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Gabriel Kotliar and Center for Materials Theory

Strong Correlation Effects in the Actinide Series. Gabriel Kotliar and Center for Materials Theory. PT Colloquium LANL May 3 rd 2007. $upport : NSF -DMR DOE-Basic Energy Sciences Collaborators: K. Haule and J. Shim Ref: Nature 446, 513, (2007). 1.

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Gabriel Kotliar and Center for Materials Theory

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  1. Strong Correlation Effects in the Actinide Series Gabriel Kotliar and Center for Materials Theory PT Colloquium LANL May 3rd 2007 $upport : NSF -DMR DOE-Basic Energy Sciences Collaborators: K. Haule and J. Shim Ref: Nature 446, 513, (2007) 1

  2. Electrons in a Solid:the Standard Model Band Theory: electrons as waves. Landau Fermi Liquid Theory. M. VanSchilfgaarde n band index, e.g. s, p, d,,f Rigid bands , optical transitions , thermodynamics, transport……… • Quantitative Tools. Density Functional Theory • Kohn Sham (1964) Static Mean Field Theory. Kohn Sham Eigenvalues and Eigensates: Excellent starting point for perturbation theory in the screened interactions (Hedin 1965) 2

  3. Strong Correlation Problem:where the standard model fails • Fermi Liquid Theory works but parameters can’t be computed in perturbation theory. • Fermi Liquid Theory does NOT work . Need new concepts to replace of rigid bands ! • Partially filled d and f shells. Competition between kinetic and Coulomb interactions. • Breakdown of the wave picture. Need to incorporate a real space perspective (Mott). • Non perturbative problem. 4

  4. 5f elements: actinide series Deocalisation Localization 1.4K 0.4K 0.9K 0.8K 52K 25K 52K s/c AF FM

  5. Delocalization Localization in Actinides Mott Transition d Pu a a d after G. Lander, Science (2003).

  6. Basic Questions • How does the electron go from being localized to itinerant. • How do the physical properties evolve. • How to bridge between the microscopic information (atomic positions) and experimental measurements. • New concepts, new techniques….. DMFT simplest approach to meet this challenge

  7. Phases of Pu A. Lawson. Los Alamos Science

  8. Small amounts of impurities stabilize d phase. A. Lawson Los Alamos Science

  9. Anomalous Resistivity Maximum metallic resistivity

  10. Specific heat and susceptibility. Pu is non magnetic J. Lashley

  11. Standard model FAILS in the late actinides • Predicts Pu and Am to be magnetic, with a large moment. (about 5 mB) • Paramagnetic DFT understimates volume of delta Pu by 25 % • Many proposals to explain why Pu is non magnetic. Mixed level model Zwicknagl and Fulde , Erickson Balatzki Wills , (5f)4 conf. LDA+U (Shick, Anisimov) (5f)6 conf • Cannot account for anomalous transport and thermodynamics

  12. DMFT Spectral Function Photoemission and correlations • Probability of removing an electron and transfering energy w=Ei-Ef, and momentum k f(w) A(w, K) M2 e • Weak Correlation • Strong Correlation n n Angle integrated spectral function 8

  13. DMFT cavity construction. A. Georges and G. Kotliar PRB 45, 6479 (1992). Happy marriage of atomic and band physics. Extremize functional of A(w) 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 (RMP 2006).

  14. Dynamical Mean Field Theory • Weiss field is a function. Multiple scales in strongly correlated materials. • Exact large coordination (Metzner and Vollhardt 89) . • Not restricted to single site-CDMFT. • Extension to real materials DFT+DMFT. Input slater integrals. Functionals of density and spectra. Review Kotliar et. al. RMP (2006) 12

  15. 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. Nick Zein Following Aryasetiwan et. al. PRB 70 195104. (2004)

  16. 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.

  17. 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) 21 (experiments from Wong et.al, Science, 22 August 2003)

  18. The “DMFT-valence” in the late actinides. Time scale of the fluctuations. Ef*

  19. Photoemission Gouder , Havela PRB 2002, 2003

  20. Photoemission Spectra[ Shim. Haule,GK Nature (2007)] alpa->delta volume collapse transition F0=4.5,F2=7.15 F0=4,F2=6.1

  21. Photoemission and Mixed valence in Pu [Ground State> =a[f5 (spd)3> +b [f6 (spd)2> <f6 ]----.<f7] <f5 ]----<f6] <f4 ]----<f5]

  22. Approach the Mott point from the right Am under pressure Experimental Equation of State (after Heathman et.al, PRL 2000) Mott Transition? “Soft” “Hard”

  23. Am equation of state. LDA+DMFT.New acceleration technique for solving DMFT equations S. Savrasov K. Haule G. Kotliar cond-mat. 0507552 (2005) Superconductivity ambient pressure J. L. Smith and R. G. Haire, Science 200, 535 (1978).

  24. Mott transition in open (right) and closed (left) shell systems. Superconductivity ? Application to Am ? S S g T Tc Log[2J+1] ??? Uc J=0 U U g ~1/(Uc-U)

  25. Resistivity of Am under pressure. J. C. Griveau et.al. PRL 94, 097002 (2005).

  26. Photoemission spectra using Hubbard I solver and Sunca . [Savrasov Haule and Kotliar cond-mat 0507552 PRL (2006)] Hubbard bands width is determined by multiplet splittings. Expt Negele, Theory Savrasov Haule

  27. Photomission Spectra of Am under pressure. Sunca. Onset of mixed valence. Savrasov Haule Kotliar (2005) PRL (2006)

  28. Conclusions • Pu and Am are unique strongly correlated elements. Unique mixed valence. • They require, new concepts, new computational methods, new algorithms, DMFT ! • Interplay of theory and experiment. • Many extensions of DMFT are possible, many strongly correlated compounds, research opportunity in correlated materials.

  29. Prospects for Extensions and Applications to More Complex Heavy Fermion Systems • More complicated crystal structures, more atoms per unit cell. 115’s , alpha Pu…… • Non local physics. Heavy fermion quantum criticality. a) Local Quantum Criticality scenario of Q. Si and collaborators. Nature 413 (2001) 804. Single site EDMFT b) Cluster Quantum Multicriticality. L. DeLeo and GK. Requires 2 impurity Kondo model for its description. • Better interface with electronic structure

  30. Conclusion Am • Americium undergoes Mott transition under pressure. [AmIII-AmIV] boundary. • Unusual superconductivity and resistivities. • Theoretical clue mixed valent due to admixture of (5f) upon application of pressure. • Realizes Mott transition from the insulating side, towards a close shell configuration..

  31. W110 =2/3<l.s> and banching ratio Moore and van der Laan, Ultramicroscopy 2007.

  32. X Ray Absortion and Branching ratio:theory ShimHaule and Kotliar Expt. K. Moore G. Van der Laan G. Haire M. Wall and A. Schartz

  33. . Mott transition in the open shell case. Heathman et. al. Science 309,110 (2006) Approach the Mott transition from the right.

  34. 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

  35. K.Haule and J. Shim 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.

  36. Conclusion • A Few References …… • A.Georges, G. K., W. Krauth and M. J. Rozenberg, Reviews of . Modern Physics 68, 13 (1996). • G. K, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C.A. Marianetti, RMP 78, 865-951, (2006). • G. K and D. Vollhardt Physics Today, Vol 57, 53 (2004). 29

  37. W110 =2/3<l.s> and banching ratio Moore and van der Laan, Ultramicroscopy 2007.

  38. J. Tobin et.al. PRB 72,085109 (2005)K. Moore et.al. XAS white lines branching ratio and EELS: Pu is closer to jj coupling

  39. 2/3<l.s> in the late actinides [DMFT results: K. Haule and J. Shim ] See the expt. work of K. Moore G. Van der Laan G. Haire M. Wall and A. Schartz Am H2

  40. The “DMFT-valence” in the late actinides. Fluctuation time scale Ef*-1

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