The Alpha to Gamma Transition in Ce: A Theoretical View From Optical Spectroscopy

1. 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. 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 Outline

3. Overview The element Ce Electron configuration of Ce Atom : [Xe]4f25d06s2 Solid or compounds : trivalent [Xe]4f1(5d6s)3, tetravalent [Xe]4f0(5d6s)4 promotional model (Ramirez, Falicov 1971) • γ-α phase transition of Ce • large volume collapse (~15%) • loss of local magnetic moment

4. Overview  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 • Transition is 1.order • ends with CP very similar to gas-liquid condesation

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

6. ab initio calculation LDA+DMFT is self-consistently determined bath for AIM contains tff and Vfd hopping • 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 Δ must self-consistently determined)while in KVC Δ is calculated for a fictious impurity (and needs to be rescaled to fit exp.)

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

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

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

10. LDA and LDA+U ferromagnetic f DOS total DOS

11. LDA+DMFT alpha DOS TK(exp)=1000-200K

12. LDA+DMFT gamma DOS TK(exp)=60-80K

13. Photoemission&experiment

14. K.Held, A.K.McMahan,R.T. Scalettar, PRL 87,276404(2001) 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) B. Amadon, S. Biermann, A. Georges, F. Aryasetiawan, cond-mat/0504732 Non-self consistent one shot calculation

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

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

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

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

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

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

21. Local spectral function g a

22. n.k.p.=16x16x16=4096 Bath spectral function g a

23. Conclusion • 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