Collaborators: Ji-Hoon Shim, G.Kotliar Kristjan Haule, Physics Department and Center for Materials Theory Rutgers University Uncovering the secrets of Actinides using Dynamical Mean Field Theory. SCES 07 - Houston

Standard theory of solids Band Theory: electrons as waves: Rigid band picture: En(k) versus k Landau Fermi Liquid Theory applicable Very powerful quantitative tools: LDA,LSDA,GW Predictions: total energies, stability of crystal phases optical transitions M. Van Schilfgarde

Fermi Liquid Theory does NOT work. Need new concepts to replace rigid bands picture! Breakdown of the wave picture. Need to incorporate a real space perspective (Mott). Non perturbative problem. Strong correlation – Standard theory fails

V2O3V2O3 Ni 2-x Se x  organics Universality of the Mott transition First order MIT Critical point Crossover: bad insulator to bad metal 1B HB model (DMFT):

Delocalization Localization

Basic questions How to bridge between the microscopic information (atomic positions) and experimental measurements. New concepts, new techniques….. DMFT simplest approach to meet this challenge

DMFT + electronic structure method Effective (DFT-like) single particle Spectrum consists of delta like peaks Spectral density usually contains renormalized quasiparticles and Hubbard bands Basic idea of DMFT: reduce the quantum many body problem to a problem of an atom in a conduction band, which obeys DMFT 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 (G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).

Trivalent metals with nonbonding f shell f’s participate in bonding Partly localized, partly delocalized Volume of actinides

Anomalous Resistivity Maximum metallic resistivity :  =e 2 k F /h

Dramatic increase of specific heat Heavy-fermion behavior in an element

Am doping -> lattice expansion Expecting unscreened moments! Does not happen! NO Magnetic moments! Pauli-like from melting to lowest T No curie Weiss up to 600K

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 hole in the f shell One more electron in the f shell  No magnetic moments,  large mass  Large specific heat,  Many phases, small or large volume  Magnetic moments! (Curie-Weiss law at high T,  Orders antiferromagnetically at low T)  Small effective mass (small specific heat coefficient)  Large volume

Standard theory of solids:  DFT: All Cm, Am, Pu are magnetic in LSDA/GGA LDA: Pu(m~5   ), Am (m~6   ) Cm (m~4   ) Exp: Pu (m=0), Am (m=0) Cm (m~7.9   )  Non magnetic LDA/GGA predicts volume up to 30% off.  In atomic limit, Am non-magnetic, but Pu magnetic with spin ~ 5  B  Can LDA+DMFT account for anomalous properties of actinides?  Can it predict which material is magnetic and which is not? Many proposals to explain why Pu is non magnetic:  Mixed level model (O. Eriksson, A.V. Balatsky, and J.M. Wills) (5f)4 conf. +1itt.  LDA+U, LDA+U+FLEX (Shick, Anisimov, Purovskii) (5f)6 conf.  Cannot account for anomalous transport and thermodynamics

Increasing F’s an SOC NAtomF2F4F6  92U Np Pu Am Cm Very strong multiplet splitting Atomic multiplet splitting crucial -> splits Kondo peak Used as input to DMFT calculation - code of R.D. Cowan

Starting from magnetic solution, Curium develops antiferromagnetic long range order below Tc above Tc has large moment (~7.9  close to LS coupling) Plutonium dynamically restores symmetry -> becomes paramagnetic J.H. Shim, K.H., G. Kotliar, Nature 446, 513 (2007).

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 Magnetization of Cm:

Valence histograms Density matrix projected to the atomic eigenstates of the f-shell (Probability for atomic configurations) f electron fluctuates between these atomic states on the time scale t~h/Tk (femtoseconds) One dominant atomic state – ground state of the atom Pu partly f 5 partly f 6 Probabilities: 5 electrons 80% 6 electrons 20% 4 electrons <1% J.H. Shim, K. Haule, G. Kotliar, Nature 446, 513 (2007).

Gouder, Havela PRB 2002, 2003 Fingerprint of atomic multiplets - splitting of Kondo peak

Photoemission and valence in Pu |ground state > = |a f 5 (spd) 3 >+ |b f 6 (spd) 2 > f 5 f 6 f 5 ->f 4 f 6 ->f 7 Af()Af() approximate decomposition

core valence 4d 3/2 4d 5/2 5f 5/2 5f 7/2 Excitations from 4d core to 5f valence Electron energy loss spectroscopy (EELS) or X-ray absorption spectroscopy (XAS) Energy loss [eV] Core splitting~50eV 4d 5/2 ->5f 7/2 & 4d 5/2 ->5f 5/2 4d 3/2 ->5f 5/2 Measures unoccupied valence 5f states Probes high energy Hubbard bands! hv Core splitting~50eV Probe for Valence and Multiplet structure: EELS&XAS A plot of the X-ray absorption as a function of energy B=B0 - 4/15 /(14-n f ) Branching ration B=A 5/2 /(A 5/2 +A 3/2 )

LDA+DMFT 2/3 =-5/2(B-B0) (14-n f ) One measured quantity B, two unknowns Close to atom (IC regime) Itinerancy tends to decrease [a] G. Van der Laan et al., PRL 93, (2004). [b] G. Kalkowski et al., PRB 35, 2667 (1987) [c] K.T. Moore et al., PRB 73, (2006). [d] K.T. Moore et al., PRL in press

Specific heat Purovskii et.al. cond-mat/ : f6 configuration gives smaller  in  Pu than  Pu (Shick, Anisimov, Purovskii) (5f) 6 conf Could Pu be close to f 6 like Am?

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

Pu-Am mixture, 50%Pu,50%Am Lattice expands -> Kondo collapse is expected f 6 : Shorikov, et al., PRB 72, (2005); Shick et al, Europhys. Lett. 69, 588 (2005). Pourovskii et al., Europhys. Lett. 74, 479 (2006). Our calculations suggest charge transfer Pu  phase stabilized by shift to mixed valence nf~5.2->nf~5.4 Hybridization decreases, but nf increases, Tk does not change significantly!

Americium "soft" phase f localized "hard" phase f bonding Mott Transition? f 6 -> L=3, S=3, J=0 A.Lindbaum, S. Heathman, K. Litfin, and Y. Méresse, Phys. Rev. B 63, (2001) J.-C. Griveau, J. Rebizant, G. H. Lander, and G.Kotliar Phys. Rev. Lett. 94, (2005)

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

Am within LDA+DMFT n f =6 Comparisson with experiment from J=0 to J=7/2 “Soft” phase not in local moment regime since J=0 (no entropy) "Hard" phase similar to  Pu, Kondo physics due to hybridization, however, nf still far from Kondo regime n f =6.2 Exp: J. R. Naegele, L. Manes, J. C. Spirlet, and W. Müller Phys. Rev. Lett. 52, (1984) Theory: S. Y. Savrasov, K.H., and G. Kotliar Phys. Rev. Lett. 96, (2006) V=V 0 Am I V=0.76V 0 Am III V=0.63V 0 Am IV

Pu and Am (under pressure) are unique strongly correlated elements. Unique mixed valence. They require, new concepts, new computational methods, new algorithms, DMFT! Many extensions of DMFT are possible, many strongly correlated compounds, research opportunity in correlated materials. Conclusion

Many strongly correlated compounds await the explanation: CeCoIn 5, CeRhIn 5, CeIrIn 5

Photoemission of CeIrIn 5

LDA+DMFT DOS Comparison to experiment Photoemission of CeIrIn 5

Optics of CeIrIn5 LDA+DMFT K.S. Burch et.al., cond-mat/ Experiment:

New continuous time QMC, expansion in terms of hybridization General impurity problem Diagrammatic expansion in terms of hybridization  +Metropolis sampling over the diagrams Contains all: “Non-crossing” and all crossing diagrams! Multiplets correctly treated k

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 Conclusions

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 Basic questions

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).

Singlet-type Mott state (no entropy) goes mixed valence under pressure -> Tc enhanced (Capone et.al, Science 296, 2364 (2002))

DMFT in actinides and their compounds (Spectral density functional approach). Examples: –Plutonium, Americium, Curium. –Compounds: PuAm Observables: –Valence, Photoemission, and Optics, X-ray absorption Overview

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

Overview of actinides Two phases of Ce,  and  with 15% volume difference 25% increase in volume between  and  phase Many phases

Current: Expressed in core valence orbitals: The f-sumrule: can be expressed as Branching ration B=A 5/2 /(A 5/2 +A 3/2 ) Energy loss [eV] Core splitting~50eV 4d 5/2 ->5f 7/2 4d 3/2 ->5f 5/2 B=B0 - 4/15 /(14-n f ) A 5/2 area under the 5/2 peak Branching ratio depends on: average SO coupling in the f-shell average number of holes in the f-shell n f B 0 ~3/5 B.T. Tole and G. van de Laan, PRA 38, 1943 (1988) Similar to optical conductivity: f-sumrule for core-valence conductivity