f-electron Fermi surface exclusion above T K in CeRu 2 Si 2 Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 1

Transcription

1 f-electron Fermi surface exclusion above TK in CeRu_Si_ f-electron Fermi surface exclusion above T K in CeRu Si Luttinger counting theorem Conjecture (Fulde & Zwicknagl, 9) f-electrons counted in Fermi surface IF f-moments quenched. (no matter what route to Fermi liquid) f-electrons excluded from FS above Kondo temperature T K Difficult to test with low-t dhva. dhva paradigm (Tautz et al, 995) large Z-point hole FS f LaRu Si f CeRu Si high field (metamag) f CeRu Ge ferromagnet reduced "pillow" hole FS counts ½ Ce f- electron in Kondo CeRu Si --at low temperature LDA band hole Fermi surface no f- electron ½ extra f-electron here ( ½ f-electron in other multiply-connected complex FS piece) University of Michigan LLNL Talk--April, LDA for LaRu Si and CeRu Si compared La Ce band Z- hole pocket University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/)

2 f-electron Fermi surface exclusion above TK in CeRu_Si_ Fermi surface of CeRu Si Lonzarich Tautz 95 Zwicknagl Relativistic LDA Z (Σ) X Χ - Χ Χ ξ, ξ, µ, µ, ν ν ε ε α α δ, δ, γ, γ, β β m*/m m*/m e e 3 3,,.5,..5,. C*/T C*/T 9 9 Binding Energy (ev) Binding Energy (ev) E.K.R. Runge, R.C. Albers, N.E. Christensen & G. Zwicknagl, Phys. Rev B. 5, 375 (995). Renormalized LDA Z (Σ) X G. Zwicknagl, Adv. Phys., 3 (99). γ = 35 mj/mol-k University of Michigan LLNL Talk--April, Ce Spin State & Fermi Surface of CeRu Si f ψ Frequency (kt) LaRu Si CeRu Si [] [] [] η δ ω β γ ε - Field Direction (deg) ψ α Frrequency (kt) CeRu Si : H<H m & T<<T K CeRu Si : H//[] β γ below, ψ δ 5 f ω ω H m H (T) above 5 Frequency (kt) [] [] [] LaRu Si CeRu Ge ω - Field Direction (deg) LaRu Si CeRu Ge CeRu Si : H>H m *or T>>T K high field metamag CeRu Si FS like LaRu Ge ferromagnetic CeRu Ge FS like LaRu Ge Exclude f s from FS for for T>>T K??? *Zwicknagl Physica Scripta T9, 3 (993) University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/)

3 f-electron Fermi surface exclusion above TK in CeRu_Si_ XRu Si 3d crystal k-space arcs for varying photon energy ARPES arcs Brillouin Zone <> <> 7 Χ Χ (Σ) <> 5 k z k z <> Χ k x k x University of Michigan LLNL Talk--April, LaRu Si Fermi surface from ARPES J.D. Denlinger (data from ALS) (a) k y (Å - ) - hν = ev 5 ev LDA (b) (c) Χ - - k y (Å - ) k y ( Å - ) - ev - 5 ev - hν fixes k z and map center' s BZ point - - k X ( Å - ) Hole sheets (center = Z) Electron sheets (center = ) University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/) 3

4 f-electron Fermi surface exclusion above TK in CeRu_Si_ Same large hole FS for LaRu Si and CeRu Si for T T K > T K J. D. Denlinger et al, samples J. Sarrao LANL University of Michigan LLNL Talk--April, Experimental Fermi Surface f weight at low mass,, Z points for CeRu Si hν = 9 ev hν = ev (a) (b) (c) LDA k y (Å - ) - k y (Å - ) - k y ( Å - ) - Χ - 9 ev - ev - dhva: m/m e =,.5,., m/m e = - - k X ( Å - ) m/m e = 3, Hole sheets (center = Z) Electron sheets (center = ) University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/)

5 f-electron Fermi surface exclusion above TK in CeRu_Si_ CeRu Si ARPES good and bad cleaves good bad University of Michigan LLNL Talk--April, CeRu Si angle integrated Good surface angle-integrated d RESPES from ARPES 53 angles, normalize at 5 ev, average Avg All θ = ± Binding Energy (ev) Polar (deg) University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/) 5

6 f-electron Fermi surface exclusion above TK in CeRu_Si_ Surface effect in CeRu Si Bold angle summed spectrum Solid lines extremum behavior of this data set Dashed lines extremum behavior in set with better angle resolution University of Michigan LLNL Talk--April, Low hνh OK for CeRu Si Evidence that bulk behavior can be seen in d RESPES of this material (d) Ce 3d edge RESPES with. ev resolution (consistent with SPring data) (c) angle summed d edge RES-ARPES (a) and (b) ARPES from center of normal emission Z-point Denlinger et al, SCES proceedings University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/)

7 f-electron Fermi surface exclusion above TK in CeRu_Si_ CeRu Si why bulk at low hν? h Crystal structure admits two cleavage planes, with and without Ce Good cleaves probably from surface without Ce. I.e., buried active layer important for cuprates Really flat surface missing edges and steps, less surface sensitive. University of Michigan LLNL Talk--April, renormalized hybridization (a) to d E - EF (ev). E F Anderson Lattice Model -band low energy ansatz E+ E- renormalized f near E F k F k F '. k (Å - ). ε d (k) Qualitatively similar to LDA for CeRu Si possible origin of success for LDA FS of Ce materials. University of Michigan LLNL Talk--April, ε f ' ε f E - E F (ev).. -. (b) (c) k (Å - ) d k (Å - ) f Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/) 7

8 f-electron Fermi surface exclusion above TK in CeRu_Si_ f-d d mixing CeRu Si ( ev, ~Z) URu Si ( ev, ~X) J. D. Denlinger et al, samples: Maple, Fisk, Sarrao f, γ=35 5f, γ= University of Michigan LLNL Talk--April, Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/7/)