Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov

Kristjan Haule, Physics Department and

Center for Materials TheoryRutgers University

Many-body Electronic Structure of AcMany-body Electronic Structure of Actinides: A Dynamical Mean Field Perstinides: A Dynamical Mean Field Pers

pective.pective.

Half Moon Bay

• DMFT in actinides and their compounds (Spectral density functional approach). Examples: – Plutonium, Americium, Curium. – Compounds: PuO2, PuAmObservables:– Valence, Photoemission, and Optics, X-ray absorption

• Extensions of DMFT to clusters. Examples:– Coherence in the Hubbard and t-J modelNew general impurity solver (continuous time QMC)

developed (can treat clusters and multiplets)

OverviewOverview

V2O3Ni2-xSex organics

Universality of the Mott transitionUniversality of the Mott transition

First order MITCritical point

Crossover: bad insulator to bad metal

1B HB model 1B HB model (DMFT):(DMFT):

Coherence incoherence crossover in the Coherence incoherence crossover in the

1B HB model (DMFT)1B HB model (DMFT)

Phase diagram of the HM with partial frustration at half-fillingPhase diagram of the HM with partial frustration at half-filling

M. Rozenberg et.al., Phys. Rev. Lett. M. Rozenberg et.al., Phys. Rev. Lett. 7575, 105 (1995)., 105 (1995).

DMFT + electronic structure methodDMFT + electronic structure method

Effective (DFT-like) single particle Spectrum consists of delta like peaks

Spectral density usually contains renormalized quasiparticles and Hubbard bands

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 GWFor correlated bands (f or d): with DMFT add all local diagrams

How good is single site DMFT for f systems?

f5

L=5,S=5/2 J=5/2

f6

L=3,S=3 J=0

f7

L=0,S=7/2 J=7/2

PuO2

PuAm

Compounds:

Elements:

Overview of actinides

Two phases of Ce, and with 15% volume difference

25% increase in volume between and phase

Many phases

Trivalent metals with nonbonding f shell

f’s participate in bonding

Partly localized, partly delocalized

Overview of actinides?

Why is Plutonium so special?

Heavy-fermion behavior in an element

No curie Weiss up to 600K

Typical heavy fermions (large mass->small TkCurie Weis at T>Tk)

Ga doping stabilizes -Pu at low T, lattice contraction

Am doping -> lattice expansionExpecting unscreened moments!

Does not happen!

Plutonium puzzle?

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

No magnetic moments,large massLarge specific heat, Many phases, small or large volume

Magnetic moments! (Curie-Weiss law at high T, Orders antiferromagnetically at low T) Small effective mass (small specific heat coefficient)Large volume

Density functional based electronic structure calculations:All Cm, Am, Pu are magnetic in LDA/GGA LDA: Pu(m~5), Am (m~6) Cm (m~4)

Exp: Pu (m=0), Am (m=0) Cm (m~7.9)Non magnetic LDA/GGA predicts volume up to 30% off. Treating f’s as core overestimates volume of -Pu, reasonable volume for Cm and Am

Can LDA+DMFT predict which material is magnetic and which is not?

Incre

asin

g F’s a

n

SO

C

N Atom F2 F4 F6 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

Very strong multiplet splitting

Atomic multiplet splitting crucial

-Plutonium

0

1

2

3

4

-6 -4 -2 0 2 4 6

DO

S (

stat

es/e

V)

Total DOS

f DOS

Curium

0

1

2

3

4

-6 -4 -2 0 2 4 6ENERGY (eV)

DO

S (

stat

es/e

V)

Total DOS f, J=5/2,jz>0f, J=5/2,jz<0 f, J=7/2,jz>0f, J=7/2,jz<0

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

cond-mat/0611760

-Plutonium

0

1

2

3

4

-6 -4 -2 0 2 4 6

DO

S (

stat

es/e

V)

Total DOS

f DOS

Curium

0

1

2

3

4

-6 -4 -2 0 2 4 6ENERGY (eV)

DO

S (

stat

es/e

V)

Total DOS f, J=5/2,jz>0f, J=5/2,jz<0 f, J=7/2,jz>0f, J=7/2,jz<0

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

Curium

0.0

0.3

0.6

0.9

-6 -4 -2 0 2 4 6ENERGY (eV)

Pro

bab

ility

N =8

N =7

N =6

J=7/

2, =

0

J=5,

=0

J=6,

=0

J=4,

=0

J=3,

=0

J=2,

=0

J=5,

=0

J=2,

=0

J=1,

=0

J=0,

=0

J=6,

=0

J=4,

=0

J=3,

=0

f

f

f

-Plutonium

0.0

0.3

0.6

Pro

bab

ility

N =6

N =5

N =4

JJ=

0, =

0J=

1, =

0J=

2, =

0J=

3, =

0J=

4, =

0J=

5, =

0

J=6,

=1

J=4,

=0

J=5,

=0

J=2,

=0

J=1,

=0

J=2,

=1

J=3,

=1

J=5/

2,

=0

J=7/

2, =

0J=

9/2,

=0

f

f

f

Valence histograms

Density matrix projected to the atomic eigenstates of the f-shell(Probability for atomic configurations)

f electron fluctuates between

theseatomic states on the time scale t~h/Tk(femtosecond

s)One dominant atomic state – ground state of the atom

Pu partly f5 partly f6

core

vale

nce

4d3/2

4d5/2

5f5/2

5f7/2

Exci

tati

ons

from

4d c

ore

to 5

f vale

nce

Electron energy loss spectroscopy (EELS) orX-ray absorption spectroscopy (XAS)

Energy loss [eV]

Core splitting~50eV

4d5/2->5f7/2

4d3/2->5f5/2

Measures unoccupied valence 5f statesProbes high energy Hubbard bands!

hv

Core

split

ting~

50

eV

Probe for Valence and Multiplet structure: EELS&XAS

A plot of the X-ray absorption as a function of energy

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)

A5/2 area under the 5/2 peak

Branching ratio depends on: •average SO coupling in the f-shell <l.s>

•average number of holes in the f-shell nf

B0~3/5

B.T. Tole and G. van de Laan, PRA 38, 1943 (1988)

Similar to optical conductivity:

f-sumrule for core-valence conductivity

One measured quantity B, two unknownsClose to atom (IC regime)

Itinerancy tends to decrease <l.s>

B=B0 - 4/15<l.s>/(14-nf)

[a] G. Van der Laan et al., PRL 93, 97401 (2004).[b] G. Kalkowski et al., PRB 35, 2667 (1987)[c] K.T. Moore et al., PRB 73, 33109 (2006).

LD

A+

DM

FT

2p->5f5f->5f

Pu: similar to heavy fermions (Kondo type conductivity) Scale is large MIR peak at 0.5eVPuO2: typical semiconductor with 2eV gap, charge transfer

Optical conductivity

Pu-Am mixture, 50%Pu,50%Am

Lattice expands -> Kondo collapse is expected

f6: Shorikov, et al., PRB 72, 024458 (2005); Shick et al, Europhys. Lett. 69, 588 (2005). Pourovskii et al., Europhys. Lett. 74, 479 (2006).

Could Pu be close to f6 like Am?

Inert shell can not account for large cv anomalyLarge resistivity!Absence of preadge structure in XAS

Our calculations suggest charge transfer

Pu phase stabilized by shift tomixed valence nf~5.2->nf~5.4

Hybridization decreases, but nf increases,

Tk does not change significantly!

Americium

"soft" phase

f localized

"hard" phase

f bonding

Mott Transition?

f6 -> L=3, S=3, J=0

A.Lindbaum, S. Heathman, K. Litfin, and Y. Méresse, Phys. Rev. B 63, 214101 (2001)

J.-C. Griveau, J. Rebizant, G. H. Lander, and G.KotliarPhys. Rev. Lett. 94, 097002 (2005)

Am within LDA+DMFT

S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)

F(0)=4.5 eV F(2)=8.0 eVF(4)=5.4 eV F(6)=4.0 eV

Large multiple effects:

Am within LDA+DMFT

nf=6

Comparisson with experiment

from J=0 to J=7/2

•“Soft” phase not in local moment regime since J=0 (no entropy)

•"Hard" phase similar to Ce or Pu,

Kondo physics due to hybridization, however, nf still far from Kondo regime

nf=6.2

Exp: J. R. Naegele, L. Manes, J. C. Spirlet, and W. MüllerPhys. Rev. Lett. 52, 1834-1837 (1984)

Theory: S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)

V=V0 Am IV=0.76V0 Am IIIV=0.63V0 Am IV

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

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*, on the Fermi surface

•Non trivial insulator (frustrated magnets)

•Non-local interactions (spin-spin, long range Columb,correlated hopping..)

Present in DMFT:•Quantum time fluctuations

Present in cluster DMFT:•Quantum time fluctuations•Spatially short range quantum fluctuations

Optimal doping: Coherence scale seems

to vanish

Tc

underdoped

overdoped

optimally

scattering at Tc

New continuous time QMC, expansion in terms of hybridization

General impurity problem

Diagrammatic expansion in terms of hybridization +Metropolis sampling over the diagrams

Contains all: “Non-crossing” and all crossing diagrams!Multiplets correctly treated

k

Phys. Rev. B 75, 155113 (2007)

Hubbard model self-energy on imaginary axis, 2x2

Far from Mott transitioncoherent

Low frequency

very different

Close to Mott transitionVery incoherent

Optimal doping in the t-J model

~0.16)has largest low energy

self-energyVery incoherent

at optimal doping

Optimal doping in the Hubbard model (~0.1)has largest low energy

self-energy

Very incoherentat optimal doping

• 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

Conclusions