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Alexander Shick Institute of Physics, Academy of Sciences of the Czech  Republic, Prague. Electronic structure and spectral properties of actinides: f -electron challenge. Outline. d - Pu and Am Density functional theory (LDA/GGA): magnetism and photoemission Beyond LDA I: LDA+U.

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alexander shick institute of physics academy of sciences of the czech republic prague
Alexander Shick

Institute of Physics, Academy of Sciencesof the Czech  Republic, Prague

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

slide3

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

electronic structure theory
Electronic Structure Theory

Many-Body Interacting Problem

slide6

Kohn-Sham Dirac Eqs.

Scalar-relativistic Eqs.

SOC

-

lda gga calculations for pu
LDA/GGA calculations for Pu

Non-Magnetic GGA+SO

P. Soderlind, EPL (2001)

  • GGA works reasonably for low-volume phases
  • Fails for d-Pu!
slide8

Is Plutonium magnetic?

Experimentally, Am hasnon magnetic f6 ground state with J=0.

slide10

Rotationally invariant AMF-LSDA+U

includes all spin-diagonal and spin-off-diagonal elements

how amf lsda u works
How AMF-LSDA+U works?

d-Plutonium

AMF-LSDA+U works for ground state properties

Non-integer 5.44 occupation of 5f-manifold

slide12

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
slide14

Photoemission

Experimental PES

LSDA+U fails for Photoemission!

slide16

Extended LDA+U method:

Hubbard-I approximation

local density matrix approximation
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.

slide19

U = 4.5 eVK. Haule et al., Nature (2007)

K. Moore, and G. van der Laan, Rev. Mod. Phys. (2008).

slide20

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

slide21

LDMA: Americium 5f-occupation of 5.95

Experimental PES

Good agreement with experimental data

and previous calculations

slide22

LDMA: Curium 5f-occupation of 7.07

K. Haule et al., Nature (2007)

LDA+DMFT SUNCA

Good agreement with previous calculations

slide23

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!

slide24

LDMA vsXAS/EELSExperiment

Very reasonable agreement with experimental data

and atomic intermediate coupling (IC)

slide25

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

slide26

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

conclusions
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
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)