Elemental Plutonium: Electrons at the Edge

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Elemental Plutonium Electrons at the Edge

• Gabriel Kotliar
• Physics Department and
• Center for Materials Theory
• Rutgers University

SFU September 2003

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Outline , Collaborators, References

• Plutonium Puzzles
• Solid State Theory, Old and New (DMFT)
• Results
• Conclusions

Los Alamos Science,26, (2000) S. Savrasov and G.
Kotliar Phys. Rev. Lett. 84, 3670-3673, (2000).
S.Savrasov G. Kotliar and E. Abrahams, Nature
410, 793 (2001). X. Dai,S. Savrasov, G.
Kotliar,A. Migliori, H. Ledbetter, E. Abrahams 
Science,  Vol300, 954 (2003).

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Pu in the periodic table
actinides
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Pu is famous because of its nucleus.
Fission Pu239 absorbs a neutron and breaks apart
into pieces releasing energy and more neutrons.
Pu239 is an alpha emitter, making it into a
most toxic substance.
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Mott transition in the actinide series (Smith
Kmetko phase diagram)
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Electronic Physics of Pu
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Small amounts of Ga stabilize the d phase (A.
Lawson LANL)
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Elastic Deformations
Uniform compressionDp-B DV/V
Volume conserving deformations
F/Ac44 Dx/L
F/Ac Dx/L
In most cubic materials the shear does not depend
strongly on crystal orientation,fcc Al,
c44/c1.2, in Pu C44/C 6 largest shear
anisotropy of any element.
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The electron in a solid wave picture
Sommerfeld

Bloch, Landau Periodic potential, waves form
bands , k in Brillouin zone .
Landau Interactions renormalize parameters ,
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Anomalous Resistivity
Maximum metallic resistivity
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Pu Specific Heat
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Electronic specific heat
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Localized model of electron in solids.
(Mott)particle picture.SolidCollection of atoms
L, S, J

• Think in real space , solid collection of atoms
• High T local moments, Low T spin-orbital order

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Specific heat and susceptibility.
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(Spin) Density Functional Theory.

• Focus on the density (spin density ) of the
  solid.
• Total energy is obtained by minimizing a
  functional of the density (spin density).
• Exact form of the functional is unknown but good
  approximations exist. (LDA, GGA)
• In practice, one solves a one particle
  shrodinger equation in a potential that depends
  on the density.
• A band structure is generated (Kohn Sham
  system).and in many systems this is a good
  starting point for perturbative computations of
  the spectra (GW).
• Works exceedingly well for many systems.
• W. Kohn, Nobel Prize in Chemistry on October 13,
  1998 for its development of the
  density-functional theory

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Kohn Sham system
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Delta phase of Plutonium Problems with LDA

• Many studies and implementations.(Freeman,
  Koelling 1972)APW methods, ASA and FP-LMTO
  Soderlind et. Al 1990, Kollar et.al 1997,
  Boettger et.al 1998, Wills et.al. 1999).all give
  an equilibrium volume of the d phase Is 35
  lower than experiment this is the largest
  discrepancy ever known in DFT based calculations.
• LSDA predicts magnetic long range (Solovyev
  et.al.) Experimentally d Pu is not magnetic.
• If one treats the f electrons as part of the core
  LDA overestimates the volume by 30

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DFT Studies of a Pu

• DFT in GGA predicts correctly the volume of the a
  phase of Pu, when full potential LMTO (Soderlind
  Eriksson and Wills) is used. This is usually
  taken as an indication that a Pu is a weakly
  correlated system
• .

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One Particle Local Spectral Function and Angle
Integrated Photoemission
e

• Probability of removing an electron and
  transfering energy wEi-Ef,
• f(w) A(w) M2
• Probability of absorbing an electron and
  transfering energy wEi-Ef,
• (1-f(w)) A(w) M2
• Theory. Compute one particle greens function and
  use spectral function.

n
n
e
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Dynamical Mean Field Theory

• Focus on the local spectral function A(w) of the
  solid.
• Write a functional of the local spectral function
  such that its stationary point, give the energy
  of the solid.
• No explicit expression for the exact functional
  exists, but good approximations are available.
• The spectral function is computed by solving a
  local impurity model. Which is a new reference
  system to think about correlated electrons.
• Ref A. Georges G. Kotliar W. Krauth M.
  Rozenberg. Rev Mod Phys 68,1 (1996) .
  Generalizations to realistic electronic
  structure. (G. Kotliar and S. Savrasov 2001-2002 )

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Mean-Field Classical vs Quantum
Classical case
Quantum case
A. Georges, G. Kotliar (1992)
Phys. Rev. B 45, 6497
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Canonical Phase Diagram of the Localization
Delocalization Transition.
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DMFT has bridged the gap between band theory and
atomic physics.

• Delocalized picture, it should resemble the
  density of states, (perhaps with some additional
  shifts and satellites).
• Localized picture. Two peaks at the ionization
• and affinity energy of the atom.

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One electron spectra near the Mott transition.
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What is the dominant atomic configuration? Local
moment?

• Snapshots of the f electron
• Dominant configuration(5f)5
• Naïve view Lz-3,-2,-1,0,1
• ML-5 mB
• S5/2 Ms5 mB
• Mtot0
• More refined estimates ML-3.9 Mtot1.1
• This bit is quenches by the f and spd electrons

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Pu DMFT total energy vs Volume (Savrasov
Kotliar and Abrahams 2001)
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Double well structure and d Pu

• Qualitative explanation
  of negative thermal expansion
• Sensitivity to impurities which easily raise the
  energy of the a -like minimum.

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Generalized phase diagram
T
U/W
Structure, bands, orbitals
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Minimum in melting curve and divergence of the
compressibility at the Mott endpoint
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Cerium
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Photoemission Technique

• Density of states for removing (adding ) a
  particle to the sample.
• Delocalized picture, it should resemble the
  density of states, (perhaps with some
  satellites).
• Localized picture. Two peaks at the ionization
• and affinity energy of the atom.

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Lda vs Exp Spectra
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Pu Spectra DMFT(Savrasov) EXP (Arko Joyce Morales
Wills Jashley PRB 62, 1773 (2000)
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Alpha and delta Pu
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Phonon Spectra

• Electrons are the glue that hold the atoms
  together. Vibration spectra (phonons) probe the
  electronic structure.
• Phonon spectra reveals instablities, via soft
  modes.
• Phonon spectrum of Pu had not been measured until
  recently.

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Phonon freq (THz) vs q in delta Pu X. Dai et. al.
Science vol 300, 953, 2003
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Inelastic X Ray. Phonon energy 10 mev, photon
energy 10 Kev.
E Ei - Ef Q ki - kf
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Expt. Wong et. al.
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Wong et. al.
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Expts Wong et. al.
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Epsilon Plutonium.
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Phonon frequency (Thz ) vs q in epsilon Pu.
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Phonons epsilon
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Conclusions

• Pu is a unique ELEMENT, but by no means unique
  material. It is one among many strongly
  correlated electron system, materials for which
  neither the standard model of solids, either for
  itinerant or localized electrons works well.
• The Mott transition across the actinide series
  B. Johansson Phil Mag. 30,469 (1974) concept has
  finally been worked out!
• They require, new concepts, new computational
  methods, new algorithms, DMFT provides all of the
  above, and is being used in many other problems.

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Conclusions

• Constant interplay between theory and experiment
  has lead to new advances.
• General anomalies of correlated electrons and
  anomalous system specific studies, need for a
  flexible approach. (DMFT).
• New understanding of Pu. Methodology applicable
  to a large number of other problems, involving
  correlated electrions, thermoelectrics,
  batteries, optical devices, memories, high
  temperature superconductors, ..

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Conclusions

• DMFT produces non magnetic state, around a
  fluctuating (5f)5 configuraton with correct
  volume the qualitative features of the
  photoemission spectra, and a double minima
  structure in the E vs V curve.
• Correlated view of the alpha and delta phases of
  Pu. Interplay of correlations and electron
  phonon interactions (delta-epsilon).
• Calculations can be refined in many ways,
  electronic structure calculations for correlated
  electrons research program, MINDLAB, .

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What do we want from materials theory?

• New concepts , qualitative ideas
• Understanding, explanation of existent
  experiments, and predictions of new ones.
• Quantitative capabilities with predictive
• power.
• Notoriously difficult to achieve in strongly
  correlated materials.

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Some new insights into the funny properties of Pu

• Physical anomalies, are the result of the unique
  position of Pu in the periodic table, where the f
  electrons are near a localization delocalization
  transition. We learned how to think about this
  unusual situation using spectral functions.
• Delta and Alpha Pu are both strongly correlated,
  the DMFT mean field free energy has a double
  well structure, for the same value of U. One
  where the f electron is a bit more localized
  (delta) than in the other (alpha). Negative
  thermal expansion, multitude of phases.

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Quantitative calculations

• Photoemission spectra,equilibrium volume, and
  vibration spectra of delta. Good agreement with
  experiments given the approximations made.Many
  systematic improvements are needed.
• Work is at the early stages, only a few
  quantities in one phase have been considered.
• Other phases? Metastability ? Effects of
  impurities? What else, do electrons at the edge
  of a localization localization do ? See epsilon
  Pu spectra

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Collaborators, Acknowledgements References

• Collaborators S. Savrasov ( Rutgers-NJIT)
• X. Dai ( Rutgers), E. Abrahams (Rutgers), A.
  Migliori (LANL),H Ledbeter(LANL).
• Acknowledgements G Lander (ITU) J Thompson(LANL)
• Funding NSF, DOE, LANL.

Los Alamos Science,26, (2000) S. Savrasov and G.
Kotliar Phys. Rev. Lett. 84, 3670-3673, (2000).
S.Savrasov G. Kotliar and E. Abrahams, Nature
410, 793 (2001). X. Dai,S. Savrasov, G.
Kotliar,A. Migliori, H. Ledbetter, E. Abrahams 
Science,  Vol300, 954 (2003).

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Acknowledgements Development of DMFT
Collaborators V. Anisimov, R. Chitra, V.
Dobrosavlevic, X. Dai, D. Fisher, A. Georges,
H. Kajueter, W.Krauth, E. Lange, A.
Lichtenstein, G. Moeller, Y. Motome, G.
Palsson, M. Rozenberg, S. Savrasov, Q. Si, V.
Udovenko, I. Yang, X.Y. Zhang
Support NSF DMR 0096462 Support
Instrumentation. NSF DMR-0116068 Work on Fe
and Ni ONR4-2650 Work on Pu DOE
DE-FG02-99ER45761 and LANL subcontract No.
03737-001-02
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The delta epsilon transition

• The high temperature phase, (epsilon) is body
  centered cubic, and has a smaller volume than the
  (fcc) delta phase.
• What drives this phase transition?
• Having a functional, that computes total energies
  opens the way to the computation of phonon
  frequencies in correlated materials (S. Savrasov
  and G. Kotliar 2002)

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Phonon entropy drives the epsilon delta phase
transition

• Epsilon is slightly more metallic than delta, 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 neglecting the
• Electronic entropy TC 600 K.

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Results for NiO Phonons
Solid circles theory, open circles exp. (Roy
et.al, 1976)
DMFT Savrasov and GK PRL 2003
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• Two models of a solid. Itinerant and localized.
• Mott transition between the two.
• Spectral function differentiates between the two
  phases.
• Insert the phase diagram that I like.

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LDADMFT functional
F Sum of local 2PI graphs with local U matrix and
local G
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The electron in a solid particle picture.

• NiO, MnO, Array of atoms is insulating if
  agtgtaB. Mott correlations localize the electron
• e_ e_ e_
  e_

• Superexchange

• Think in real space , solid collection of atoms
• High T local moments, Low T spin-orbital order

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Summary
Spectra
Method
E vs V
LDA
LDAU
DMFT
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For future reference.
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Shear anisotropy.

• C(C11-C12)/2 4.78
• C44 33.59 19.70
• C44/C 6 Largest shear anisotropy in any
  element!

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Electronic specific heat
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DMFT BOX
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Anomalous Resistivity
Maximum metallic resistivity 200 mohm cm
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Magnetic moment

• L5, S5/2, J5/2, MtotMsmB gJ .7 mB
• Crystal fields G7 G8
• GGAU estimate (Savrasov and Kotliar 2000)
  ML-3.9 Mtot1.1
• This bit is quenched by Kondo effect of spd
  electrons DMFT treatment
• Experimental consequence neutrons large
  magnetic field induced form factor (G. Lander).