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Electronic Structure of Elemental Plutonium: A Dynamical Mean Field Perspective (DMFT)

Electronic Structure of Elemental Plutonium: A Dynamical Mean Field Perspective (DMFT). Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University. MRS Boston 2003. Collaborators, References. S. Savrasov and G. Kotliar PRL 84 3670 (2000).

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Electronic Structure of Elemental Plutonium: A Dynamical Mean Field Perspective (DMFT)

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  1. Electronic Structure of Elemental Plutonium: A Dynamical Mean Field Perspective (DMFT) Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University MRS Boston 2003

  2. Collaborators, References 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). S. Murthy Rutgers Ph.D Thesis (2004). Introduction: basic questions and alternative theories. Dynamical Mean Field Theory (DMFT). Alpha and Delta Pu. Both phases are strongly correlated and differ in only in the distribution of one electron spectral weight. Delta and Epsilon Pu differ dramatically in their phonon spectra. Epsilon Pu is strongly anharmonic. Outlook. Support: Dynamical mean field method NSF. Actinides DOE Basic Energy Sciences

  3. Pu phases Small amounts of Ga stabilize the d phase (A. Lawson LANL) Los Alamos Science,26, (2000). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  4. Americium under pressure (Lindbaum et. al. PRB 2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  5. 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 30% lower than experiment This is the largest discrepancy ever known in DFT based calculations. More conventional electronic structure approaches THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  6. 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 Alternative approach to delta Pu, Wills et. al. (5f)4 core+ 1f(5f)in conduction band. [SIC-LDA] DFT Studies THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

  8. A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)] Lichtenstein Katsnelson and Kotliar cond-mat-0211076 K. Held et.al. , Psi-k Newsletter 56 (April 2003). Dynamical Mean Field Theory (Reviews) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  9. 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 Phys. Rev. B 45, 6497, 1992]. Atom in a medium = Quantum impurity model. Solid in a frequency dependent potential. 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 GKPhys. Rev. B62, 12715 (2000). and S. Savrasov cond-matt 0308053]. Allows computation of total energy AND one electron spectra. Dynamical Mean Field Theory THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

  11. Electronic structure. LMTO’s ASA , LMTO full potential. Crystal field splitting in the self energies is neglected. W(r,r’) (w) replaced by U on the f electrons. 4 ev. No multiplet splittings. Non perturbative treatment of spin orbit coupling. Approximate Impurity Solver. Interpolative Perturbation Theory and Hubbard I. Approximations THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  12. W (ev) vs (a.u. 27.2 ev) N.Zein G. Kotliar and S. Savrasov THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  13. What is the dominant atomic configuration? • 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 realistic calculations, Mtot 0 is quenched by crystal Fields and Kondo effect. Moment lives at high q • Contrast Am:(5f)6 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  14. Pu: DMFT total energy vs volume Savrasov Kotliar and Abrahams Nature 410,793 (2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  15. Qualitative explanation of negative thermal expansion Double well structure and d Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  16. LDA+DMFT calculations for fcc Americium S. Murthy and G. K(2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  17. 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 earlier studies of the Mott transition 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

  18. Alpha and delta Pu Photoemission Spectra DMFT(Savrasov et.al.) EXP (Arko Joyce Morales Wills Jashley PRB 62, 1773 (2000)) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  19. 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 and near the Mott limit. a Pu and delta Pu differ electronically by the distribution of spectral weight in the resonance and the Hubbard band. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  20. Anomalous Resistivity PRL 91,061401 (2003) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  21. Pu is NOT MAGNETIC, alpha and delta have comparable susceptibility and specifi heat. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  22. Proximity to the Mott Transition. Redistribution of spectral weight. Simultaneous description of band physics and atomic physics. All captured by DMFT in the approximations used.! Important Physics THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  23. Pu phases Small amounts of Ga stabilize the d phase (A. Lawson LANL) Los Alamos Science,26, (2000). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  24. The high temperature phase, (epsilon) is body centered cubic, and has a smaller volume than the (fcc) delta phase. What drives this phase transition? LDA+DMFT functional computes total energies opens the way to the computation of phonon frequencies in correlated materials (S. Savrasov and G. Kotliar 2002). Combine linear response and DMFT. The delta –epsilon transition THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

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

  27. Good agreement over the majority of the Brillouin zone, is significant. The phonon frequencies depend on the forces acting on the atoms as a result of their displacement. Ability to compute forces, is a first step to derive potentials, and do molecular dynamics. Discrepancies along (111) are significant. Role of temperature ? Improve the impurity solver ? Non local corrections, and deviations from DMFT. Comparison of theory and experiment. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  28. C11 (GPa) C44 (GPa) C12 (GPa) C'(GPa) Theory 34.56 33.03 26.81 3.88 Expt 36.28 33.59 26.73 4.78 Elastic constants theory (LDA+DMFT with a Hubbard1 solver, Dai et. al. and experiments,( Letbetter and Moment ). Large c44/c’ ratio. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  29. 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

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

  31. 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 G. 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

  32. Transverse Phonon along (0,1,1) in epsilon Pu in self consistent Born approximation. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  33. Negative thermal expansion of Pu revisited. • The distortion described by C' is very soft, nearly like a liquid, . C' measures the rigidity against the volume conserving tetragonal deformation. This is in fact the deformation from fcc towards a bcc along a Bain path. Previous LDA+ U study [Bouchet et. al. ] and our DMFT study show that the total energy difference between  phase and  phases is quite small and is around 1000K. Soft behavior along the Bain path.  Pu can sample the bcc structure, which has lower volume by the thermal fluctuation along Bain path. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  34. 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. The Mott transition across the actinide series [ B. Johansson Phil Mag. 30,469 (1974)] concept has finally been worked out! .We learned how to think about this unusual situation using DMFT, Weiss fields, local spectral functions etc. Insights into the anomalous properties of Pu THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  35. DMFT produces non magnetic state, around a fluctuating (5f)^5 configuration with correct volume the qualitative features of the photoemission spectra, quasiparticle resonance and Hubbard band, 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 account for delta-epsilon transition. Anomalous phonons in epsilon Pu. Calculations can be refined, include multiplets, better impurity solvers, frequency dependent U’s, electronic entropy. User friendly interfaces. Conclusions THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  36. Model of Wills et al. : 4 (5f) electrons are core-like and 1 is delocalized. DMFT picture: all the 5 (5f) electrons are equivalent, they are localized over short time scales and itinerant over long time scales resulting in Hubbard band and quasiparticle resonance in the spectra. Both pictures require strong correlations in the delta phase but how to differentiate between them experimentally ? Alpha phase. Resonant Photoemission (J. Tobin et. al. ) Probe unoccupied states. Upper Hubbard band, BIS. Optics. X ray absortion. Etc.. Fermi Surface Probes. Is Luttinger theorem obeyed ? Experiments and Theory are Needed to test the different pictures of the elctronic structure of PU THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  37. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  38. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  39. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  40. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  41. Is the softening along the 110 direction in delta Pu, temperature dependent ? Is the discrepancy between theory and experiments the result of not including the resonance in the phonon calculation or the result of not including non local corrections ? Open questions ? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  42. J. Tobin et. al. PHYSICAL REVIEW B 68, 155109 ,2003 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  43. A. Arko et. al. PRB 15. (2000), 1773. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  44. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  45. Acknowledgements: Development of DMFT Collaborators: E. Abrahams,V. Anisimov, R. Chitra, V. Dobrosavlevic, X. Dai, D. Fisher, A. Georges, K. Haule H. Kajueter, W.Krauth, E. Lange, A. Lichtenstein, G. Moeller, Y. Motome, G. Palsson, A. Poteryaev, 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

  46. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

  48. 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

  49. LDA+DMFT functional F Sum of local 2PI graphs with local U matrix and local G THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  50. Static limit of the LDA+DMFT functional , with FatomFHF reduces to the LDA+U functional of Anisimov Andersen and Zaanen. Crude approximation. Reasonable in ordered Mott insulators. Short time picture of the systems. Total energy in DMFT can be approximated by LDA+U with an effective U . Extra screening processes in DMFT produce smaller Ueff. ULDA+U < UDMFT LDA+DMFT and LDA+U THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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