collaborators: ji-hoon shim, g.kotliar kristjan haule, physics department and center for materials...
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![Page 1: Collaborators: Ji-Hoon Shim, G.Kotliar Kristjan Haule, Physics Department and Center for Materials Theory Rutgers University Uncovering the secrets of](https://reader030.vdocuments.site/reader030/viewer/2022032703/56649d375503460f94a10146/html5/thumbnails/1.jpg)
Collaborators: Ji-Hoon Shim, G.Kotliar
Kristjan Haule, Physics Department and
Center for Materials TheoryRutgers University
Uncovering the secrets of Actinides using Dynamical
Mean Field Theory.
SCES 07 - Houston
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Standard theory of solidsStandard theory of solids
Band Theory: electrons as waves: Rigid band picture: En(k) versus k
Landau Fermi Liquid Theory applicable
Very powerful quantitative tools: LDA,LSDA,GWVery powerful quantitative tools: LDA,LSDA,GW
Predictions:
•total energies,
•stability of crystal phases
•optical transitions
M. Van SchilfgardeM. Van Schilfgarde
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• Fermi Liquid Theory does NOT work . Need new concepts to replace rigid bands picture!
• Breakdown of the wave picture. Need to incorporate a real space perspective (Mott).
• Non perturbative problem.
Strong correlation – Strong correlation –
Standard theory failsStandard theory fails
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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):
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Delocalization Localization
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Basic questionsBasic questions
• How to bridge between the microscopic information (atomic positions) and experimental measurements.
• New concepts, new techniques….. DMFT simplest approach to meet this challenge
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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 problemof an atom in a conduction band, which obeys DMFT 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(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).
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Trivalent metals with nonbonding f shell
f’s participate in bonding
Partly localized, partly delocalized
Volume of actinides
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Anomalous Resistivity
Maximum metallic resistivity:
=e2 kF/h
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Dramatic increase of specific heat
Heavy-fermion behavior in an element
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Am doping -> lattice expansionExpecting unscreened moments!
Does not happen!
NO Magnetic moments!
Pauli-like from melting to lowest T
No curie Weiss up to 600K
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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
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Standard theory of solids:DFT:
All Cm, Am, Pu are magnetic in LSDA/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.In atomic limit, Am non-magnetic, but Pu magnetic with spin ~5B
Can LDA+DMFT account for anomalous properties of actinides?
Can it predict which material is magnetic and which is not?
Many proposals to explain why Pu is non magnetic: Mixed level model (O. Eriksson, A.V. Balatsky, and J.M. Wills) (5f)4 conf. +1itt. LDA+U, LDA+U+FLEX (Shick, Anisimov, Purovskii) (5f)6 conf.
Cannot account for anomalous transport and thermodynamics
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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 -> splits Kondo peak
Used as input to DMFT calculation - code of R.D. Cowan
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-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
J.H. Shim, K.H., G. Kotliar, Nature 446, 513 (2007).
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-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
Magnetization of Cm:
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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,g =
0
J=5,
g =0
J=6,
g =0
J=4,
g =0
J=3,
g =0
J=2,
g =0
J=5,
g =0
J=2,
g =0
J=1,
g =0
J=0,
g =0
J=6,
g =0
J=4,
g =0
J=3,
g =0
f
f
f
-Plutonium
0.0
0.3
0.6
Pro
bab
ility
N =6
N =5
N =4
JJ=
0,g =
0J=
1,g =
0J=
2,g =
0J=
3,g =
0J=
4,g =
0J=
5,g =
0
J=6,
g =1
J=4,
g =0
J=5,
g =0
J=2,
g =0
J=1,
g =0
J=2,
g =1
J=3,
g =1
J=5/
2, g
=0
J=7/
2,g =
0J=
9/2,
g =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
(femtoseconds)
One dominant atomic state – ground state of the atom
Pu partly f5 partly f6
Probabilities:
•5 electrons 80%
•6 electrons 20%
•4 electrons <1%
J.H. Shim, K. Haule, G. Kotliar, Nature 446, 513 (2007).
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Gouder , Havela PRB
2002, 2003
Fingerprint of atomic multiplets - splitting of Kondo peak
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Photoemission and valence in Pu
|ground state > = |a f5(spd)3>+ |b f6 (spd)2>
f5<->f6
f5->f4
f6->f7
Af(
)
approximate decomposition
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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 &
4d5/2->5f5/2
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
B=B0 - 4/15<l.s>/(14-nf)
Branching ration B=A5/2/(A5/2+A3/2)
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LD
A+
DM
FT
2/3<l.s>=-5/2(B-B0) (14-nf)
One measured quantity B, two unknownsClose to atom (IC regime)
Itinerancy tends to decrease <l.s>
[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).[d] K.T. Moore et al., PRL in press
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Specific heat
Purovskii et.al. cond-mat/0702342:
f6 configuration gives smaller gin Pu than Pu
(Shick, Anisimov, Purovskii) (5f)6 conf
Could Pu be close to f6 like Am?
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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
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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).
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!
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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)
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Am within LDA+DMFT
S. Y. Savrasov, K.H., 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:
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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 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.H., and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)
V=V0 Am IV=0.76V0 Am IIIV=0.63V0 Am IV
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• Pu and Am (under pressure) are unique strongly correlated elements. Unique mixed valence.
• They require, new concepts, new computational methods, new algorithms, DMFT!
• Many extensions of DMFT are possible, many strongly correlated compounds, research opportunity in correlated materials.
Conclusion
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Many strongly correlated compounds await the explanation:
CeCoIn5, CeRhIn5, CeIrIn5
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Photoemission of CeIrIn5
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LDA+DMFT DOS
Comparisonto experiment
Photoemission of CeIrIn5
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Optics of CeIrIn5
LDA+DMFT
K.S. Burch et.al., cond-mat/0604146
Experiment:
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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
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• 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
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• How does the electron go from being localized to itinerant.
• How do the physical properties evolve.
• How to bridge between the microscopic information (atomic positions) and experimental measurements.
• New concepts, new techniques….. DMFT simplest approach to meet this challenge
Basic questions
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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).
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Singlet-type Mott state (no entropy) goes mixed valence under pressure-> Tc enhanced (Capone et.al, Science 296, 2364 (2002))
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• DMFT in actinides and their compounds (Spectral density functional approach). Examples: – Plutonium, Americium, Curium. – Compounds: PuAmObservables:– Valence, Photoemission, and Optics, X-ray
absorption
OverviewOverview
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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)
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Overview of actinides
Two phases of Ce, and gwith 15% volume difference
25% increase in volume between and phase
Many phases
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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