Elemental Plutonium Electrons at the Edge Gabriel Kotliar
Elemental Plutonium: Electrons at the Edge Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University SFU September 2003
Outline , Collaborators, References Plutonium Puzzles n. Solid State Theory, Old and New (DMFT) n. Results n. Conclusions n 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, Vol 300, 954 (2003).
Pu in the periodic table actinides THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Pu is famous because of its nucleus. Fission: Pu 239 absorbs a neutron and breaks apart into pieces releasing energy and more neutrons. Pu 239 is an alpha emitter, making it into a most toxic substance. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Mott transition in the actinide series (Smith Kmetko phase diagram) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Electronic Physics of Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Small amounts of Ga stabilize the d phase (A. Lawson LANL) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Elastic Deformations Uniform compression: Dp=-B Volume conserving DV/Vdeformations: F/A=c 44 Dx/L F/A=c’ Dx/L In most cubic materials the shear does not depend strongly on crystal orientation, fcc Al, c 44/c’=1. 2, in Pu C 44/C’ ~ 6 largest shear anisotropy of any element. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
The electron in a solid: wave picture Sommerfeld Bloch, Landau: Periodic potential, waves form bands , k in Brillouin zone. Landau: Interactions renormalize parameters , THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Anomalous Resistivity Maximum metallic resistivity THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Pu Specific Heat THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Electronic specific heat THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Localized model of electron in solids. (Mott)particle picture. Solid=Collection of atoms 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
Specific heat and susceptibility. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
(Spin) Density Functional Theo n n n n 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
Kohn Sham system THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Delta phase of Plutonium: Problems with LDA o n n 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% THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
DFT Studies of a Pu n 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
One Particle Local Spectral Fun e Probability of removing an electron and transfering energy w=Ei-Ef, f(w) A(w) M 2 n Probability of absorbing an electron and transfering energy w=Ei-Ef, (1 -f(w)) A(w) M 2 n Theory. Compute one particle greens function and use spectral function. n n n e THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Dynamical Mean Field Theory n n n 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
Mean-Field : Classical vs Quantum Classical case Phys. Rev. B 45, 6497 Quantum case THE STATE UNIVERSITY OF NEW JERSEY RUTGERS A. Georges, G. Kotliar (1992)
Canonical Phase Diagram of the Localization Delocalization Transition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
DMFT has bridged the gap be n 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. n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
One electron spectra near the Mott transition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
What is the dominant atomic configuration? Local moment? n n n n Snapshots of the f electron Dominant configuration: (5 f)5 Naïve view Lz=-3, -2, -1, 0, 1 ML=-5 m. B S=5/2 Ms=5 m. B 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
Pu: DMFT total energy vs Volume (Savrasov Kotliar and Abrahams 2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
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. RUTGERS THE STATE UNIVERSITY OF NEW JERSEY
Generalized phase diagram T Structure, bands, orbital s U/W THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Minimum in melting curve and divergence of the compressibility at the Mott endpoint THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Cerium THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Photoemission Technique Density of states for removing (adding ) a particle to the sample. n Delocalized picture, it should resemble the density of states, (perhaps with some satellites). n Localized picture. Two peaks at the ionization and affinity energy of the atom. n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Lda vs Exp Spectra THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Pu Spectra DMFT(Savrasov) EXP (Arko Joyce Morales Wills Jashley PRB 62, 1773 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Alpha and delta Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Phonon Spectra n n n 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
Phonon freq (THz) vs q in delta Pu X. Dai et. al. Science vol 300, 953, 2003 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Inelastic X Ray. Phonon energy 10 mev, photon energy 10 Kev. E = Ei - Ef Q =ki - kf THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Expt. Wong et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Wong et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Expts’ Wong et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Epsilon Plutonium. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Phonon frequency (Thz ) vs q in epsilon Pu. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Phonons epsilon THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Conclusions n n n 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
Conclusions n n n 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
Conclusions n n n DMFT produces non magnetic state, around a fluctuating (5 f)^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
What do we want from materials theory? New concepts , qualitative ideas n Understanding, explanation of existent experiments, and predictions of new ones. n Quantitative capabilities with predictive power. n Notoriously difficult to achieve in strongly correlated materials. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Some new insights into the funny properties of Pu n n 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
Quantitative calculations n n n 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 do ? [ See epsilon Pu spectra ] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
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, Vol 300, 954 (2003).
THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
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: ONR 4 -2650 Work on Pu: DOE DE-FG 02 -99 ER 45761 and LANL subcontract No. 03737 -001 -02 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
The delta –epsilon transition n 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
Phonon entropy drives the epsilon delta phase transition n n 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. n THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Results for Ni. O: Phonons Solid circles – theory, open circles – exp. (Roy et. al, 1976) DMFT Savrasov and GK PRL 2003
n n 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
LDA+DMFT functional F Sum of local 2 PI graphs with local U matrix and local G THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
The electron in a solid: particle picture. n Ni. O, Mn. O, …Array of atoms is insulating if a>>a. B. Mott: correlations localize the electron 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
Summary Spectra Method LDA+U DMFT E vs V
For future reference. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Shear anisotropy. n C’=(C 11 -C 12)/2 n C 44= 33. 59 n 4. 78 19. 70 C 44/C’ ~ 6 Largest shear anisotropy in any element! THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Electronic specific heat THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
DMFT BOX THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Anomalous Resistivity Maximum metallic resistivity 200 mohm cm THE STATE UNIVERSITY OF NEW JERSEY RUTGERS
Magnetic moment n n n L=5, S=5/2, J=5/2, Mtot=Ms=m. B g. J =. 7 m. B Crystal fields G 7 +G 8 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
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