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Plutonium Futures Asilomar July 9-13 (2006).

Explore valence changes and Mott transitions in late actinides using Dynamical Mean Field Theory (DMFT). Investigate interactions between electronic and structural properties, magnetism, phase transformations across the actinide series.

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Plutonium Futures Asilomar July 9-13 (2006).

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  1. Correlations Magnetism and Structure across the actinide series : a Dynamical Mean Field Theory Perspective G.Kotliar Physics Department and Center for Materials Theory Rutgers University. . Collaborators E. Abrahams K. Haule Ji-Hoon Shim A. Toropova (Rutgers) S. Savrasov (UCDavis ) L. Pourovski (E. Polytechnique). Plutonium Futures Asilomar July 9-13 (2006). Support: DOE- BES DOE-NNSA . Expts. : M. Fluss J. C Griveaux G Lander A. Lawson A. Migliori J.Singleton J.Smith J Thompson J. Tobin

  2. Outline • Experimental motivation • Brief introduction to DMFT ideas. • Valence changes across the late actinides a SUNCA-DMFT study [ K. Haule J. Shim] • Interplay of electronic and structural properties in phase transformations . • Conclusion

  3. . Mott transition in the open shell case. Heathman et. al. Science 309,110 (2006)

  4. Pu phases: A. Lawson Los Alamos Science 26, (2000) Experimentally Pu is not magnetic. No trace of ordered or low frequency fluctuating local moments. [Lashley et. al. cond-matt 0410634] PRB 054416(2005). Approach the Mott transition from the left. (delocalized side).

  5. Curium is magnetic Hurray et.al. Physica. B (1980) 217 m=2S+L LS coupling L=0 S=7 m=7 jj coupling J=7/2 m=3+1=4 Expt monent . is closer to L S coupling

  6. J. Tobin et.al. PRB 72,085109 (2005) XAS and EELS

  7. DMFT Cavity Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992). Happy marriage of atomic and band physics. Extremize a functional of the local spectra. Local self energy. Reviews: A. Georges G. Kotliar W. Krauth and M. Rozenberg RMP68 , 13, 1996 Gabriel Kotliar and Dieter Vollhardt Physics Today 57,(2004). G. Kotliar S. Savrasov K. Haule V. Oudovenko O. Parcollet and C. Marianetti (to appear in RMP).

  8. Mott transition in one band model. Review Georges et.al. RMP 96 T/W Phase diagram of a Hubbard model with partial frustration at integer filling. [Rozenberg et. al. PRL 1995] Evolution of the Local Spectra as a function of U,and T. Mott transition driven by transfer of spectral weight Zhang Rozenberg Kotliar PRL (1993)..

  9. Applications to actinides • S. Savrasov G.K and E. Abrahams [neglect multiplets] energy and spectra IPT imp. Solver • Phonons [Dai et.al.] [Hubbard I imp solver] • Could not address the existence of magentically ordered states. • Recent review see G. Kotliar S. Savrasov K. Haule V. Oudovenko O. Parcollet and C. Marianetti to appear in RMP. cond-mat • Recent progress : K. Haule SUNCA imp. solver, full multiplet structure and Kondo physics compete on equal footing. Can consider DMFT eqs. in different ordered phases.

  10. Curie-Weiss Tc Trends in Actinides alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=7.15 F0=4.5,F2=8.11 Curium has large magnetic moment and orders antif Pu does is non magnetic.

  11. <l.s> in the late actinides [DMFT results: K. Haule and J. Shim ]

  12. The “DMFT-valence” in the late actinides

  13. Outline • Experimental motivation • Brief introduction to DMFT ideas. • Valence changes across the late actinides a SUNCA-DMFT study [ K. Haule J. Shim] • Interplay of electronic and structural properties in phase transformations . • Conclusion

  14. Minimum in melting curve and divergence of the compressibility at the Mott endpoint

  15. C11 (GPa) C44 (GPa) C12 (GPa) C'(GPa) Theory 34.56 33.03 26.81 3.88 Experiment 36.28 33.59 26.73 4.78 DMFT Phonons in fcc d-Pu ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et.al, Science, 22 August 2003)

  16. Why is Epsilon Pu (which is smaller than delta Pu) stabilized at higher temperatures ??Compute phonons in bcc structure.

  17. Phonon entropy drives the epsilon delta phase transition • 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.

  18. Total Energy as a function of volume for Pu W(ev) vs (a.u. 27.2 ev) Moment is first reduced by orbital spin moment compensation. The remaining moment is screened by the spd and f electrons (Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu.

  19. Double well structure and d Pu Qualitative explanation of negative thermal expansion[Lawson, A. C., Roberts J. A., Martinez, B., and Richardson, J. W., Jr. Phil. Mag. B, 82, 1837,(2002). G. Kotliar J.Low Temp. Physvol.126, 1009 27. (2002)] F(T,V)=Fphonons+Finvar Natural consequence of the conclusions on the model Hamiltonian level. We had two solutions at the same U, one metallic and one insulating. Relaxing the volume expands the insulator and contract the metal.

  20. “Invar model “ for Pu-Ga. Lawson et. al.Phil. Mag. (2006) Data fits if the excited state has zero stiffness.

  21. Conclusion • DMFT studies of electrons and lattice displacements. • Valence changes and transfers of spectral weight. [ Consistent picture of Pu-Am-Cm]. • Alpha and delta Pu, screened (5f)^5 configuration. Differ in the degree of screening. Different views [ Pu non magnetic (5f)^6, Pu magnetic ] • Magnetism and defects. • Important role of phonon entropy in phase transformations .

  22. LS vs jj coupling in Am and Cm

  23. Other views on Pu non magnetic 5f6. • Shorikov Lukoyanov Korotin and Anisimov. PRB (2006). LDA+U with around the localized limit double counting. • (5f)^6 configuration stabilized by a) small Hunds rule JH=.48 ev and small U=2.5 ev. • Strong sensitivity to the value of JH. JH=.5 critical value instability to magnetic state.

  24. Other views on Pu: Pu non mangetic 5f6 • Shick A. Drachl V. Havela L. Europhysics Letters 69, 588 (2005). • Pourovskii Katsnelson Lichtenstein L Havela T Gouder F. Wastin A. Shick V. Drachl and G. Lander (2005) • LDA+U with Edc around mean field. +DMFT Flex.

  25. L. Pourovski (unpublished) Expt gd 60 mJ/Mol K2

  26. Expt gd 60 mJ/Mol K2 L. Pourovski (unpublished)

  27. Mott Transition in the Actinide Series . J. Lashley et.al.(2005)

  28. K. Haule , Pu- photoemission with DMFT using (vertex corrected )NCA. nf =5.7

  29. High energy spectroscopies theory and expt (5f)5 Intermediate or jj coupling limit. • J. Tobin et.al. PRB 68, 155109 (2003) resonant photoemission and X ray absortion. • K Moore et.al. PRL 90, 196404 (2003). Phil Mag 84,1039 (2004).

  30. J. Tobin et.al.

  31. Cm No quasiparticle peak at EF Hubbard bands at ~4eV and ~-5eV intermediate between jj and LS Pu Clear quasiparticle peak at EF Hubbard bands at ~3eV and ~-1eV closer to jj scheme than Cm Cm & Pu

  32. What is the dominant atomic configuration? Local moment? • 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

  33. Magnetic moment • 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).

  34. Curie-Weiss Tc Trends in Actinides alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=7.15 Same transition in Am under pressure F0=4.5,F2=8.11 Curium has large magnetic moment and orders antif.

  35. The “DMFT-valence” in the late actinides

  36. Many theoretical reasons to apply DMFT to Curium. • Mott transition from the right from an open shell configuration. (5f)7 • Mott transition or volume collapse ? • L.S or jj coupling ? • Underscreened Kondo lattice ? • Crucial test for DMFT: produce magnetism where there is!

  37. Hurray et. Al. Physica. B (1980) 217 m=2s+l LS coupling L=0 S=7 m=7 jj coupling J=7/2 m=3+1=4 Expt.

  38. Conclusions • Mott transition in Americium and Plutonium. In both cases theory (DMFT) and experiment suggest gradual more subtle evolution than in earlier treatments. • DMFT: Physical connection between spectra and structure. Studied the Mott transition open and closed shell cases. . • DMFT: method under construction, but it already gives quantitative results and qualitative insights. Interactions between theory and experiments. • Pu: simple picture of the phases. alpha delta and epsilon. Interplay of lattice and electronic structure near the Mott transition. • Am: Rich physics, mixed valence under pressure . Superconductivity near the Mott transition. Cm -----work in progress.

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

  40. Outline • 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

  41. Conclusions • 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. • Calculations can and should be refined and extended.

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