Elemental Plutonium: Electrons at the Edge

1. Elemental Plutonium: Electrons at the Edge Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University SFU September 2003

2. 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

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. Electronic Physics of Pu 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’ ~ 6largest 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 . 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 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

13. 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

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

15. (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 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

16. Kohn Sham system THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

17. 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

18. 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 . DFT Studies of a Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

19. 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

20. 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 ) Dynamical Mean Field Theory THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

21. Mean-Field : Classical vs Quantum Classical case Quantum case A. Georges, G. Kotliar (1992) Phys. Rev. B 45, 6497 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

23. 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

24. One electron spectra near the Mott transition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

25. 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 What is the dominant atomic configuration? Local moment? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

27. 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

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

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

30. Cerium THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

31. 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

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

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

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

35. 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. Phonon Spectra THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

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

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

39. Wong et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

40. Expts’ Wong et. al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

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

43. Phonons epsilon THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

44. 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. Conclusions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

45. 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, …….. Conclusions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

46. 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, …. Conclusions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

47. 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. What do we want from materials theory? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

48. 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. Some new insights into the funny properties of Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

49. 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 ] Quantitative calculations THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

50. 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.