Elemental Plutonium: a strongly correlated metal

1. Elemental Plutonium: a strongly correlated metal Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University Collaborators: S. Savrasov (NJIT) X. Dai( Rutgers )

2. Physics of Pu The Problem: This? Or this? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

3. Evolution of the electronic structure between the atomic limit and the band limit in an open shell situation. The “”in between regime” is ubiquitous central them in strongly correlated systems, gives rise to interesting physics. Example Mott transition across the actinide series [ B. Johansson Phil Mag. 30,469 (1974)] Revisit the problem using a new insights and new techniques from the solution of the Mott transition problem within dynamical mean field theory in the model Hamiltonian context. Use the ideas and concepts that resulted from this development to give physical qualitative insights into real materials. Turn the technology developed to solve simple models into a practical quantitative electronic structure method . For me the problem is :THIS. The Mott Phenomena THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

4. Introduction: some Pu puzzles. Results: Minimum of the melting curve, Delta Pu: Most probable valence, size of the local moment Equilibrium Volume. Photoemission Spectral. Stabilization of Epsilon Pu: Conclusions Outline 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. Small amounts of Ga stabilize the d phase (A. Lawson LANL) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

7. C’=(C11-C12)/2 4.78 C44= 33.59 19.70 C44/C’ ~ 8 Largest shear anisotropy in any element! LDA Calculations (Bouchet) C’= -48 Shear anisotropy. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

8. DFT in the LDA or GGA is a well established tool for the calculation of ground state properties. Many studies (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) give an equilibrium volume of the d phaseIs 35% lower than experiment This is the largest discrepancy ever known in DFT based calculations. Plutonium Puzzles THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

9. 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% 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 Alterantive approach Wills et. al. (5f)4 core+ 1f(5f)in conduction band. DFT Studies THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

11. Anomalous Resistivity THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

12. Pu is NOT MAGNETIC THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

14. U/W is not so different in alpha and delta The specific heat of delta Pu, is only twice as big as that of alpha Pu. The susceptibility of alpha Pu is in fact larger than that of delta Pu. The resistivity of alpha Pu is comparable to that of delta Pu. Problems with the conventional viewpoint of a Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

15. Introduction: some Pu puzzles. DMFT , qualitative aspects of the Mott transition from model Hamiltonians DMFT as an electronic structure method. DMFT results for delta Pu, and some qualitative insights. Conclusions Outline THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

16. 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. We have solved “the hydrogen atom problem” of strongly correlated electron systems. What do we want from materials theory? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

17. Evolution of the Spectral Function with Temperature Anomalous transfer of spectral weight connected to the proximity to the Ising Mott endpoint (Kotliar Lange and Rozenberg Phys. Rev. Lett. 84, 5180 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

19. Coexistence regions between localized and delocalized spectral functions. k diverges at generic Mott endpoints Qualitative phase diagram in the U, T , m plane (two band Kotliar Murthy Rozenberg PRL (2002). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

20. Mott transition in layered organic conductors S Lefebvre et al. Ito et.al, Kanoda’s talk Bourbonnais talk Magnetic Frustration THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

21. Ultrasound study of Fournier et. al. (2002) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

23. Divergence of the compressibility at the Mott transition endpoint. Rapid variation of the density of the solid as a function of pressure, in the localization delocalization crossover region. Slow variation of the volume as a function of pressure in the liquid phase Elastic anomalies, more pronounced with orbital degeneracy. Minimum of the melting point THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

25. Cerium THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

26. Introduction: some Pu puzzles. DMFT , qualitative aspects of the Mott transition in model Hamiltonians. DMFT as an electronic structure method. DMFT results for delta Pu, and some qualitative insights. Conclusions Outline THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

27. Solving the DMFT equations • Wide variety of computational tools (QMC,ED….)Analytical Methods • Extension to ordered states. • Review: A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

28. Realistic DMFT loop THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

29. LDA+DMFT-outer loop relax Edc U DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

30. Outer loop relax Edc G0 Impurity Solver Imp. Solver: Hartree-Fock G,S U SCC DMFT LDA+U THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

31. Introduction: some Pu puzzles. DMFT , qualitative aspects of the Mott transition in model Hamiltonians. DMFT as an electronic structure method. Realistic DMFT and Plutonium Conclusions Outline THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

33. LDA+U bands. (Savrasov GK ,PRL 2000). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

34. 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). Magnetic moment THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

36. 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

37. 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). Is the natural consequence of the model Hamiltonian phase diagram once electronic structure is about to vary. Dynamical Mean Field View of Pu(Savrasov Kotliar and Abrahams, Nature 2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

38. Describes only the Hubbard bands. No QP states. Single well structure in the E vs V curve. (Savrasov and Kotliar PRL) Comments on the HF static limit THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

40. Spectral Evolution at T=0 half filling full frustration X.Zhang M. Rozenberg G. Kotliar (PRL 1993) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

42. Comparaison with LDA+U THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

43. Spectra Method E vs V Summary LDA LDA+U DMFT

44. 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

45. Energy vs Volume THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

46. Energy vs Volume THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

47. Success story : Density Functional Linear Response Tremendous progress in ab initio modelling of lattice dynamics & electron-phonon interactions has been achieved (Review: Baroni et.al, Rev. Mod. Phys, 73, 515, 2001) (Savrasov, PRB 1996)

48. Results for NiO: Phonons Solid circles – theory, open circles – exp. (Roy et.al, 1976) DMFT Savrasov and GK PRL 2003

49. DMFT for Mott insulators THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

50. Phonon freq (THz) vs q in delta Pu (Dai et. al. ) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS