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