Understanding and predicting properties of f electron materials using DMFT Collaborators: K. Haule (Rutgers ) S. Savrasov (UC Davis) Useful discussions with the experimentalists T. Gouder, J. Joyce, L Havela, G. Lander, K Moore J. Tobin G. Kotliar Physics Department and Center for Materials Theory Rutgers University Dual Nature of f-Electrons The Third International Workshop – Dresden- May , 2011

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

Delocalization Localization: Actinides Mott Transition    Pu  Mott Transition in the Actinide Series around Pu. B. Johansen Phil Mag. 30, 469 (1974) Al stabilized J. C. Lashley, A. Lawson, R. J. McQueeney, and G. H. Lander, Phys. Rev. B 72, (2005).. Am stabilized Javorsky et. al. PRL 96, (2006). LDA+DMFT bring new physical aspects to the localization delocalization phenomena in actinides. S Savrasov G. Kotliar and E. Abrahams Nature 410, 793 (2001)

The standard model of solids fails near Pu Spin Density functional theory: Pu, Am, magnetic, large orbital and spin moments. Experiments (Lashley et. al ) Susceptibility, specific heat in a field, neutron quasi-elastic and inelastic scattering, …..…  Pu is non magnetic. No static or fluctuating moments. Muon Spin Resonance. Heffner et al. (2006). Very stringent limits on the magnetic moment < 10 −3 μB Paramagnetic LDA underestimates Volume of  Pu. Thermodynamic and transport properties anomalous similar to strongly correlated materials. Multitude of phases, many elastic anomalies.

Physical pictures of the dual nature of the f electron in Pu G. Zwicknagl and P Fulde Dual Model. LDA –SIC Quantum criticality. Moments are screened due to inter-site dipolar interactions. Chaplin and Fluss (2007). Theory of QCP Dominance of the (6f) 6 configuration. Pu as a strongly correlated mixed valent metal near the localization delocalization boundary. Moment screened by valence fluctuations. Shim Haule and GK Nature, 446, (2007). LDA+DMFT A. B. Shick, V. Drchal, and L. Havela, Europhys. Lett. 69, L. V. Pourovskii et. al. Europhys. Lett. 74, LDA+U [AMF]++ Mixed Level Model. 5f 4 configuration localized + 1 itinerant electron. O. Eriksson, J. M. Wills, D. Becker, and A. S. Balatsky, J. Alloys. Compd (1999).

A. Georges and G. Kotliar PRB 45, 6479 (1992). DMFT Collective field describing the localization delocalization phenomena. Atom in a medium. Bands in a frequency dependent potential.

Spectral Function-spectral weights Valence Histogram Pn 1/2

Pu as a correlated non magnetic f metal. Early LDA + DMFT results. Accounts for the correct volume of delta Pu in a paramagnetic state. [Savrasov Kotliar and Abrahams Nature 410, 793 (2001). delta Pu and alpha Pu spectra, QP + Hubbard bands, differ by a subtle redistribution of photoemission spectral weight. Predicted the phonon spectra of delta Pu [Savrasov et. al. Science (2003) ] in reasonable agreement with subsequent experiments. [Wong et. al. Science (2003)] Epsilon Pu is stabilized by phonon entropy. Caveats: primitive impurity solvers, no multiplet effects, only PM sates were considered. G. Kotliar S. Savrasov K Haule O. Parcollet V. Udovenko C. Marianetti Reviews of Modern Physiscs 78, 865, (2006).

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, (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 ]

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 ) ?

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! Average f-f hopping Average hybridization strength Average hybridization (blue) and average f - f hopping (red) as functions of atomic number along actinide series. Inset: the ratio V/t (squares) as function of atomic number Orbitals: Direct ff hopping vs f-spd hybridization in a “good “basis set

What is the valence in the late actinides ? Plutonium is MIXED VALENCE. DMFT valence histogram. Shim Haule and GK Nature, 446, (2007)

LDA+DMFT determines the Localization and Magnetic Boundary. Importance of Jhunds. alpa->delta volume collapse transition Curium has large magnetic moment and orders antiferromagnetically. Pu non magnetic. F0=4,F2=6.1 F0=4.5,F2=7.15 F0=4.5,F2=8.11 K Haule J. Shim and GK Nature, 446, (2007 ).

Photoemission T. Gouder, F. Wastin, J. Rebizant, and L. Havela, Phys. Rev. Lett. 84, L. Havela, T. Gouder, F. Wastin, and J. Rebizant, Phys. Rev. B 65,

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, R (2009) ] L. V. Pourovskii, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 72, adressed other aspects of these materials.

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!!!

C. Yee G. Kotliar K. Haule Phys. Rev. B 81, (2010)

Predictions for the occupied part of the spectrum. Incoherent “doublet” Tunneling. Inverse photoemision. Theory: Quasiparticle Multiplets C. Yee G. Kotliar K. Haule Phys. Rev. B 81, (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.

PuTe : Discussion in the literature: mixed valent (Wachter P. Wachter, Solid State Commun. 127, ) Kondo Insulator. LDA+DMFT, more complete physical picture and theory of the Pu chalcogenides and pnictides : Quasiparticle Multiplets C. Yee G. Kotliar K. Haule Phys. Rev. B 81, (2010)

CTQMC calculations (Livermore)

Valence Histograms and occupancies PuTe lattice constant is not consistent with Pu ++ (5f)6

Nf=5.2 Nf=5 Red: our LDA+DMFT occupations Ladislav Havela, Alexander Shick, and Thomas Gouder

XAS Branching ratio d 5/2 electron can be excited into either the f 5/2 and f 7/2 level. d 3/2 electron can only be excited into the f 5/2 level. Moore and van der Laan, Ultramicroscopy Thole and Van der Laan. Shim Haule and Kotliar. Typical XAS or EELS spectrum d 3/2 d 5/2 Plutonium cannot be (5f)6 K.T. Moore, M. A.Wall, A. J. Schwartz, B.W. Chung, D. K. Shuh, R. K. Schulze, and J.G. Tobin PRL (2003)

J. Shim K. Haule and G. K. Nature 446, (2007). Moore, K. T., van der Laan, G., Haire, R. G., Wall, M. A., Schwartz, A. J., and Söderlind, P., 2007, Phys. Rev. Lett. 98, Moore, K. T., van der Laan, G., Wall, M. A., Schwartz, A. J., and Haire, R. G., 2007, Phys. Rev. B 76,

LDA results Finding the f occupancy. Shim Haule and GK. EPL (2008) Curium : correct prediction! PuO strong disagreement with expt.

Magnetic form factors can be sensitive to valence. So far they theory available has been either in the fully localized and fully atomic limit. Implementation in LDA+DMFT removes this limitation. M. Pezzoli K. Haule and GK

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

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: ] Tool for material exploration in strongly correlated materials.,