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Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov

Many-body Electronic Structure of Actinides: A Dynamical Mean Field Perspective. Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov. Kristjan Haule , Physics Department and Center for Materials Theory Rutgers University. Half Moon Bay. Overview.

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Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov

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  1. Many-body Electronic Structure of Actinides: A Dynamical Mean Field Perspective. Collaborators:G.Kotliar, Ji-Hoon Shim, S. Savrasov Kristjan Haule, Physics Department and Center for Materials Theory Rutgers University Half Moon Bay

  2. Overview • DMFT in actinides and their compounds (Spectral density functional approach). Examples: • Plutonium, Americium, Curium. • Compounds: PuO2, PuAm Observables: • Valence, Photoemission, and Optics, X-ray absorption • Extensions of DMFT to clusters. Examples: • Coherence in the Hubbard and t-J model New general impurity solver (continuous time QMC) developed (can treat clusters and multiplets)

  3. Universality of the Mott transition Crossover: bad insulator to bad metal Critical point First order MIT Ni2-xSex k organics V2O3 1B HB model (DMFT):

  4. Coherence incoherence crossover in the 1B HB model (DMFT) Phase diagram of the HM with partial frustration at half-filling M. Rozenberg et.al., Phys. Rev. Lett. 75, 105 (1995).

  5. Effective (DFT-like) single particle Spectrum consists of delta like peaks Spectral density usually contains renormalized quasiparticles and Hubbard bands DMFT + electronic structure method • Basic idea of DMFT: reduce the quantum many body problem to a one site • or a cluster of sites problem, in a medium of non interacting electrons obeying a • self-consistency condition. (A. Georges et al., RMP 68, 13 (1996)). • DMFT in the language of functionals: DMFT sums up all local diagrams in BK functional Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated bands (s,p): use LDA or GW For correlated bands (f or d): with DMFT add all local diagrams

  6. How good is single site DMFT for f systems? f7 L=0,S=7/2 J=7/2 Elements: f5 L=5,S=5/2 J=5/2 f6 L=3,S=3 J=0 PuO2 Compounds: PuAm

  7. Overview of actinides Many phases 25% increase in volume between a and d phase Two phases of Ce, a and g with 15% volume difference

  8. Overview of actinides? Trivalent metals with nonbonding f shell Partly localized, partly delocalized f’s participate in bonding

  9. Why is Plutonium so special? Heavy-fermion behavior in an element Typical heavy fermions (large mass->small Tk Curie Weis at T>Tk) No curie Weiss up to 600K

  10. Plutonium puzzle? Ga doping stabilizes d-Pu at low T, lattice contraction Am doping -> lattice expansion Expecting unscreened moments! Does not happen!

  11. Curium versus Plutonium nf=6 -> J=0 closed shell (j-j: 6 e- in 5/2 shell) (LS: L=3,S=3,J=0) One more electron in the f shell One hole in the f shell • Magnetic moments! (Curie-Weiss law at high T, • Orders antiferromagnetically at low T) • Small effective mass (small specific heat coefficient) • Large volume • No magnetic moments, • large mass • Large specific heat, • Many phases, small or large volume

  12. Density functional based electronic structure calculations: • All Cm, Am, Pu are magnetic in LDA/GGA LDA: Pu(m~5mB), Am (m~6mB) Cm (m~4mB) Exp: Pu (m=0), Am (m=0) Cm (m~7.9mB) • Non magnetic LDA/GGA predicts volume up to 30% off. • Treating f’s as core overestimates volume of d-Pu, reasonable volume for Cm and Am Can LDA+DMFT predict which material is magnetic and which is not?

  13. Very strong multiplet splitting Atomic multiplet splitting crucial Increasing F’s an SOC

  14. Starting from magnetic solution, Curium develops antiferromagnetic long range order below Tc above Tc has large moment (~7.9mB close to LS coupling) Plutonium dynamically restores symmetry -> becomes paramagnetic cond-mat/0611760

  15. Multiplet structure crucial for correct Tk in Pu (~800K) and reasonable Tc in Cm (~100K) Without F2,F4,F6: Curium comes out paramagnetic heavy fermion Plutonium weakly correlated metal

  16. Valence histograms Density matrix projected to the atomic eigenstates of the f-shell (Probability for atomic configurations) Pu partly f5 partly f6 f electron fluctuates between these atomic states on the time scale t~h/Tk (femtoseconds) One dominant atomic state – ground state of the atom

  17. 5f7/2 valence 5f5/2 4d5/2->5f7/2 4d3/2->5f5/2 Excitations from 4d core to 5f valence hv Core splitting~50eV 4d3/2 Energy loss [eV] core 4d5/2 Probe for Valence and Multiplet structure: EELS&XAS Electron energy loss spectroscopy (EELS) or X-ray absorption spectroscopy (XAS) A plot of the X-ray absorption as a function of energy Core splitting~50eV Measures unoccupied valence 5f states Probes high energy Hubbard bands!

  18. 4d5/2->5f7/2 4d3/2->5f5/2 Core splitting~50eV Energy loss [eV] f-sumrule for core-valence conductivity Similar to optical conductivity: Current: Expressed in core valence orbitals: The f-sumrule: can be expressed as Branching ration B=A5/2/(A5/2+A3/2) B=B0 - 4/15<l.s>/(14-nf) B0~3/5 • Branching ratio depends on: • average SO coupling in the f-shell <l.s> • average number of holes in the f-shell nf A5/2 area under the 5/2 peak B.T. Tole and G. van de Laan, PRA 38, 1943 (1988)

  19. B=B0 - 4/15<l.s>/(14-nf) LDA+DMFT [a] G. Van der Laan et al., PRL 93, 97401 (2004). [b] G. Kalkowski et al., PRB 35, 2667 (1987) [c] K.T. Moore et al., PRB 73, 33109 (2006). One measured quantity B, two unknowns Close to atom (IC regime) Itinerancy tends to decrease <l.s>

  20. 2p->5f 5f->5f Optical conductivity Pu: similar to heavy fermions (Kondo type conductivity) Scale is large MIR peak at 0.5eV PuO2: typical semiconductor with 2eV gap, charge transfer

  21. Pu-Am mixture, 50%Pu,50%Am Lattice expands -> Kondo collapse is expected Could Pu be close to f6 like Am? Inert shell can not account for large cv anomaly Large resistivity! Absence of preadge structure in XAS Our calculations suggest charge transfer Pu d phase stabilized by shift to mixed valence nf~5.2->nf~5.4 Hybridization decreases, but nf increases, Tk does not change significantly! f6: Shorikov, et al., PRB72, 024458 (2005); Shick et al, Europhys. Lett.69, 588 (2005). Pourovskii et al., Europhys. Lett.74, 479 (2006).

  22. Americium f6 -> L=3, S=3, J=0 Mott Transition? "soft" phase f localized "hard" phase f bonding A.Lindbaum, S. Heathman, K. Litfin, and Y. Méresse, Phys. Rev. B 63, 214101 (2001) J.-C. Griveau, J. Rebizant, G. H. Lander, andG.KotliarPhys. Rev. Lett. 94, 097002 (2005)

  23. Am within LDA+DMFT Large multiple effects: F(0)=4.5 eV F(2)=8.0 eV F(4)=5.4 eV F(6)=4.0 eV S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)

  24. Am within LDA+DMFT from J=0 to J=7/2 Comparisson with experiment V=V0 Am I V=0.76V0 Am III V=0.63V0 Am IV nf=6.2 nf=6 Exp: J. R. Naegele, L. Manes, J. C. Spirlet, and W. MüllerPhys. Rev. Lett. 52, 1834-1837 (1984) • “Soft” phase not in local moment regime • since J=0 (no entropy) Theory: S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006) • "Hard" phase similar toaCe or d Pu, • Kondo physics due to hybridization, however, • nf still far from Kondo regime

  25. What is captured by single site DMFT? • Captures volume collapse transition (first order Mott-like transition) • Predicts well photoemission spectra, optics spectra, • total energy at the Mott boundary • Antiferromagnetic ordering of magnetic moments, • magnetism at finite temperature • Branching ratios in XAS experiments, Dynamic valence fluctuations, • Specific heat • Gap in charge transfer insulators like PuO2

  26. Beyond single site DMFT What is missing in DMFT? • Momentum dependence of the self-energy m*/m=1/Z • Various orders: d-waveSC,… • Variation of Z, m*,t on the Fermi surface • Non trivial insulator (frustrated magnets) • Non-local interactions (spin-spin, long range Columb,correlated hopping..) • Present in cluster DMFT: • Quantum time fluctuations • Spatially short range quantum fluctuations • Present in DMFT: • Quantum time fluctuations

  27. Optimal doping: Coherence scale seems to vanish underdoped scattering at Tc optimally overdoped Tc

  28. k New continuous time QMC, expansion in terms of hybridization General impurity problem Diagrammatic expansion in terms of hybridization D +Metropolis sampling over the diagrams Contains all: “Non-crossing” and all crossing diagrams! Multiplets correctly treated Phys. Rev. B 75, 155113 (2007)

  29. Low frequency very different Far from Mott transition coherent Close to Mott transition Very incoherent Hubbard model self-energy on imaginary axis, 2x2 Optimal doping in the t-J model (d~0.16) has largest low energy self-energy Very incoherent at optimal doping Optimal doping in the Hubbard model (d~0.1) has largest low energy self-energy Very incoherent at optimal doping

  30. Conclusions • LDA+DMFT can describe interplay of lattice and electronic structure near Mott transition. Gives physical connection between spectra, lattice structure, optics,.... • Allows to study the Mott transition in open and closed shell cases. • In actinides and their compounds, single site LDA+DMFT gives the zero-th order picture • 2D models of high-Tc require cluster of sites. Some aspects of optimally doped regime can be described with cluster DMFT on plaquette: • Large scattering rate in normal state close to optimal doping

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