L J. C. Fuggle et al., PRB 83 A. Fujimori, PRB 83

9 Single-impurity Anderson model analysis of Ce 4f-derived photoemission spectra f 0 c-f hybridization f 1 L one-electron energy E = 0 ε f f-electron emission E = ε f - ε dominant in ground state E = - ε E = ε f - ε - ε Binding energy µ O. Gunnarsson and K. Schonhammer, PRB 83

10 Single-impurity Anderson model analysis of photoemission spectra Ce 3d XPS spectrum Ce 4f-derived spectrum O. Gunnarsson et al., PRB 83

11 Valence fluctuation/kondo effect one-electron energy f 0 c-f hybridization f 1 L ε f E = 0 E = ε f - ε many-electron energy f 0 f 1 L k B T K E = ε f Kondo singlet S =0 conduction electron/hole f electron

12 Heavy Fermion systems Kondo peak

13 Physical properties of Kondo lattice χ(0) = Cn f / T K γ = π 2 k B n f / 3T K ~T K /3 Wilson ratio: π 2 R W (π 2 k B /3C)(χ(0)/γ) ~ 1

14 f-electron density of states of valence fluctuation/kondo systems Photoemission Inverse-photoemission Ce (f 0 f 1 ) Yb (f 13 f 14 ) (Yb 3+ Yb 2+ ) f-electron density of states ρ f (ω) f 1 f 0 f 13 f 12 µ U Photoemission Energy ω Kondo peak (f 0 f 1 ) ε f = k B T K U Kondo peak (f 14 f 13 ) ε f = k B T K Yb 3+ Yb 2+ µ f 1 f 2 Ce 3+ Ce 3+ Ce 4+ Inverse-photoemission f 13 f 14 Yb 3+ n f = /[ +πt K /N f ]

15 f-electron density of states in valence fluctuating/kondo Yb compounds Kondo temperature: T K

16 High-resolution photoemission spectroscopy α-ce Garnier et al E = 5 mev Patthey et al, 1985 E = 20 mev Wieliczka et al E = 100 mev Wieliczka et al E = 400 mev EF

17 Photoemission spectra of valence fluctuating YbAl 2 f 14 f 13 Yb 3+ f 13 f 12 Yb 2+ Yb 2+ surface bulk E ~ 150 mev S.-J. Oh et al. PRB 88

18 Temperature dependence of the Kondo peak in YbAl 2 T K ~ 400 K n f ~ 0.77 ~ 0.05 ev E ~ 40 mev L. H. Tjeng et al. PRL 93 Anderson-impurity model fit

19 Argument against the Kondo scenario Anderson-impurity model fit E ~ 60 mev single crystals J. J. Joyce et al. Physica B, 95

20 Beamline 23SU at SPring-8 RI expt. hall Helical undulator PGM monochromator bulk sensitive high-resolution photoemission expts with hν = ev is made. See, A. Sekiyama et al., Nature 1999

21 Physical properties of Yb 2 Co 3 X 9 (X=Ga Ga,, Al) Yb 2 Co 3 Ga 9 : T K ~ 260 K Yb 2 Rh 3 Ga 9 : T K ~ 120 K, Yb 2 Ir 3 Ga 9 : T K ~ 250 K Yb 2 Co 3 Al 9 : T N = 1.2 K, T K < 1 K Yb 2 Rh 3 Al 9 : T N = 3.5 K, Yb 2 Ir 3 Al 9 : T N = 5.5 K X=Ga, Al S.K. Dhar et al. Physica B, 99 O. Trovarelli et al., PRB 99

22 Photoemission spectra of Yb 2 Co 3 X 9 T K ~ 260 K n f ~ 0.9 ~ 0.1 ev Co 3d Co 3d E ~ 5 mev T. Okane et al., PRB Binding Energy (mev)

23 Photoemission spectra of Yb 2 Co 3 Ga 9 4f density of states Temperature dependence T. Okane et al., PRB 02

24 Anderson-impurity model analyses of the Kondo peak --- NCA and beyond Yb 2 Co 3 Ga 9 Energy (ev) NCA+Doniach-Sunjic asymmetric broadening NCA+Lorentzian-Gaussian broadening see, O. Gunnarsson and K. Shonhammer, PRB 40, 4160 (1989) T. Okane et al., PRB 02

25 Asymmetric broadening of the Kondo peak beyond NCA NCA electron-hole pair excitation asymmetric broadening see, O. Gunnarsson and K. Shonhammer, PRB 89

26 Thermoelectric material skutterudite-type YbFe 4 Sb Sb 12 Thermoelectric figure of merit Z = S σ κ 3 2 m* µ κ 2 / High carrier mobility High thermopower Low thermal conductivity Electrical resisitivity l Yb Fe Sb Thermopower S & thermal conductivity κ Dilley et al. PRB 00 T. Okane et al. unpublished

27 Heavy Fermion systems Kondo insulator

28 Physical properties of Kondo insulator χ( 0 ) = Cn f / T K ~TK /3 γ = π 2 k B n f / 3T K

29 Renormalized band picture for Kondo insulator f band d, s band G. Aeppli and Z. Fisk, Comments Cond. Matt. Phys. 92

30 Kondo insulator versus band insulator Band insulator Kondo insulator

31 Physical properties of YbB 12 Yb B T K ~ 260 K

32 Photoemission spectra of YbB 12 E ~ 30 mev T. Susaki et al. PRL 96 T K ~ 260 K n f ~ 0.85 ~ 0.1 ev

33 Yb 4f density of states and self-energy analysis in YbB 12 T. Susaki et al. PRL 96

34 Photoemission spectra of YbB 12 ~100 mev peudogap ~10 mev (peudo)gap E ~ 7 mev T. Susaki et al. PRL 99

35 Effects of Yb dilution on the gap of YbB 12 T. Susaki et al. JPSJ 01

36 Heavy Fermion systems Band structure and Fermi surface

37 Pressure-induced superconductivity in quasi-2d heavy Fermion system CeRhIn 5 In Rh, Ir antiferromagnetic Ce supercond. Superconductivity at ambient pressure in CeIrIn 5 (T C = 0.4 K) and CeCoIn 5 (T C = 2.2 K) coexistence of AF and supercond H. Hegger et al. PRL 00 R. Movshovich et al. PRL 01

38 Superconductivity near quantum critical point Doniach s phase diagram CeRhIn 5 CeCoIn 5 Non-Fermi liquid Antferromagnetic metal CeIrIn 5 superconductor Fermi liquid quantum critical point S. Doniach

39 Beamline 23SU at SPring-8

40 Bulk-sensitive photoemission at Hi-SOR S.I. Fujimori et al., cond-mat LT23 proceedings

41 ARPES spectra of CeRhIn 5 CeRhIn 5 Γ-X (Z-R) He I T = 14 K CeRhIn 5 Γ-M (Z-A) He I T = 14 K hν = 21.2 ev Photoemission Intensity (arb. units) θ = Photoemission Intensity (arb. units) θ = Binding Energy (ev) E F Binding Energy (ev) E F -5 S.I. Fujimori et al., cond-mat

42 CeRhIn 5 : Comparison with band calculations S.I. Fujimori et al., cond-mat

43 CeIrIn 5 : Comparison with band calculations S.I. Fujimori et al., cond-mat

44 ARPES Fermi surface in CeIrIn 5 Fermi surface mapping -comparison with LDA- LDA calculation of Fermi surface H. Harima A M The cylindrical Fermi surface centered at M(A) is observed. S.I. Fujimori et al., cond-mat

45 Band calculations for CeRhIn 5 and LaRhIn 5 H. Harima

46 Heavy Fermion systems d-electron heavy Fermion and Kondo insulators

47 Heavy Fermion behavior of LiV 2 O 4 LDA + U calc. Li V O a 1g : localized states e g : conduction electrons Kondo effect C. Urano et al., PRL 00 V.I.Anisimov et al., PRL 99

48 Electronic structure of LiV 2 O 4 Incoherent coherent * No preferential occupation of a 1g * T-dependent spectral weight transfer as predicted by Hubbard model DMFT J. Matsuno et al., PRB 99, Physca B 00

49 Z. Schlesinger, PRL 93 V. Jaccarino, PR 67 Kondo-insulator behavior of FeSi Electrical resisitivity Magnetic susceptibility fitted with local moment distorted from NaCl Optical conductivity or narrow band T(K) = Gap ~ 600 cm Transition ~ 150 K Nonmagnetic insulator Paramagnetic metal

50 T. Saitoh et al., Sol. St. Commun. 95 T. Susaki et al., PRB 98 Electronic structure of FeSi narrow band gap L.F. Mattheiss and D.R. Hamann, PRB 93

51 Renormalized band picture for Kondo insulator f band d, s band G. Aeppli and Z. Fisk, Comments Cond. Matt. Phys. 92

52 Kondo insulator versus band insulator Band insulator Kondo insulator