The alpha to gamma transition in Cerium: a theoretical view from optical spectroscopy Kristjan Haule a,b and Gabriel Kotliar b a Jožef Stefan Institute, Ljubljana, Slovenia b Department of Physics and Center for Material Theory, Rutgers University, Piscataway, NJ, USA Classical theories of alpha to gamma phase transition Classical theories of alpha to gamma phase transition estimated T K (exp)=2000K estimated T K (exp)=60-80K 4f 5d 6s orbitally resolved "fat" optics for alpha phase LDA compared to LDA+DMFT ff contribution to optics <<fd<<dd ff contribution to optics <<fd<<dd Conclusions Conclusions The main features of the optical spectra in Cerium are a consequence The main features of the optical spectra in Cerium are a consequence of a of a different hybridization strength different hybridization strength between between f f and and spd spd orbitals in orbitals in the two phases the two phases Kondo peak in low T alpha phase appears due to hybridization with Kondo peak in low T alpha phase appears due to hybridization with sp sp d d bands bands Optics conductivity has mostly d character Optics conductivity has mostly d character Optics shows Optics shows a narrow Drude peak, a narrow Drude peak, hybridization hybridization ( ( pseudo pseudo ) ) gap gap and mid infrared and mid infrared peak at 1eV peak at 1eV in alpha phase in alpha phase Optics in gamma phase show Optics in gamma phase show a a broad Drude like response (of d bands only) broad Drude like response (of d bands only) " " K K ondo volume collapse ondo volume collapse model model " " explains the Cerium properties explains the Cerium properties better than better than the the TC A Luttinger Ward functional local (eigen)state - full atomic base , where general AIM: ( ) two band Hubbard model, Bethe lattice, U=4D three band Hubbard model, Bethe lattice, U=5D, T=0.0625D three band Hubbard model, Bethe lattice, U=5D, T=0.0625D Using a novel approach to calculate optical properties of strongly correlated systems, we address the old question of the physical origin of the alpha to gamma transition in Cerium. We find that the Kondo collapse model, involving both the f and the spd electrons, describes the optical data better than a Mott transition picture involving the f electrons only. Our results compare well with existing experiments on thin films. We predict the full temperature dependence of the optical spectra and find the development of a hybridization pseudogap in the vicinity of the alpha to gamma phase transition. solution AIM DMFT SCC local in localized LMTO base Impurity problem (14x14): Impurity solvers (expansion in hybridization strength) Impurity solvers (expansion in hybridization strength) • Mott transition (B. Johansson, 1974): Mott transition (B. Johansson, 1974): Hubbard model Hubbard model changes and causes Mott tr. changes and causes Mott tr. • Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): Anderson (impurity) model Anderson (impurity) model changes changes → chnange of T chnange of T K bath either constant or taken from LDA and rescaled ab initio calculation ab initio calculation contains t contains t ff ff and V and V fd fd hopping hopping is self-consistently determined is self-consistently determined bath for AIM bath for AIM Kondo volume colapse model resembles DMFT picture: Kondo volume colapse model resembles DMFT picture: Solution of the Solution of the Anderson impurity model Kondo physics → Anderson impurity model Kondo physics → Difference Difference : : with DMFT the lattice problem is solved (and therefore with DMFT the lattice problem is solved (and therefore Δ must self- consistently determined) while in KVC Δ is calculated for a fictious impurity (and needs to be rescaled to fit exp.) LDA+DMFT LDA+DMFT NCA OC A TC A Tests of the impurity solver Tests of the impurity solver •Quasiparticle renormalization amplitude •Imaginary axis data •Real axis data Electron configuration of Ce Atom : [Xe]4f 2 5d 0 6s 2 Solid or compounds : trivalent [Xe]4f 1 (5d6s) 3 , tetravalent [Xe]4f 0 (5d6s) 4 promotional model promotional model (Ramirez, Falicov 1971) (Ramirez, Falicov 1971) •Transition is 1.order •ends with CP very similar to gas-liquid condesation Various phases : isostructural phase transition (T=298K, P=7kbar) (fcc) phase [ magnetic moment (Curie-Wiess law), large volume, stable high-T, low-p] (fcc) phase [ loss of magnetic moment (Pauli-para), smaller volume, stable low-T, high-p] with large volume collapse v/v 15 35.2Å 3 34.4Å 3 24.7Å 3 28Å 3 LDA+U LDA exp. volumes fermionic bath fermionic bath mapping mapping LDA+DMFT formalism LDA+DMFT formalism LDA+DMFT results: Photoemission LDA+DMFT results: Photoemission Optics calculation within LDA+DMFT Optics calculation within LDA+DMFT LDA+DMFT results: Optics LDA+DMFT results: Optics • comparison to experiment comparison to experiment • partial density of states partial density of states • temperature dependence of optics temperature dependence of optics (developement of a hybridization pseudogap) (developement of a hybridization pseudogap)