Understanding and predicting properties of f electron materials using DMFT

1. Understanding and predicting properties of f electron materials using DMFT Duality and DMFT. Ab initio vs model hamiltonians. Physical Pictures vs Computations. Duality and DMFT. Ab initio vs model hamiltonians. Physical Pictures vs Computations.

2. Outline Very brief introduction to the context. What is the basic physical picture of elemental Pu and its compounds ? Photoemission. The Quasiparticle Multiplet concept and its realization in PuSe and delta Pu. [with Chuck Yee, K. Haule ] Determination of the Valence thru XAS and LDA+DMFT [with Jihoon Shim and K. Haule] Corroborating the valence count with LDA+DMFT polarized neutron form factors. [ with M. Pezzoli and K Haule ] Where is the Pu magnetic moment ? specific heat under pressure, and Pu-Am mixtures. Conclusions

3. Delocalization Localization: Actinides Moreover, it has been measured in both and -Pu, and the value of in the phase (43 and 64 mJ K-2 mol-1 in -Pu, stabilized by Ga and Al, respectively [8, 25]; in the range of 35-55 mJ K-2 mol-1 in the Pu92Am8 alloy [26]) is substantially larger than in -Pu (17 mJ K-2 mol-1 [25]).Moreover, it has been measured in both and -Pu, and the value of in the phase (43 and 64 mJ K-2 mol-1 in -Pu, stabilized by Ga and Al, respectively [8, 25]; in the range of 35-55 mJ K-2 mol-1 in the Pu92Am8 alloy [26]) is substantially larger than in -Pu (17 mJ K-2 mol-1 [25]).

4. The standard model of solids fails near Pu Spin Density functional theory: Pu , Am, magnetic, large orbital and spin moments. Experiments (Lashley et. al. 2005 ) Susceptibility, specific heat in a field, neutron quasi-elastic and inelastic scattering, …..… d Pu is non magnetic. No static or fluctuating moments. Muon Spin Resonance. Heffner et al. (2006) . Very stringent limits on the magnetic moment < 10-3µB

5. Physical pictures of the dual nature of the f electron in Pu 

6. A. Georges and G. Kotliar PRB 45, 6479 (1992).

7. Spectral Function-spectral weights Valence Histogram

8. Pu as a correlated non magnetic f metal. Early LDA + DMFT results.

9. LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Limitations of early implementations were removed in the third generation of LDA+DMFT methods (see for ex. K. Haule K. Kim and C. Yee Phys. Rev. B 81, 195107 (2010) for a detailed description ) . Still LDA+DMFT is not a fully ab-initio method, yet. Depends on parameters, F0, F2, F4, F6 (F0 “screened U”) and Edc ( close to that of localized limit ). More important depends on the choice of orbital or projector.[besides one electron stuff + imp solver ]

10. Where is the magnetic boundary ?Where is the localization delocalization boundary ? What parameters control its location ? Basic Issues : Is the localization delocalization transition in the actinide series described in the multiorbital Hubbard picture ( U/tff ) or the Anderson lattice picture (U, V, Ef ) ?

11. A. Toropova, C. Marianetti K. Haule and G. K . PRB (2006).Established the validity of the Anderson lattice point of view !! The Multiorbital Hubbard picture is not valid!

13. LDA+DMFT determines the Localization and Magnetic Boundary. Importance of Jhunds.

15. Questions. Does the triple peak structure visible or not in delta Pu ? What is its origin ? Is it part of the Quasiparticle Peak (Coherent contribution) ? Is the ordinary multiplet fingerprint in the photoemission spectra. Part of the incoherent spectral weight (Hubbard-like bands). Connection with mixed valence. A lot of discussion and controversy in the literature. No real theory of this effect. Adress this issue in the context of the Plutonium Chalcogenide materials, where all the photoemission groups agree its present and clearly visible. Mixed valent and elastic anomalies in Pu chalcogenides. (Wachter). Other LDA+DMFT work on Pu chalcogenides Suzuki and Openeer[ PRB 80, 161103R (2009) ] L. V. Pourovskii, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 72, 115106 2005. adressed other aspects of these materials.

16. Origin of Landau quasi-particles, at low energies Coulomb interactions renormalize away (k-space) Multiplet structure in photoemission is also easy to understand. Take a configuration, add an electron project on other configurations. Hubbard bands with multiplet structure. Seen in many compounds. Mixed valence, two characteristic sets of multiplets in photoemission. At high energies, Coulomb interactions are strong. Multiplet structure remains in correlated metals. Splitting in quasiparticle bands, due to magnetic fields, crystal field splitting etc. are also common. But Coulomb interactions were not supposed to affect the quasiparticle band structure by definition!!!

18. Predictions for the occupied part of the spectrum.Incoherent “doublet”Tunneling.Inverse photoemision.

19. Theory: Quasiparticle MultipletsC. Yee G. Kotliar K. Haule Phys. Rev. B 81, 035105 (2010)  Occupied part of the photoemission triplet of peaks is part of the COHERENT part of the spectral function, hence the word quasiparticle. Low energy manifestation of the multiplet atomic structure in the high energy Hamiltonian. [hence the word multiplets]. This is IN ADDITION to the multiplet structure of the Hubbard band which still is present (and is very broad due to inelastic effects). Temperature dependent features. Only present if the coherence temperature is sufficiently high. More visible in the mixed valence regime , which has a large T_coh. Lost when the f electron localizes.

20. PuTe : Discussion in the literature: mixed valent (Wachter P. Wachter, Solid State Commun. 127, 599 2003.) Kondo Insulator. LDA+DMFT, more complete physical picture and theory of the Pu chalcogenides and pnictides

22. Valence Histograms and occupancies

25. J. Shim K. Haule and G. K. Nature 446, 513-516 (2007).

28. Expt: G.H.Lander et al., Phys. Rev. Lett. 53, 2262 (1984). Theory: M. Pezzoli, K. Haule and G.K.

31. Conclusion What is the basic physical picture of elemental Pu and its compounds ? LDA+DMFT (in state of the art implementations ) brings to the table: Understanding: Concept of quasiparticle multiplets. Development of the idea of mixed valence…………… Reconciles different spectroscopies, XAS, photoemission, in a coherent picture [ subjective statement ]………….. Some Predictive Power: Pu phonon spectra, Cm branching ratio, signature of QP multiplets in the occupied part of the spectra ………. Alternative Interpretation experiments: Pu115 form factors . Photoemission …….. Further advances: more accurate determination of LDA+DMFT parameters [ Kutepov et. al. . arXiv:1005.0885 ] Tool for material exploration in strongly correlated materials. ,

35. AMF dc and the standard dcf6 - - vs f5 ++nf=5.45 vs nf=5.2

37. Polarized Neutron Form factors (in magnetically ordered systems or field induced). M.Pezzoli K Haule and GK,  many useful discussions with G. Lander and A. Heiss. Compute within LDA+DMFT. Motivation, all previous interpretations of experiments were based in a fully localized picture or a fully intinerant picture. Sometimes it leads to surprising statements which one would like to understand better. Form factor is a good indicator of valence. Can it tell if nf=5 is good for PuSb ? And nf=5.2 is good for PuTe , Pu 115’s and delta Pu ??

38. Physics of Pu1-x-Amx mixtures

39. Searching for the 5f5 moment. Pu- Am mixtures: Javorski et al. PRL 96 (2006) Baclet et. al. PRB (2007).

44. Outline Some comments on Dynamical Mean Field Theory and its applications to actinides. Dynamical Mean Field Theory and theoretical spectroscopy. The case of delta Pu and their copounds.

45. Conclusions The electrons in Pu compounds not fully localized nor fully itinerant. In different properties one aspect or the other might shows up more (duality) but neither description is satsifactory. Quantitative framework: DMFT ? Pu is in a regime close to a localization delocalization boundary (Johanssen xx) many body non perturbative effects and concepts are important (savrasov kotliar and abrahams) delta Pu is a strongly correlated f-metal well described in LDA+DMFT it require new concepts [transfer of spectral weight – QP peak + H . B ] to distinguish between phases.

46. Conclusions Usefulness of the ab-initio framework. Successful rediction of phonon spectra in delta Pu. Important of phonon entropy in epsilon Pu. [Dai et. al ] Localization delocalization transition is controlled by f – hybridization and not by f-f hopping. Anderson lattice (right framework) not the degenerate Hubbard model (wrong framework) as surmised in the 70’s. [ Toropova Marianetti Haule Kotliar ] . Beyond the Hill (plot).

47. Conclusions Plutonium is a correlated mixed valent metal with nf=5.2 . Important interplay of hybridization, Hunds rule and spin orbit coupling determining the localization-delocalization phase boundary. [ Shim et al. ] Cm is localized with nf=5.0 . Prediction for the XAS branching ratio. [Shim et. al. ] Challenge of PuO2 and better modeling] Photoemission spectra of delta-Pu displays the universal Pu triplet of Havela et. al. Interpretation: quasiparticle multiplets. [ Yee Kotliar Haule ]

48. Localization-Delocalizaton boundary and looking for the elusive Pu moment Expanding Pu with Am the charge transfer effect. Pu moment. Expanding Pu with negative pressure. [ C. Marianetti CTQMC calculations with 14 correlated bands ] Physical understanding within DMFT of the Havela Gouder photoemission triplet: Quasiparticle Multiplets. More DMFT based theoretical spectroscopies. Magnetic form factor of Pu and Np 115’s. [ theory M. Pezzoli K Haule and GK, expt: A. Hiess and G. Lander] Accumulating evidence that we have a coherent consistent and predictive theory of Pu and its compounds based on LDA+DMFT.

50. DMFT concepts

51. Valence Fluctuations and Quasiparticle Multiplets in Pu Chalcogenides and Pnictides C. Yee G. Kotliar K. Haule Phys. Rev. B 81, 035105 (2010)

52. Form Factors

53. J. J. Joyce,*J.M.Wills, T. , Durakiewicz, M.T. Butterfield, E. Guziewicz, J. L. Sarrao, L. A. Morales, and A. J. Arko PRL, 91 , 176401 (2003)

54. Ladislav Havela, Alexander Shick and ThomasGouder, Journal of Applied Physics 105, 07E130(2009)

57. Plutonium antimonide

58. Phys. Rev. B 81, 035105 (2010) Chuck-Hou Yee, Gabriel Kotliar, Kristjan Haule

59. Pu Am mixtures

65. Confusion in the literature The three-peak structure observed in the Pu chalcogenides appears to be a common feature, and does not depend on the nature of the sample preparation. Gouder33 has argued that this feature arises from the 5f6 intermultiplet transition, transitions from 5f6-5f5, whereas the peak B at higher binding energy represents the stable Pu3+ configuration with transition from 5f4-5f4. The latter represents a “localized” level and should be responsible for the magnetic properties.

66. Wachter et al.34–36 have argued that the Pu chalcogenides are intermediate valent, and has shown that, as also found in UTe, the Poisson ratio of PuTe is negative. In Ref. 36 the peak at around 4 eV binding energy in PuSe, not well resolved at 40.8 eV photon energy, was proposed to indicate the Pu3+ configuration, which is in contrast with earlier attributions.33 However, from the HeI scans this particular peak in PuSe seems much more like Se4p emission, with the peak intensity growing significanly with de

67. Theory explains many puzzles Why room temperature specific heat of the chalcogenides (i.e. PuSe) is large. Low temperature resistivity indicates a small gap. Lattice constant indicates Pu has not full shell. Contrast with the pnictides, (i.e PuTe) which are magnetic, with 5f^5 configurations. High energy photoemission peak correlates with moment. Hybridization is larger in the chalcogenides than in in the pnictides. The f level is deeper in the chalcogenides than in the pnictides.

74. occupation nf is increased substantially from nf ˜ 5 in LSDA and FLL-LDA+U to nf = 5.44 (see table I) meaning that there is a substantial deviation from the 5f5 ionic state. The around-mean-field LSDA+U correlated band theory is applied to investigate the electronic and magnetic structure of fcc-Pu-Am alloys. Despite a lattice expansion caused by the Am atoms, neither a tendency to 5f localization nor the formation of local magnetic moments on Pu atoms in Pu-Am alloys is found. The 5f manifolds in the alloys are calculated, being very similar to a simple weighted superposition of elemental Pu and Am 5f states.

76. e) Standard metal with strong electron phonon interactions. Graf et.al (2005

77. Figure 2. DFT atomic volumes for the actinide metals in the body-centered-cubic and observed crystal structures. The theory is corrected by (experimental) thermal expansion to 300 K except for d-Pu. Spin-orbit coupling is included for all metals and spin and orbital polarization for d-Pu, Am, and Cm.4

78. Notice the agreement. Usefulness of theory. Notice the discreapancy. Scientfici opportunity. Put U.Notice the agreement. Usefulness of theory. Notice the discreapancy. Scientfici opportunity. Put U.

79. Main DMFT Concepts Valence Histograms. Describes the history of the “atom” in the solid, multiplets!

80. Qualitative Phase diagram :frustrated Hubbard model, integer filling M. Rozenberg et.al. PRL,75, 105 (1995) Different way of thinking was generated by the study of the Mott transition at integer filling. Universality and system specificity. . Bridge atomic physic and band physics. Crossovers with changing degrees of freedom. Different way of thinking was generated by the study of the Mott transition at integer filling. Universality and system specificity. . Bridge atomic physic and band physics. Crossovers with changing degrees of freedom.

81. Third Generation LDA+DMFT (K. Haule) Relativistic Effects, Spin Orbit Coupling Realistic band structure, complex structures Atomic Multiplet effects (F0 F2 F4 F6 ) Treat localization –delocalization on the same footing. LDA+DMFT. Fully self consistent charge density and spectra. Interaction applied to an orbital with almost pure f character-almost orthogonal. Can treat magnetically ordered phases. Advanced Impurity solvers CTQMC, OCA, Sunca, …

82. Bistability of a material near the Mott transition. Model realization of the Johanssen ideas. Central for understanding the physics of Pu.. New paradigm for thinking, about materials.Bistability of a material near the Mott transition. Model realization of the Johanssen ideas. Central for understanding the physics of Pu.. New paradigm for thinking, about materials.

83. Physical Picture of the Actinides Plutonium correlated metal near the localization delocalization boundary. Apply DMFT ideas, continous degree of localization [ quantified by the DMFT Weiss field, and the transfer of spectral weight between QP and Hubbard bands]

87. QP multiplets (C.H. Yee et. al.) [m > = plutonium multiplets [0 > = Am ground state Electron creation= d+a ~ Sm[0><m] Fma Slave boson representation: [0><m] = b+ fm H = em fm+ fm + Ak+ Ak + Vk Ak+ fm b+ + cc Gmm(w)-1 = <fm fm+>-1=w- em+l – D(w)

90. XAS What is your f occupancy. But before you ask that, you should ask: what is your f orbital .

91. f^6 configuration as a starting point [ (5f)6 J=0> singlet ground state. [ 5/2,3/2,1/2,-1/2,-3/2,-5/2 > Schick et.al (2005) . Pourovski et. al.(2006)

92. Early Theoretical results.

93. Shorikov et. al. (2006),

94. d) Mixed level model, Zwignagl Fulde, Erickson Wills et. al. LDA-SIC.1 f itinerant electron. 4 localized f electron. Non magnetic Xfield level.

95. IOP Conf. Series: Materials Science and Engineering 9 (2010) 012083

98. PuSb, Pu has Pu+++Sb--- (5f)^5

99. Outline Very brief introduction to the context. What is the basic physical picture of elemental Pu and its compounds ? Photoemission. The Quasiparticle Multiplet concept and its realization in PuSe and delta Pu. [with Chuck Yee, K. Haule ] Determination of the Valence thru XAS and LDA+DMFT [with Jihoon Shim and K. Haule] Corroborating the valence count with LDA+DMFT polarized neutron form factors. [ with M. Pezzoli and K Haule ] Specific heat. [with C. Marianetti M. Fluss K. Haule and with L. Pourovskii M. Katsnelson and A. Lichtenstein] Conclusions

100. Occupied part