- 39 Views
- Uploaded on
- Presentation posted in: General

Elemental Plutonium: Electrons at the Edge

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Elemental Plutonium: Electrons at the Edge

Gabriel Kotliar

Physics Department and

Center for Materials Theory

Rutgers University

SFU September 2003

Outline , Collaborators, References

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).

Plutonium Puzzles

Solid State Theory, Old and New (DMFT)

Results

Conclusions

actinides

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Uniform compression:Dp=-B DV/V

Volume conserving deformations:

F/A=c44Dx/L

F/A=c’ Dx/L

In most cubic materials the shear does not depend strongly on crystal orientation,fcc Al, c44/c’=1.2, in Pu C44/C’ ~ 6largest shear anisotropy of any element.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Sommerfeld

Bloch, Landau: Periodic potential, waves form bands , k in Brillouin zone .

Landau: Interactions renormalize parameters,

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Maximum metallic resistivity

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

L, S, J

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

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

- 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

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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 phaseIs 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%

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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

.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

e

- Probability of removing an electron and transfering energy w=Ei-Ef,
f(w) A(w) M2

- Probability of absorbing an electron and transfering energy w=Ei-Ef,
(1-f(w)) A(w) M2

- Theory. Compute one particle greens function and use spectral function.

n

n

e

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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 )

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Classical case

Quantum case

A. Georges, G. Kotliar (1992)

Phys. Rev. B 45, 6497

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

- 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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Snapshots of the f electron

Dominant configuration:(5f)5

Naïve view Lz=-3,-2,-1,0,1

ML=-5 mB

S=5/2 Ms=5 mB

Mtot=0

More refined estimates ML=-3.9 Mtot=1.1

This bit is quenches by the f and spd electrons

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Qualitative explanation of negative thermal expansion

Sensitivity to impurities which easily raise the energy of the a -like minimum.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

T

U/W

Structure, bands, orbitals

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

E = Ei - Ef

Q =ki - kf

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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, ……..

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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, ….

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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 ]

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Collaborators, Acknowledgements References

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).

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Results for NiO: Phonons

Solid circles – theory, open circles – exp. (Roy et.al, 1976)

DMFT Savrasov and GK PRL 2003

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.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

F Sum of local 2PI graphs with local U matrix and local G

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

- NiO, MnO, …Array of atoms is insulating if a>>aB. 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

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Spectra

Method

E vs V

Summary

LDA

LDA+U

DMFT

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

C’=(C11-C12)/2 4.78

C44= 33.59 19.70

C44/C’ ~ 6 Largest shear anisotropy in any element!

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

Maximum metallic resistivity 200 mohm cm

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

L=5, S=5/2, J=5/2, Mtot=Ms=mB gJ =.7 mB

Crystal fields G7 +G8

GGA+U estimate (Savrasov and Kotliar 2000) ML=-3.9 Mtot=1.1

This bit is quenched by Kondo effect of spd electrons [ DMFT treatment]

Experimental consequence: neutrons large magnetic field induced form factor (G. Lander).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS