Correlations Magnetism and Structure across the actinide series

1
Correlations Magnetism and Structure across the
actinide series
G.Kotliar Physics Department and Center for
Materials Theory Rutgers University. CPHT Ecole
Polytechnique, France and CPHT CEA Saclay.
Support -DOE- BES Chaire International de
Recherche Blaise Pascal de lEtat et de la Region
dIlle de France geree par la Fondation de
lEcole Normale. Collaborators S. Savrasov
(UCDavis ) K. Haule (Rutgers) Ji-Hoon Shim
(Rutgers) L. Pourovski (E. Polytechnique).
Discussions M. Fluss J. C Griveaux G Lander
A. Lawson A. Migliori J.Singleton J. Thompson J.
Tobin

• IWOSMA-3 Lyon June 2-3 (2006).

2
Outline

• Brief introduction to the Mott transition
  across the Actinides series and to DMFT.
• The Mott transition from the left.DMFT results
  for Pu. f5 or f6
• The Mott transition from the right. The closed
  shell case. DMFT results for Am .
• S. Savrasov K. Haule and GK PRL(2005).
• The Mott transition from the right. Cm.

3

Smith-Kmetko phase diagram. Mott Transition in
the Actinide Series around Pu Johansen Phil
Mag. 30, 469(1974) .
Early views on the Mott transition. Strongly
discontinuous. Implementation with LDA or LDA
SIC. Approach to the Mott transition, REDUCTION
of the specific heat.
4
Pu phases A. Lawson Los Alamos Science 26,
(2000)
GGA LSDA predicts d Pu to be magnetic with a
large moment ( 5 Bohr) . Experimentally Pu is
not magnetic. Lashley et. al. cond-matt 0410634
PRB 054416(2005). Approach the Mott transition
from the left. (delocalized side).
5
Approach the Mott point from the right (localized
side) Am under pressure
Experimental Equation of State
(after Heathman et.al, PRL 2000)
Mott Transition?
Soft
Hard

• Density functional based electronic structure
  calculations
• Non magnetic LDA/GGA predicts volume 50 off.
• Magnetic GGA corrects most of error in volume but
  gives m6mB
• (Soderlind et.al., PRB 2000).
• Experimentally, Am has non magnetic f6 ground
  state with J0 (7F0)

6
. Mott transition in the open shell case.
Heathman et. al. Science 309,110 (2006)
7
DMFT Cavity Construction. A. Georges and G.
Kotliar PRB 45, 6479 (1992). Happy marriage of
atomic and band physics.
Extremize a functional of the local spectra.
Local self energy.
Reviews A. Georges G. Kotliar W. Krauth and M.
Rozenberg RMP68 , 13, 1996 Gabriel Kotliar and
Dieter Vollhardt Physics Today 57,(2004). G.
Kotliar S. Savrasov K. Haule V. Oudovenko O.
Parcollet and C. Marianetti (to appear in RMP).
8
Mott transition in one band model. Review
Georges et.al. RMP 96
T/W
Phase diagram of a Hubbard model with partial
frustration at integer filling. Rozenberg et.
al. PRL 1995 Evolution of the Local Spectra as a
function of U,and T. Mott transition driven by
transfer of spectral weight Zhang Rozenberg
Kotliar PRL (1993)..
9
Towards ab-initio DMFT.

• Incorporate band structure and orbital degeneracy
  to achieve a realistic description of materials.
  LDADMFT V. Anisimov, A. Poteryaev, M. Korotin,
  A. Anokhin and G. Kotliar, J. Phys. Cond. Mat.
  35, 7359 (1997). Related work PRB 57,6884
  (1998). Derive complex Hamiltonians solve them
  using DMFT.
• LDADMFT photoemission Allows the computation of
  realistic photoemission spectra optics etc.
• Simple concepts. Multiplet structure in the
  Hubbard bands. K space structure in the
  resonance.
• Difficult technical implementation. Various
  impurity solvers. Various basis sets. Various
  orbitals on which correlation are applied.
  Various double counting corrections.

10
Mott transition in open (right) and closed (left)
shell systems. Superconductivity ?
S
S
g T
Tc
Log2J1
???
Uc
J0
U
U
g 1/(Uc-U)
11
Mott Transition in the Actinide Series .
J. Lashley et.al.(2004)
12
Total Energy as a function of volume for Pu W
(ev) vs (a.u. 27.2 ev)
Moment is first reduced by orbital spin moment
compensation. The remaining moment is screened
by the spd and f electrons
(Savrasov, Kotliar, Abrahams, Nature ( 2001) Non
magnetic correlated state of fcc Pu.
Nick Zein Following Aryasetiwan et. al. PRB 70
195104. (2004)
13
DMFT Phonons in fcc d-Pu
( Dai, Savrasov, Kotliar,Ledbetter, Migliori,
Abrahams, Science, 9 May 2003)
(experiments from Wong et.al, Science, 22 August
2003)
14
Why is Epsilon Pu (which is smaller than delta
Pu) stabilized at higher temperatures ??Compute
phonons in bcc structure.
15
Phonon entropy drives the epsilon delta phase
transition

• Epsilon is slightly more delocalized than delta,
  has SMALLER volume and lies at HIGHER energy than
  delta at T0. But it has a much larger phonon
  entropy than delta.
• At the phase transition the volume shrinks but
  the phonon entropy increases.
• Estimates of the phase transition following
  Drumont and G. Ackland et. al. PRB.65, 184104
  (2002) (and neglecting electronic entropy).
  TC 600 K.

16
Double well structure and d Pu

• Qualitative explanation of negative thermal
  expansionLawson, A. C., Roberts J. A., Martinez,
  B., and Richardson, J. W., Jr. Phil. Mag. B, 82,
  1837,(2002). G. Kotliar J.Low Temp. Physvol.126,
  1009 27. (2002)

F(T,V)FphononsFinvar
Natural consequence of the conclusions on the
model Hamiltonian level. We had two solutions at
the same U, one metallic and one insulating.
Relaxing the volume expands the insulator and
contract the metal.
17
Invar model for Pu-Ga. Lawson et. al.Phil.
Mag. (2006) Data fits only if the excited state
has zero stiffness.
18
Alpha and delta Pu Photoemission Spectra
DMFT(Savrasov et.al.) EXP (Arko Joyce Morales
Wills Jashley PRB 62, 1773 (2000))
19
Photoemission studies of Pu. Havela Gouder.
Joyce and Arko. J. Tobin et. al. PHYSICAL REVIEW
B 68, 155109 ,2003
20
Other views on Pu non magnetic 5f6.

• Shorikov Lukoyanov Korotin and Anisimov. PRB
  (2006). LDAU with around the localized limit
  double counting.
• (5f)6 configuration stabilized by a) small Hunds
  rule JH.48 ev and small U2.5 ev.
• Strong sensitivity to the value of JH. JH.5
  critical value instability to magnetic state.

21
Other views on Pu Pu non mangetic 5f6

• Shick A. Drachl V. Havela L. Europhysics Letters
  69, 588 (2005).
• Pourovskii Katsnelson Lichtenstein L Havela T
  Gouder F. Wastin A. Shick V. Drachl and G. Lander
  (2005)
• LDAU with Edc around mean field.
• DMFT Flex.

22
L. Pourovski (unpublished)
Expt gd 60 mJ/Mol K2
23
L. Pourovski (unpublished)
Expt gd 60 mJ/Mol K2
24
Mott Transition in the Actinide Series .
J. Lashley et.al.(2005)
25
K. Haule , Pu- photoemission with DMFT using
(vertex corrected )NCA. nf 5.7
26
High energy spectroscopies theory and expt
(5f)5 Intermediate or jj coupling limit.

• J. Tobin et.al. PRB 68, 155109 (2003) resonant
  photoemission and X ray absortion.
• K Moore et.al. PRL 90, 196404 (2003). Phil Mag
  84,1039 (2004).

27
Conclusion Pu

• I still bet on the (5f)5 Kondo screened
  magnetic configuration. But..
• More work is needed to understand the correct way
  to compute nf in DMFT in order to interpret the
  high energy spectroscopy.
• How to measure, compute , valence in Pu ?

28
Approach the Mott point from the right Am under
pressure
Experimental Equation of State
(after Heathman et.al, PRL 2000)
Mott Transition?
Soft
Hard

• Density functional based electronic structure
  calculations
• Non magnetic LDA/GGA predicts volume 50 off.
• Magnetic GGA corrects most of error in volume but
  gives m6mB
• (Soderlind et.al., PRB 2000).
• Experimentally, Am has non magnetic f6 ground
  state with J0 (7F0)

29
Am equation of state. LDADMFT.New acceleration
technique for solving DMFT equations S. Savrasov
K. Haule G. Kotliar cond-mat. 0507552 (2005)
30
Mott transition in open (right) and closed (left)
shell systems. Superconductivity ? Localized
(5f)6 in L.S coupling or jj coupling ?
S
S
g T
Tc
Log2J1
???
Uc
J0
U
U
g 1/(Uc-U)
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Photoemission spectra using Hubbard I solver and
Sunca . Savrasov Haule and Kotliar cond-mat
0507552 PRL (2006) Hubbard bands width is
determined by multiplet splittings.
33
Resistivity of Am under pressure. J. C. Griveau
et.al. PRL 94, 097002 (2005).
34
Photomission Spectra of Am under pressure.
Sunca. Onset of mixed valence. Savrasov Haule
Kotliar (2005) PRL (2006)
35
Conclusion Am

• Americium undergoes Mott transition under
  pressure. AmIII-AmIV boundary.
• Unusual superconductivity and resistivities.
• Theoretical clue mixed valent due to admixture of
  (5f)7. Unlike Sm..

36
. Mott transition in the open shell case.
Heathman et. al. Science 309,110 (2006)
37
Many theoretical reasons to apply DMFT to Curium.

• Mott transition from the right from an open shell
  configuration. (5f)7
• Mott transition or volume collapse ?
• L.S or jj coupling ?
• Underscreened Kondo lattice ?
• Crucial test for DMFT produce magnetism where
  there is!

38
Hurray et. Al. Physica. B (1980) 217
m2sl
LS coupling L0 S7 m7
jj coupling J7/2 m314
Expt.
39
Conclusions

• Mott transition in Americium and Plutonium. In
  both cases theory (DMFT) and experiment suggest
  gradual more subtle evolution than in earlier
  treatments.
• DMFT Physical connection between spectra and
  structure. Studied the Mott transition open
  and closed shell cases. .
  
• DMFT method under construction, but it already
  gives quantitative results and qualitative
  insights. Interactions between theory and
  experiments.
  
  
• Pu simple picture of the phases. alpha delta
  and epsilon. Interplay of lattice and electronic
  structure near the Mott transition.
• Am Rich physics, mixed valence under pressure .
  Superconductivity near the Mott transition.
  Cm -----work in progress.
• 
  

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P63/mmc 194 a3.490 A c11.311 A Cm(1) 2a
(0,0,0) Cm(2) 2c (1/3,2/3,1/4)
Fm3m (fcc) a4.97 A under 30GPa
43
Antiferromagnetic structures in Cm II (fcc)
AFM (II) AFM ordering along (111)
AFM (I) AFM ordering along (001)
44

• AFM (I) structure of fcc-Cm (II)
• U4.5eV,J0eV
• dEdc 3.7 eV
• No experimental result

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Experiments Needed investigation of the
unoccupied states. BIS, Optics, Raman, Inelastic
XRay, etc.
48
The schematic phase diagram, the Mott (Johansen )
and the Kondo collapse (Allen-Martin) two
scenarios how to tell between the two ?

• J.W. Allen and L.Z. Liu, Phys. Rev. B 46, 5047
  (1992). Kondo impurity model elastic terms.
• DMFT phase diagram of a Hubbard model at integer
  filling, has a region between Uc1(T) and Uc2(T)
  where two solutions coexist. A. Georges G.
  Kotliar W. Krauth and M Rozenberg RMP
  68,13,(1996).
• Coupling the two solutions to the lattice gives a
  phase diagram akin to alpha gamma cerium.
  Majumdar and Krishnamurthy PRL 73 (1994).

49
Photoemissionexperiment

• A. Mc Mahan K Held and R. Scalettar (2002)
• Zoffl et. al (2002)
• K. Haule V. Udovenko S. Savrasov and GK. (2004)
• B. Amadon S. Biermann A. Georges F. Aryastiawan
  cond-mat 0511085

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To resolve the conflict between the Mott
transition and the Kondo volume collapse picture
Turn to Optics! Haule et.al.

• Qualitative idea. The spd electrons have much
  larger velocities, so optics will be much more
  senstive to their behavior.
• See if they are simple spectators (Mott
  transition picture ) or wether a Kondo binding
  unbinding takes pace (Kondo collapse picture).
• General method, bulk probe.

53
Theory Haule et. al. cond-matt 04Expt J.W.
vanderEb PRL 886,3407 (2001)
54
Temperature dependence of the optical
conductivity.
55
Origin of the features.
56
Conclusions 4f materials

• Single site DMFT describes well the
  photoemission, total energy, and optical spectra
  of alpha and gamma cerium.
• Analysis of the DMFT results favors (and
  provides a moder reformulation of) the volume
  collapse transition.
• Combining experimental and theoretical
  spectroscopies, we get new understanding.

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Overview
volumes exp. LDA LDAU
a 28Å3 24.7Å3
g 34.4Å3 35.2Å3

• ? ? -phase (localized)
• High T phase
• Curie-Weiss law (localized magnetic moment),
• Large lattice constant
• Tk around 60-80K

• ? ?-phase (delocalizedKondo-physics)
• Low T phase
• Loss of Magnetism (Fermi liquid Pauli
  susceptibility) - completely screened magnetic
  moment
• Sm
• aller lattice constant
• Tk around 1000-2000K

61
H.Q. Yuan et. al. CeCu2(Si2-x Gex). Am under
pressure Griveau et. al.
Superconductivity due to valence fluctuations ?
62
Approach the Mott point from the right Am under
pressure
Experimental Equation of State
(after Heathman et.al, PRL 2000)
Mott Transition?
Soft
Hard

• Density functional based electronic structure
  calculations
• Non magnetic LDA/GGA predicts volume 50 off.
• Magnetic GGA corrects most of error in volume but
  gives m6mB
• (Soderlind et.al., PRB 2000).
• Experimentally, Am has non magnetic f6 ground
  state with J0 (7F0)

63
Am equation of state. LDADMFT.New acceleration
technique for solving DMFT equations S. Savrasov
K. Haule G. Kotliar cond-mat. 0507552 (2005)
64
Double well structure and d Pu

• Qualitative explanation of negative thermal
  expansion G. Kotliar J.Low Temp. Physvol.126,
  1009 27. (2002)See also A . Lawson et.al.Phil.
  Mag. B 82, 1837

65
A. C. Lawson et. al. LA UR 04-6008F(T,V)Fphonons
Finvar
66
Invar model A. C. Lawson et. al. LA UR 04-6008
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Prediction of the Invar Model
69
DMFT and the Invar Model
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G. Kotliar and S. Savrasov Strongly Correlated
Systems, A. M. Tsvelik Ed. 2001 Kluwer Academic
259-301 . conmat/0208241 S. Y. Savrasov, G.
Kotliar, Phys. Rev. B 69, 245101 (2004)

• Full implementation in the context of a a one
  orbital model. P Sun and G. Kotliar Phys. Rev. B
  66, 85120 (2002). Semiconductors Zein Savrasov
  and Kotliar (2005).
•  

73
G. Kotliar and S. Savrasov Strongly Correlated
Systems, A. M. Tsvelik Ed. 2001 Kluwer Academic
259-301 . conmat/0208241 S. Y. Savrasov, G.
Kotliar, Phys. Rev. B 69, 245101 (2004)

• Full implementation in the context of a a one
  orbital model. P Sun and G. Kotliar Phys. Rev. B
  66, 85120 (2002). Semiconductors Zein Savrasov
  and Kotliar (2005).
•  

74
Next work

• Cm I 4 atoms in unit cell
• Find stable magnetic ground state
• Calculation of magnetic susceptibility.
• Finding proper parameters U, dEdc
• Predict experimental photoemission, optical
  spectrum.
• Change of transition temperature
• U, volume, dEdc etc.

75
Not fully converged result!!
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5fs Mott Transition in the Actinide Series
Johansen Phil Mag. 30, 469(1974) .
Revisit with modern DMFT tools. Savrasov and
Kotliar PRL 84,3760 (2000) .
J. Lashley et.al.(2004)
78
Total Energy as a function of volume for Pu W
(ev) vs (a.u. 27.2 ev)
(Savrasov, Kotliar, Abrahams, Nature ( 2001) Non
magnetic correlated state of fcc Pu.
Zein Savrasov and Kotliar (2005) Following
Aryasetiwan et. al. PRB 70 195104. (2004)
79
Phonon freq (THz) vs q in delta Pu X. Dai et. al.
Science vol 300, 953, 2003
80
Inelastic X Ray. Phonon energy 10 mev, photon
energy 10 Kev.
E Ei - Ef Q ki - kf
81
Expt. Wong et. al. IXRS at Grenoble.
82
Conclusion Pu

• Realistic DMFT calculations provide
• an overall good description of phonon spectra of
  delta Pu.
• Deviations along the (111) direction. Many
  possibilities, fruitful area of research.
• Interplay of theory and experiment. DMFT can
  enhance joint theoretical- experimental advances
  in the field of correlated electron materials.

83
Approach the Mott point from the right Am under
pressure
Experimental Equation of State
(after Heathman et.al, PRL 2000)
Mott Transition?
Soft
Hard

• Density functional based electronic structure
  calculations
• Non magnetic LDA/GGA predicts volume 50 off.
• Magnetic GGA corrects most of error in volume but
  gives m6mB
• (Soderlind et.al., PRB 2000).
• Experimentally, Am has non magnetic f6 ground
  state with J0 (7F0)

84
Am equation of state. LDADMFT.New acceleration
technique for solving DMFT equations S. Savrasov
K. Haule G. Kotliar cond-mat. 0507552 (2005)
85
Resistivity of Am under pressure. J. C. Griveau
Rebizant Lander and Kotliar PRL 94, 097002 (2005).
86
Photoemission spectra using Hubbard I solver
Lichtenstein and Katsnelson, PRB 57, 6884,(1998
), Svane cond-mat 0508311 and Sunca . Savrasov
Haule and Kotliar cond-mat 0507552 Hubbard
bands width is determined by multiplet
splittings.
87
Photomission Spectra of Am under pressure.
Sunca. Onset of mixed valence. Savrasov Haule
Kotliar (2005)
88
Conclusion Am

• Americium undergoes Mott transition under
  pressure. AmIII-AmIV boundary.
• Unusual superconductivity and resistivities.
• Theoretical clue mixed valent due to admixture of
  (5f)7. Unlike Sm..

89
The schematic phase diagram, the Mott (Johansen )
and the Kondo collapse (Allen-Martin) two
scenarios how to tell between the two ?

• J.W. Allen and L.Z. Liu, Phys. Rev. B 46, 5047
  (1992). Kondo impurity model elastic terms.
• DMFT phase diagram of a Hubbard model at integer
  filling, has a region between Uc1(T) and Uc2(T)
  where two solutions coexist. A. Georges G.
  Kotliar W. Krauth and M Rozenberg RMP
  68,13,(1996).
• Coupling the two solutions to the lattice gives a
  phase diagram akin to alpha gamma cerium.
  Majumdar and Krishnamurthy PRL 73 (1994).

90
How good is the local approximation ??? Exact in
infinite dimensions , very good also in one
dimension!
Cellular DMFT Kotliar et. al. PRL (2001) Test
in 1d Hubbard model Capone Civelli Sarma
Castellani and Kotliar PRB 69,195105 (2004)
91
Pu HAS SEVEN STABLE PHASES AT LOW PRESSURE
0 388 473
583 725 753
913 T(K)
g distorted diamond
a monoclinic
d fcc
d distorted bcc
e bcc
b monoclinic
L liquid
Non magnetic LDA-GGA understimates the volume of
d Pu by about 25 .DFT-GGA succesfully predicts
the volume of all phases of plutonium. However it
also predicts that all phases of plutonium are
magnetic in dsiagreement with experiment.
92
.

• LDADMFT , Hubbard U matrix and Double Counting
  Correction Matrix Edc.
• Functionals of Wloc and Gloc, simultaneous
  determination of U and Edc.
• Chitra and Kotliar PRB 2001
• Recent test on semiconductors, agree well with
  experiments, with clusters as small as 3
  coordination spheres. Zein Savrasov Kotliar
  cond-mat 2005
• Approximate Impurity solvers for Hubbard I, PT
  in hybridization, SUNCA, rational interpolative
  solvers, QMC. Compromise between speed and
  accuracy.

93
Phonon freq (THz) vs q in delta Pu X. Dai et. al.
Science vol 300, 953, 2003
94
Inelastic X Ray. Phonon energy 10 mev, photon
energy 10 Kev.
E Ei - Ef Q ki - kf
95

• Functional formulation (Chitra and Kotliar 2000)
  Phys. Rev. B 62, 12715 (2000). Self consistent
  determination of electronic structure. Full
  implementation S. Savrasov G. Kotliar (2001-2005)
  . Phys. Rev. B 69, 245101 (2004). Frequency
  dependent generalization of the Kohn Sham
  potential, whose role is to give the exact
  local Greens function. Frequency dependent
  Kohn-Sham like equations can be derived by
  extremizing a functional which gives the total
  energy. Application to Pu. Savrasov et al. Nature
  (2001)
• Llinear response phonon spectra Savrasov and
  Kotliar Phys. Rev. Lett. 90, 056401 (2003). .
  Speed up of the method. DMFT quality at LDA
  speed. Reduction of the DMFT equations, to Kohn
  Sham equations with additional orbitals. Total
  energy of complicated structures. Savrasov Haule
  and Kotliar Am PRL cond-mat. 0507552 (2005).

96
Conclusion Pu

• Realistic DMFT calculations provide
• an overall good description of phonon spectra of
  delta Pu.
• Deviations along the (111) direction. Many
  possibilities, fruitful area of research.
• Interplay of theory and experiment. DMFT can
  enhance joint theoretical- experimental advances
  in the field of correlated electron materials.

97
Contrasting View.

• Anisimov.
• Havela.
• PlutoniumAm Mixtures.

98
More recent work.

• Line of research.
• Connection with Van Der Laand.

99

• How to define the valence of Plutonium
• Correctly . New Tools.

100
High energy spectroscopies, experiment and
theory.