Electronic structure and spectral properties of actinides: f -electron challenge

1. Alexander Shick Institute of Physics, Academy of Sciencesof the Czech  Republic, Prague Electronic structure and spectral properties of actinides:f-electron challenge

2. Outline • d-Pu and Am Density functional theory (LDA/GGA): magnetism and photoemission Beyond LDA I: LDA+U • Beyond LDA II: LDA+DMFT Hubbard I + Charge density selfconsistency “Local density matrix approximation” (LDMA) • Applications of LDMA to d-Pu, Am, Cm PES & XAS/EELS Local Magnetic Moments in Paramagnetic Phase

3. Plutonium puzzle No local magnetic moments No Curie-Weiss up to 600K Pu: 25% increase in volume between  and  phase Theoretical understanding of electronic, magnetic and spectroscopic propertiesofactinides

4. Electronic Structure Theory Many-Body Interacting Problem

5. Density functional theory

6. Kohn-Sham Dirac Eqs. Scalar-relativistic Eqs. SOC -

7. LDA/GGA calculations for Pu Non-Magnetic GGA+SO P. Soderlind, EPL (2001) • GGA works reasonably for low-volume phases • Fails for d-Pu!

8. Is Plutonium magnetic? Experimentally, Am hasnon magnetic f6 ground state with J=0.

9. Beyond LDA: LDA+U

10. Rotationally invariant AMF-LSDA+U includes all spin-diagonal and spin-off-diagonal elements

11. How AMF-LSDA+U works? d-Plutonium AMF-LSDA+U works for ground state properties Non-integer 5.44 occupation of 5f-manifold

12. fcc-Americium f6 -> L=3, S=3, J=0 • LSDA/GGA gives magnetic ground state similar tod-Pu • AMF-LSDA+U gives correct non-magnetic ground state

13. Density of States

14. Photoemission Experimental PES LSDA+U fails for Photoemission!

15. Dynamical Mean-Field Theory

16. Extended LDA+U method: Hubbard-I approximation

17. Self-consistency over charge density

18. Local density matrix approximation nimp = nloc Quantum Impurity Solver (Hubbard-I) LDA+U + self-consistency over charge density nf , Vdc Subset of general DMFT condition that the SIAM GF = local GF in a solid On-site occupation matrix nimp is evaluated in a many-body Hilbert space rather than in a single-particle Hilbert Space of the conventional LDA+U Self-consistent calculations for the paramagnetic phase of the local moment systems.

19. U = 4.5 eVK. Haule et al., Nature (2007) K. Moore, and G. van der Laan, Rev. Mod. Phys. (2008).

20. How LDMA works? LDMA 5f-Pu = 5.25 Good agreement with experimental PES and previous calculations K. Haule et al., Nature (2007) LDA+DMFT SUNCA 5f-Pu = 5.2.. -4 -2 0 2 4

21. LDMA: Americium 5f-occupation of 5.95 Experimental PES Good agreement with experimental data and previous calculations

22. LDMA: Curium 5f-occupation of 7.07 K. Haule et al., Nature (2007) LDA+DMFT SUNCA Good agreement with previous calculations

23. Probe for Valence and Multiplet structure: EELS&XAS K. Moore, and G. van der Laan, Rev. Mod. Phys. (2008). branching ratio B and spin-orbit coupling strength w110 Dipole selection rule Not a direct measurement of f-occupation!

24. LDMA vsXAS/EELSExperiment Very reasonable agreement with experimental data and atomic intermediate coupling (IC)

25. LDMA corresponds to IC f5/2-PDOS and f7/2–PDOS overlap: LSDA/GGA, LSDA+U: due to exchange splitting LDMA: due to multiplet transitions

26. Local Magnetic Moment in Paramagnetic Phase G. Huray, S. E. Nave, in Handbook on the Physics and Chemistry of the Actinides, 1987 Pu: S=-L=2.42, J=0 meff =0 Am:S=-L=2.33,J=0meff =0 Cm:S=3.3 L=0.4, J=3.5meff =7.9 mB Experimentalmeff~8 mB Bk:S=2.7 L=3.4, J=6.0meff=9.5 mB Experimentalmeff ~9.8 mB

27. Conclusions LDMA calculations are in reasonable agreement with LDA+DMFT. Include self-consistency over charge density. Good description of multiplet transitions in PES. Good description of XAS/EELS branching ratios. . A. Shick, J. Kolorenc, A. Lichtenstein, L. Havela, arxiv:0903.1998

28. Acknowledgements Ladia Havela Sasha Lichtenstein Vaclav Drchal J. Kolorenc (IoPASCR and NCSU) Research support: German-Czech collaboration program (Project 436TSE113/53/0-1, GACR 202/07/J047)