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Elemental Plutonium: Electrons at the Edge The Mott transition across the actinide series.

Elemental Plutonium: Electrons at the Edge The Mott transition across the actinide series. Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University. Santa Fe November 2003. Outline , Collaborators, References. Los Alamos Science,26, (2000).

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Elemental Plutonium: Electrons at the Edge The Mott transition across the actinide series.

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  1. Elemental Plutonium: Electrons at the EdgeThe Mott transition across the actinide series. Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University Santa Fe November 2003

  2. Outline , Collaborators, References Los Alamos Science,26, (2000). S. Savrasov and G. Kotliar PRL 84 3670 (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). Physical properties of plutonium. Dynamical Mean Field Theory (DMFT) DMFT study of elemental plutonium. Conclusions

  3. Pu in the periodic table actinides THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  4. 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. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  5. Mott transition in the actinide series (Smith-Kmetko phase diagram) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  6. Phases of Pu (A. Lawson LANL) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  7. Small amounts of Ga stabilize the d phase (A. Lawson LANL) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  8. Elastic Deformations 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’ ~ 7largest shear anisotropy of any element. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  9. The electron in a solid: wave picture Sommerfeld Bloch, Landau: Periodic potential, waves form bands , k in Brillouin zone . [Density functional theory ] Landau: Interactions renormalize parameters. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  10. Anomalous Resistivity Maximum metallic resistivity THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  11. Pu Specific Heat THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  12. Electronic specific heat(J Lashley et.al. LANL) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  13. Localized model of electron in solids. (Peierls 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

  14. Specific heat and susceptibility. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  15. Density Functional Theory and Kohn Sham Reference System. • Total energy is minimizes 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). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  16. 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% Delta phase of Plutonium: Problems with LDA THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  17. 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 Alternative models:1) For the delta phase a model with 4 5f electrons localized and 1 electron as itinerant was proposed by Wills et. al, in the spirit of SIC corrected LDA. This model produces correct volume of delta. 2) Strong random potential. (B. Cooper). . DFT Studies of Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  18. Basic idea: reduce the quantum many body problem to a one site or a cluster of sites, in a medium of non interacting electrons obeying a self consistency condition.[A. Georges and GK 1992] Basic idea: instead of using functionals of the density, use more sensitive functionals of the one electron spectral function. [density of states for adding or removing particles in a solid, measured in photoemission] [GK R. Chitra and S. Savrasov 2000,2002] Dynamical Mean Field Theory THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  19. DMFT Reference System A. Georges, G. Kotliar (1992) Phys. Rev. B 45, 6497 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  20. One Particle Local Spectral Function and Angle Integrated Photoemission 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

  21. Simple interface with electronic structure. Treat the spd electrons within LDA (static self energy approximated by xc potential). Treat the f electrons with DMFT. LDA+DMFT. Extensions. Treat the electric field and the electronic fields using DMFT. [E-DMFT] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  22. 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, by making systematic truncations in the range of the BK functional. 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 ) DMFT functional formulation. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  23. Canonical Phase Diagram of the Localization Delocalization Transition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  24. Pressure Driven Mott transition THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  25. More recent work, organics, Limelette et. al. PRL 91,061401 (2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  26. 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. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  27. One electron spectra near the Mott transition. Transfer of Spectral Weight. [Zhang Rozenberg and Kotliar 93] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  28. DMFT studies of elemental Plutonium THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  29. 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 L=5, S=5/2, J=5/2, Mtot=Ms=mB gJ =.7 mB Crystal fields G7 +G8 GGA+U estimate ML=-3.9 Mtot=1.1 (Savrasov GK 2000) This bit is quenches by the f and spd electrons Neutron Scattering in a field (Lander) What is the dominant atomic configuration? Local moment? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  30. Pu: DMFT total energy vs Volume (Savrasov Kotliar and Abrahams 2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  31. Qualitative explanation of negative thermal expansion Sensitivity to impurities which easily raise the energy of the a -like minimum. Double well structure and d Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  32. Generalized phase diagram T U/W Structure, bands, orbitals THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  33. Minimum in melting curve and divergence of the compressibility at the Mott endpoint THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  34. Cerium THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  35. 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. Photoemission Technique THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  36. Lda vs Exp Spectra THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  37. Pu Spectra DMFT(Savrasov) EXP (Arko Joyce Morales Wills Jashley PRB 62, 1773 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  38. Alpha and delta Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  39. Alpha phase is also a correlated metal. It differs from delta in the relative weight of the resonance and the Hubbard band. Consistent with resistivity and specific heat measurements. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  40. 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. Short distance behavior of the elastic moduli. Phonon Spectra THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  41. Phonon freq (THz) vs q in delta Pu X. Dai et. al. Science vol 300, 953, 2003 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  42. Inelastic X Ray. Phonon energy 10 mev, photon energy 10 Kev. E = Ei - Ef Q =ki - kf THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  43. Expt. Wong et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  44. Expts’ Wong et. al. Science 301. 1078 (2003) Theory Dai et. al. Science 300, 953, (2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  45. C’=(C11-C12)/2 = 4.78 GPa C’=3.9 GPa C44= 33.59 GPa C44=33.0 GPa C44/C’ ~ 7 Largest shear anisotropy in any element! C44/C’ ~ 8.4 Shear anisotropy. Expt. vs Theory THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  46. 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 delta –epsilon transition THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  47. Epsilon Plutonium. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  48. Phonon frequency (Thz ) vs q in epsilon Pu. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  49. Epsilon is slightly more delocalized than delta, has SMALLER volume and lies at HIGHER energy than delta at T=0. 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 Ackland et. al. PRB.65, 184104 (2002); (and neglecting electronic entropy). TC ~ 600 K. Phonon entropy drives the epsilon delta phase transition THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  50. Phonons epsilon THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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