1. Many-body Electronic Structure of Actinides: A Dynamical Mean Field Perspective.
Kristjan Haule,
Physics Department and
Center for Materials Theory
Rutgers University
Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov
Half Moon Bay

2. Overview
DMFT in actinides and their compounds (Spectral density functional approach).
Examples:
Plutonium, Americium, Curium.
Compounds: PuO2, PuAm
Observables:
Valence, Photoemission, and Optics, X-ray absorption
Extensions of DMFT to clusters.
Coherence in the Hubbard and t-J model
New general impurity solver (continuous time QMC) developed (can treat clusters and multiplets)

3. Crossover: bad insulator to bad metal
Universality of the Mott transition
Crossover: bad insulator to bad metal
Critical point
First order MIT
Ni2-xSex
V2O3
k organics
1B HB model (DMFT):

4. Coherence incoherence crossover in the 1B HB model (DMFT)
Phase diagram of the HM with partial frustration at half-filling
M. Rozenberg et.al., Phys. Rev. Lett. 75, 105 (1995).

5. DMFT + electronic structure method
Basic idea of DMFT: reduce the quantum many body problem to a one site
or a cluster of sites problem, in a medium of non interacting electrons obeying a
self-consistency condition. (A. Georges et al., RMP 68, 13 (1996)).
DMFT in the language of functionals: DMFT sums up all local diagrams in BK functional
Basic idea of DMFT+electronic structure method (LDA or GW):
For less correlated bands (s,p): use LDA or GW
For correlated bands (f or d): with DMFT add all local diagrams
Effective (DFT-like) single particle
Spectrum consists of delta like peaks
Spectral density usually contains renormalized
quasiparticles and Hubbard bands

6. How good is single site DMFT for f systems?
L=0,S=7/2 J=7/2
Elements: f5
L=5,S=5/2 J=5/2 f6
L=3,S=3 J=0
Compounds:
PuO2
PuAm

7. Overview of actinides Many phases
25% increase in volume between a and d phase
Two phases of Ce, a and g
with 15% volume difference

8. Overview of actinides? Trivalent metals with nonbonding f shell
Partly localized,
partly delocalized
f’s participate in bonding

9. Why is Plutonium so special?
Heavy-fermion behavior
in an element
Typical heavy fermions
(large mass->small Tk
Curie Weis at T>Tk)
No curie Weiss up to 600K

10. Plutonium puzzle? Ga doping stabilizes d-Pu
at low T, lattice contraction
Am doping -> lattice expansion
Expecting unscreened moments!
Does not happen!

11. Curium versus Plutonium
nf=6 -> J=0
closed shell
(j-j: 6 e- in 5/2 shell)
(LS: L=3,S=3,J=0)
One hole in the f shell
One more electron in the f shell
Magnetic moments! (Curie-Weiss law at high T,
Orders antiferromagnetically at low T)
Small effective mass (small specific heat coefficient)
Large volume
No magnetic moments,
large mass
Large specific heat,
Many phases, small or large volume

12. Can LDA+DMFT predict which material is magnetic and which is not?
Density functional based electronic structure calculations:
All Cm, Am, Pu are magnetic in LDA/GGA
LDA: Pu(m~5mB), Am (m~6mB) Cm (m~4mB)
Exp: Pu (m=0), Am (m=0) Cm (m~7.9mB)
Non magnetic LDA/GGA predicts volume up to 30% off.
Treating f’s as core overestimates volume of d-Pu,
reasonable volume for Cm and Am
Can LDA+DMFT predict which material
is magnetic and which is not?

13. Very strong multiplet splitting
Atomic multiplet splitting crucial N
Atom F2 F4 F6 x 92 U
8.513
5.502
4.017
0.226 93 Np
9.008
5.838
4.268
0.262 94 Pu
8.859
5.714
4.169
0.276 95 Am
9.313
6.021
4.398
0.315 96 Cm
10.27
6.692
4.906
0.380
Increasing F’s an SOC

14. Starting from magnetic solution,
Curium develops antiferromagnetic long range order below Tc
above Tc has large moment (~7.9mB close to LS coupling)
Plutonium dynamically restores symmetry -> becomes paramagnetic
cond-mat/

15. Multiplet structure crucial for correct Tk in Pu (~800K)
and reasonable Tc in Cm (~100K)
Without F2,F4,F6: Curium comes out paramagnetic heavy fermion
Plutonium weakly correlated metal

16. Valence histograms
Density matrix projected to the atomic eigenstates of the f-shell
(Probability for atomic configurations)
Pu partly f5 partly f6
f electron fluctuates between these
atomic states on the time scale t~h/Tk
(femtoseconds)
One dominant atomic state – ground state of the atom

17. Probe for Valence and Multiplet structure: EELS&XAS
Electron energy loss spectroscopy (EELS) or
X-ray absorption spectroscopy (XAS)
core
valence
4d3/2
4d5/2
5f5/2
5f7/2
Excitations from 4d core to 5f valence
A plot of the X-ray absorption
as a function of energy
Energy loss [eV]
Core splitting~50eV
4d5/2->5f7/2
4d3/2->5f5/2 hv
Core splitting~50eV
Measures unoccupied valence 5f states
Probes high energy Hubbard bands!

18. f-sumrule for core-valence conductivity
Similar to optical conductivity:
Current:
Expressed in core valence orbitals:
The f-sumrule:
can be expressed as
Branching ration B=A5/2/(A5/2+A3/2)
Energy loss [eV]
Core splitting~50eV
4d5/2->5f7/2
4d3/2->5f5/2
B=B0 - 4/15<l.s>/(14-nf)
B0~3/5
Branching ratio depends on:
average SO coupling in the f-shell <l.s>
average number of holes in the f-shell nf
A5/2 area under the 5/2 peak
B.T. Tole and G. van de Laan, PRA 38, 1943 (1988)

19. LDA+DMFT B=B0 - 4/15<l.s>/(14-nf)
[a] G. Van der Laan et al., PRL 93, (2004).
[b] G. Kalkowski et al., PRB 35, 2667 (1987)
[c] K.T. Moore et al., PRB 73, (2006).
One measured quantity B, two unknowns
Close to atom (IC regime)
Itinerancy tends to decrease <l.s>

20. Optical conductivity
2p->5f
5f->5f
Pu: similar to heavy fermions (Kondo type conductivity)
Scale is large MIR peak at 0.5eV
PuO2: typical semiconductor with 2eV gap, charge transfer

21. Pu-Am mixture, 50%Pu,50%Am
Lattice expands -> Kondo collapse is expected
Could Pu be close to f6 like Am?
Inert shell can not account for large cv anomaly
Large resistivity!
Absence of preadge structure in XAS
Our calculations suggest
charge transfer
Pu d phase stabilized by shift to
mixed valence nf~5.2->nf~5.4
Hybridization decreases, but nf increases,
Tk does not change significantly!
f6: Shorikov, et al., PRB 72, (2005);
Shick et al, Europhys. Lett. 69, 588 (2005).
Pourovskii et al., Europhys. Lett. 74, 479 (2006).

22. A.Lindbaum, S. Heathman, K. Litfin, and Y. Méresse,
Americium
f6 -> L=3, S=3, J=0
Mott Transition?
"soft" phase
f localized
"hard" phase
f bonding
A.Lindbaum, S. Heathman, K. Litfin, and Y. Méresse,
Phys. Rev. B 63, (2001)
J.-C. Griveau, J. Rebizant, G. H. Lander, and G.Kotliar Phys. Rev. Lett. 94, (2005)

23. Large multiple effects:
Am within LDA+DMFT
Large multiple effects:
F(0)=4.5 eV
F(2)=8.0 eV
F(4)=5.4 eV
F(6)=4.0 eV
S. Y. Savrasov, K. Haule, and G. Kotliar Phys. Rev. Lett. 96, (2006)

24. Comparisson with experiment
Am within LDA+DMFT
from J=0 to J=7/2
Comparisson with experiment
V=V0 Am I
V=0.76V0 Am III
V=0.63V0 Am IV
nf=6.2
nf=6
Exp: J. R. Naegele, L. Manes, J. C. Spirlet, and W. Müller Phys. Rev. Lett. 52, (1984)
“Soft” phase not in local moment regime
since J=0 (no entropy)
Theory: S. Y. Savrasov, K. Haule, and G. Kotliar Phys. Rev. Lett. 96, (2006)
"Hard" phase similar to a Ce or d Pu,
Kondo physics due to hybridization, however,
nf still far from Kondo regime

25. What is captured by single site DMFT?
Captures volume collapse transition (first order Mott-like transition)
Predicts well photoemission spectra, optics spectra,
total energy at the Mott boundary
Antiferromagnetic ordering of magnetic moments,
magnetism at finite temperature
Branching ratios in XAS experiments, Dynamic valence fluctuations,
Specific heat
Gap in charge transfer insulators like PuO2

26. Beyond single site DMFT
What is missing in DMFT?
Momentum dependence of the self-energy m*/m=1/Z
Various orders: d-waveSC,…
Variation of Z, m*,t on the Fermi surface
Non trivial insulator (frustrated magnets)
Non-local interactions (spin-spin, long range Columb,correlated hopping..)
Present in cluster DMFT:
Quantum time fluctuations
Spatially short range quantum fluctuations
Present in DMFT:
Quantum time fluctuations

27. Optimal doping: Coherence scale seems to vanish
underdoped
scattering
at Tc
optimally
overdoped Tc

28. Multiplets correctly treated
New continuous time QMC, expansion in terms of hybridization
General impurity problem
Diagrammatic expansion in terms of hybridization D
+Metropolis sampling over the diagrams k
Contains all: “Non-crossing” and all crossing diagrams!
Multiplets correctly treated
Phys. Rev. B 75, (2007)

29. Very incoherent at optimal doping
Hubbard model self-energy on imaginary axis, 2x2
Far from Mott transition
coherent
Low frequency
very different
Close to Mott transition
Very incoherent
Optimal doping in
the t-J model
(d~0.16)
has largest low energy
self-energy
Very incoherent
at optimal doping
Optimal doping in the
Hubbard model (d~0.1)
has largest low energy
self-energy
Very incoherent
at optimal doping

30. Conclusions
LDA+DMFT can describe interplay of lattice and electronic structure near Mott transition. Gives physical connection between spectra, lattice structure, optics,....
Allows to study the Mott transition in open and closed shell cases.
In actinides and their compounds, single site LDA+DMFT gives the zero-th order picture
2D models of high-Tc require cluster of sites. Some aspects of optimally doped regime can be described with cluster DMFT on plaquette:
Large scattering rate in normal state close to optimal doping