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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.

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Presentation on theme: "Electronic structure and spectral properties of actinides: f-electron challenge Alexander Shick Institute of Physics, Academy of Sciences of the Czech."— Presentation transcript:

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

2 Outline PuAm   -Pu and Am magnetism and Density functional theory (LDA/GGA): magnetism andphotoemission LDA+U Beyond LDA I: LDA+U LDA+DMFT   eyond LDA II: LDA+DMFT Hubbard I + Charge density selfconsistency LDMA “Local density matrix approximation” (LDMA) LDMAPuAm, Cm  Applications of LDMA to  -Pu, Am, Cm PES & XAS/EELS Local Magnetic MomentsParamagnetic Local Magnetic Moments in Paramagnetic Phase

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

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  -Pu!

8 Is Plutonium magnetic? Experimentally, Am has non magnetic f 6 ground state with J=0.

9 Beyond LDA: LDA+U

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

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

12 f 6 -> L=3, S=3, J=0 LSDA/GGA gives magnetic ground state similar to  -Pu AMF-LSDA+U gives correct non-magnetic ground state fccAmericium fcc-Americium

13 Density of States

14 LSDA+U fails for Photoemission! Experimental PES Photoemission

15 Dynamical Mean-Field Theory

16 Hubbard-I approximation Extended LDA+U method:

17 Self-consistency over charge density

18 Local density matrix approximation Quantum Impurity Solver (Hubbard-I) (Hubbard-I) LDA+U + self-consistency over charge density over charge density n imp = n loc n f, V dc Subset of general DMFT condition that the SIAM GF = local GF in a solid On-site occupation matrix n imp 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 NAtomF2F4F6  LDA) 94Pu7.765.053.100.30 95Am8.075.263.860.35 96Cm8.375.464.010.36 97Bk8.655.654.150.42 U = 4.5 eV K. Haule et al., Nature (2007) K. Moore, and G. van der Laan, Rev. Mod. Phys. (2008).

20 LDMA 5f - Pu = 5.25 K. Haule et al., Nature (2007) LDA+DMFT SUNCA 5f - Pu = 5.2.. How LDMA works? Good agreement with experimental PES and previous calculations 0 -224-4

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

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

23 K. Moore, and G. van der Laan, Rev. Mod. Phys. (2008). branching ratio B and spin-orbit coupling strength w 110 Probe for Valence and Multiplet structure: EELS&XAS Dipole selection rule Not a direct measurement of f-occupation!

24 LDMA vs XAS/EELS Experiment PuAmCm f-occupation 5.255.957.07 B-LDMA0.8130.9020.737 B-at. IC0.8160.9160.750 B-Exp.0.8260.9300.794 Very reasonable agreement with experimental data and atomic intermediate coupling (IC)

25 n 5/2 /n 7/2 Pu Am Cm LDMA4.25/1.005.16/0.794.04/3.03 IC4.23/0.775.28/0.724.10/2.90 jj 5/0 6/0 6/1 LS 3/23.14/2.86 3/4 LDMA corresponds to IC f 5/2 -PDOS and f 7/2 –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:, J=0 Pu: S=-L=2.42, J=0  eff = 0 Am: J=0  eff =0 Am: S=-L=2.33, J=0  eff =0 Cm: J  eff =7.9  Cm: S=3.3 L=0.4, J=3.5  eff =7.9  B Experimental  eff Experimental  eff ~8  B Bk:  eff =9.5  Bk: S=2.7 L=3.4, J=6.0  eff =9.5  B Experimental  eff Experimental  eff ~9.8  B

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

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

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