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Electronic structure and spectral properties of actinides: f-electron challenge Alexander Shick Institute of Physics, Academy of Sciences of the Czech Republic, Prague Outline and Am Density functional theory (LDA/GGA): magnetism and photoemission Beyond LDA I: LDA+U d-Pu LDA II: LDA+DMFT Hubbard I + Charge density selfconsistency “Local density matrix approximation” (LDMA) Beyond Applications of LDMA to d-Pu, Am, Cm PES & XAS/EELS Local Magnetic Moments in Paramagnetic Phase Plutonium puzzle Pu: 25% increase in volume between and d phase No local magnetic moments No Curie-Weiss up to 600K Theoretical understanding of electronic, magnetic and spectroscopic properties of actinides Electronic Structure Theory Many-Body Interacting Problem Density functional theory Kohn-Sham Dirac Eqs. Scalar-relativistic Eqs. SOC - LDA/GGA calculations for Pu Non-Magnetic GGA+SO P. Soderlind, EPL (2001) • GGA works reasonably for low-volume phases • Fails for d-Pu! Is Plutonium magnetic? Experimentally, Am has non magnetic f6 ground state with J=0. Beyond LDA: LDA+U Rotationally invariant AMF-LSDA+U includes all spin-diagonal and spin-off-diagonal elements How AMF-LSDA+U works? d-Plutonium AMF-LSDA+U works for ground state properties Non-integer 5.44 occupation of 5f-manifold fcc-Americium f6 -> L=3, S=3, J=0 • LSDA/GGA gives magnetic ground state similar to d-Pu • AMF-LSDA+U gives correct non-magnetic ground state Density of States Photoemission Experimental PES LSDA+U fails for Photoemission! Dynamical Mean-Field Theory Extended LDA+U method: Hubbard-I approximation Self-consistency over charge density 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. U = 4.5 eV K. Haule et al., Nature (2007) K. Moore, and G. van der Laan, Rev. Mod. Phys. (2008). N 94 Atom F2 Pu 7.76 F4 5.05 F6 3.10 x(LDA) 0.30 95 Am 8.07 5.26 3.86 0.35 96 Cm 8.37 5.46 4.01 0.36 97 Bk 8.65 5.65 4.15 0.42 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 LDMA: Americium 5f-occupation of 5.95 Experimental PES Good agreement with experimental data and previous calculations LDMA: Curium 5f-occupation of 7.07 K. Haule et al., Nature (2007) LDA+DMFT SUNCA Good agreement with previous calculations 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! LDMA vs XAS/EELS Experiment Pu Am Cm f-occupation 5.25 5.95 7.07 B-LDMA 0.813 0.902 0.737 B-at. IC 0.816 0.916 0.750 B-Exp. 0.826 0.930 0.794 Very reasonable agreement with experimental data and atomic intermediate coupling (IC) n5/2 /n7/2 LDMA IC Pu Am Cm 4.25/1.00 5.16/0.79 4.04/3.03 4.23/0.77 5.28/0.72 4.10/2.90 jj 5/0 6/0 6/1 LS 3/2 3.14/2.86 3/4 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 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=0 meff =0 Cm: S=3.3 L=0.4, J=3.5 meff =7.9 mB Experimental meff ~8 mB Bk: S=2.7 L=3.4, J=6.0 meff =9.5 mB Experimental meff ~9.8 mB 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 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)