Electronic structure and spectral properties of actinides: felectron challenge

1
Electronic structure and spectral properties of
actinides f-electron challenge

• Alexander Shick
• Institute of Physics, Academy of Sciencesof the
  Czech  Republic, Prague

2
Outline

• d-Pu and Am
• Density functional theory (LDA/GGA) magnetism
  and
• photoemission
• Beyond LDA I LDAU

• Beyond LDA II LDADMFT
• 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 properties of
actinides
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 GGASO P. Soderlind, EPL (2001)

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

8
Is Plutonium magnetic?
Experimentally, Am has non magnetic f6 ground
state with J0.
9
Beyond LDA LDAU
10
Rotationally invariant AMF-LSDAU
includes all spin-diagonal and spin-off-diagonal
elements
11
How AMF-LSDAU works?
d-Plutonium
AMF-LSDAU works for ground state properties
Non-integer 5.44 occupation of 5f-manifold
12
fcc-Americium
f6 -gt L3, S3, J0

• LSDA/GGA gives magnetic ground state similar to
  d-Pu

• AMF-LSDAU gives correct non-magnetic ground
  state

13
Density of States
14
Photoemission
Experimental PES
LSDAU fails for Photoemission!
15
Dynamical Mean-Field Theory
16
Extended LDAU method
Hubbard-I approximation
17
Self-consistency over charge density
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Local density matrix approximation
nimp nloc
Quantum Impurity Solver (Hubbard-I)
LDAU 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
LDAU
Self-consistent calculations for the paramagnetic
phase of the local
moment systems.
19
U 4.5 eV K. 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) LDADMFT
SUNCA
5f-Pu 5.2..
0
-2
2
4
-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) LDADMFT
SUNCA
Good agreement with previous calculations
23
Probe for Valence and Multiplet structure
EELSXAS
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 vs XAS/EELS Experiment
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, LSDAU 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-L2.42, J0 meff 0
• Am S-L2.33, J0 meff 0
• Cm S3.3 L0.4, J3.5 meff 7.9 mB
• Experimental meff 8 mB
• Bk S2.7 L3.4, J6.0 meff 9.5 mB
• Experimental meff 9.8 mB

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Conclusions
LDMA calculations are in reasonable agreement
with LDADMFT. 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, arxiv0903.1998
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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)