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IJS The Alpha to Gamma Transition in Ce: A Theoretical View From Optical Spectroscopy K. Haule, V. Oudovenko, S. Savrasov, G. Kotliar DMFT(SUNCA method)

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Presentation on theme: "IJS The Alpha to Gamma Transition in Ce: A Theoretical View From Optical Spectroscopy K. Haule, V. Oudovenko, S. Savrasov, G. Kotliar DMFT(SUNCA method)"— Presentation transcript:

1 IJS The Alpha to Gamma Transition in Ce: A Theoretical View From Optical Spectroscopy K. Haule, V. Oudovenko, S. Savrasov, G. Kotliar DMFT(SUNCA method) two-band Hubbard model Bethe lattice, U=4D

2 IJS Outline Some facts about Ce, why is it an interesting material? Classical theories explaining Ce volume collapse LDA+DMFT Photoemission results LDA+DMFT Optics calculation and results

3 IJS Overview Electron configuration of Ce Atom : [Xe]4f 2 5d 0 6s 2 Solid or compounds : trivalent [Xe]4f 1 (5d6s) 3, tetravalent [Xe]4f 0 (5d6s) 4 The element Ce γ-α phase transition of Ce large volume collapse (~15%) loss of local magnetic moment promotional model (Ramirez, Falicov 1971)

4 IJS Overview volumesexp.LDALDA+U  28Å 3 24.7Å 3  34.4Å 3 35.2Å 3 Transition is 1.order ends with CP very similar to gas- liquid condesation  Various phases : isostructural phase transition ends in a critical point at (T=600K, P=2GPa)   (fcc) phase [ magnetic moment (Curie-Wiess law), large volume, stable high-T, low-p]   (fcc) phase [ loss of magnetic moment (Pauli-para), smaller volume, stable low-T, high-p] with large volume collapse  v/v  15 

5 IJS Mott transition (B. Johansson, 1974): Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): Classical theories Hubbard model Anderson (impurity) model changes and causes Mott tr. changes → chnange of T K bath either constant or taken from LDA and rescaled

6 IJS LDA+DMFT ab initio calculation is self-consistently determined contains t ff and V fd hopping bath for AIM Kondo volume colapse model resembles DMFT picture: Solution of the Anderson impurity model → Kondo physics Difference: with DMFT the lattice problem is solved (and therefore Difference: with DMFT the lattice problem is solved (and therefore Δ must self- consistently determined) while in KVC Δ is calculated for a fictious impurity (and needs to be rescaled to fit exp.)

7 IJS LDA+DMFT Formalism local in localized LMTO base Impurity problem (14x14): fermionic bath mapping solution AIM DMFT SCC

8 IJS Slave particle diagrammatic impurity solvers NCA OCA TC A Luttinger Ward functional local (eigen)state - full atomic base, where general AIM: ( )

9 IJS SUNCA vs QMC two band Hubbard model, Bethe lattice, U=4D three band Hubbard model, Bethe lattice, U=5D, T=0.0625D three band Hubbard model, Bethe lattice, U=5D, T=0.0625D

10 IJS LDA and LDA+U f DOS total DOS volumesexp.LDALDA+U  28Å 3 24.7Å 3  34.4Å 3 35.2Å 3 ferromagnetic

11 IJS LDA+DMFT alpha DOS T K (exp)=1000-200K

12 IJS LDA+DMFT gamma DOS T K (exp)=60-80K

13 IJS Photoemission&experiment

14 IJS Thermodynamics of the transition The impurity level is calculated by the constraint LDA calculation and fixed and is not calculated from the high frequency expansion of LDA-SCC (Edc is not needed) Non-self consistent one shot calculation B. Amadon, S. Biermann, A. Georges, F. Aryasetiawan, cond-mat/0504732 K.Held, A.K.McMahan,R.T. Scalettar, PRL 87,276404(2001)

15 IJS Optics calculation double pole single pole for ATM One divergence integrated out!

16 IJS ATM in short Analytic tetrahedron method: Integral is analytic and simple (combination of logarithms)

17 IJS Optical conductivity 1eV alpha peak 0.5 eV gamma depletion 0.33 eV alpha shoulder 5K 300K 580K 1160K * *

18 IJS Partial DOS 4f 5d 6s Z=0.33

19 IJS Optical conductivity orbitally resolved "fat" optics for alpha phase LDA compared to LDA+DMFT ff contribution to optics <<fd<<dd ff hopping very small ff hopping very small, Kondo resonance mostly due to hybridization with d Mott transition not the right explanation (even if Mott transition is understood in modern sense)

20 IJS Hybridization pseudogap peak in f spectra scatters d electrons dd contribution largest, some df

21 IJS Local spectral function  

22 IJS Bath spectral function   n.k.p.=16x16x16=4096

23 IJS  d,s,p conducting bands are important for explaining properties of Ce  Kondo peak in low T alpha phase appears due to hybridization with d bands  Optics conductivity has mostly d character  Optics shows hybridization pseudogap up to 1eV in alpha phase and no pseudogap in gamma phase  KVC model better than MT scenario Conclusion

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