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Understanding f-electron materials using Dynamical Mean Field Theory

Understanding f-electron materials using Dynamical Mean Field Theory. Gabriel Kotliar and Center for Materials Theory. Solid State Seminar U. Oregon January 15 th 2010. $upport : NSF -DMR DOE-Basic Energy Sciences Collaborators: K. Haule and J. Shim. 1. Outline.

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Understanding f-electron materials using Dynamical Mean Field Theory

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  1. Understanding f-electron materials using Dynamical Mean Field Theory Gabriel Kotliar and Center for Materials Theory Solid State Seminar U. Oregon January 15th 2010 $upport : NSF -DMR DOE-Basic Energy Sciences Collaborators: K. Haule and J. Shim 1

  2. Outline • Introduction to Correlated Materials • Introduction to Dynamical Mean Field Theory • Applications to f electrons: • CeIrIn5 • URu2Si2 • Pu-Am-Cm • PuSe PuTe • Conclusions

  3. Electrons in a Solid:the Standard Model Landau Fermi Liquid Excitation spectrum of a Fermi system has the same structure as the excitation spectrum of a perfect Fermi gas. Bloch waves in a periodic potential Rigid bands , optical transitions , thermodynamics, transport……… n band index, e.g. s, p, d,,f Kohn Sham Density Functional Theory Static Mean Field Theory. Kohn Sham Eigenvalues and Eigensates: Excellent starting point for perturbation theory in the screened interactions (Hedin 1965) 2

  4. GW= First order PT in screened Coulomb interactions around LDA • Quantum mechanical description of the states in metals and semiconductors. Bloch waves. En(k). • Inhomogenous systems. Doping. Theory of donors and acceptors . Interfaces. p-n junctions. Transistors. Integrated circuits computers. Physical Insights into Materials -> Technology 3

  5. Transition metal oxides transition metal ion Oxygen Correlated materials: simple recipe Cage : e.g 6 oxygen atoms (octahedra) or other ligands/geometry Transition metal inside Transition metal ions Rare earth ions Build a microscopic crystal with this building block Layer the structure Actinides 4

  6. LixCoO2Nax CoO2 YBa2Cu3O7 VO2 5

  7. How do we know that the electrons are heavy ? Heavy Fermions: intermetallics containing 4f elements Cerium, and 5f elements Uranium. Broad spd bands + atomic f open shells.

  8. 300 CeAl3 -1 (emu/mol)-1 200 UBe13 100 0 0 100 200 T(K) Heavy Fermion Metals Coherence Incoherence Crossover Magnetic Oscillations

  9. A Very Selected Class of HF

  10. U Ru Si A signature problem ? URu2Si2

  11. Correlated Electron Systems Pose Basic Questions in CMT: from atoms to solids • How to describe electron from localized to itinerant ? • How do the physical properties evolve ? • Non perturbative techniques Needed!! (Dynamical) mean field theory for this problem , 8

  12. Mean-Field : Classical vs Quantum ,……………………………………... • Prushke T. et. al Adv. Phys. (1995) • Georges Kotliar Krauth Rosenberg RMP (1996) Kotliar et. al. RMP (2006) Classical case Quantum case Hard!!! Easy!!! but doable QMC, PT , ED , DMRG……. A. Georges, G. Kotliar (1992)

  13. Dynamical Mean Field Theory • Describes the electron both in the itinerant (wave-like) and localized (particle-like) regimes and everything in between!. • Follow different mean field states (phases) Compare free energies. • Non Gaussian reference frame for correlated materials. • Reference frame can be cluster of sites CDMFT 11

  14. LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Spectra=- Im G(k,w) Determine energy and and S self consistently from extremizing a functional . Savrasov and Kotliar PRB 69, 245101, (2001) Full self consistent implementation 12

  15. DMFT Concepts Valence Histograms. Describes the history of the “atom” in the solid, multiplets! Weiss Weiss field, collective hybridizationfunction, quantifies the degree of localization Functionals of density and spectra give total energies

  16. Photoemission Spectral functions and the State of the Electron A(k, w) A(k, w) Probability of removing an electron and transfering energy w=Ei-Ef, and momentum k f(w) A(w, K) M2 e w • Weak correlations • Strong correlation: FL parameters can’t be evaluated in PT or FLT does not work. Angle integrated spectra 9

  17. Qualitative Phase diagram :frustrated Hubbard model, integer filling M. Rozenberg et.al. PRL,75, 105 (1995) CONCEPT: Quasiparticle bands, T*, and Hubbard bands CONCEPT: (orbitally resolved) spectral function. Transfer of spectral weight. CONCEPT: (orbital selective) Mott transition. T/W 13

  18. Outline • Introduction to Correlated Materials • Introduction to Dynamical Mean Field Theory • Applications to f electrons: • CeIrIn5 • Pu-Am-Cm • PuSe PuTe • URu2Si2 • Conclusions

  19.  CeRhIn5: TN=3.8 K;   450 mJ/molK2CeCoIn5: Tc=2.3 K;   1000 mJ/molK2; CeIrIn5: Tc=0.4 K;   750 mJ/molK2 Ir In Ce 4f’s heavy fermions, 115’s, CeMIn5 M=Co, Ir, Rh out of plane in-plane 21

  20. Optical conductivity in LDA+DMFT Shim, HK Gotliar Science (2007)‏ D. Basov et.al. K. Burch et.al. • At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) • At 10K: • very narrow Drude peak • First MI peak at 0.03eV~250cm-1 • Second MI peak at 0.07eV~600cm-1

  21. 10K eV In Ce In Structure Property Relation: Ce115’s Optics and Multiple hybridization gaps J. Shim et. al. Science non-f spectra 300K • Larger gap due to hybridization with out of plane In • Smaller gap due to hybridization with in-plane In

  22. more localized Co Ir Rh more itinerant “good” Fermi liquid magnetically ordered superconducting Difference between Co,Rh,Ir 115’s Total and f DOS f DOS Haule Yee and Kim arXiv:0907.0195

  23. U Ru Si A signature problem ? URu2Si2

  24. Two Broken Symmetry Solutions Weiss field Hidden Order LMA K. Haule and GK

  25. Valence Histogram Hidden order parameter Paramagnetic phase low lying singlets f^2 Order parameter: Different orientation gives different phases: “adiabatic continuity” explained. Hexadecapole order testable by resonant X-ray In the atomic limit:

  26. Simplified toy model phase diagram mean field theory Mean field Exp. by E. Hassinger et.al. PRL 77, 115117 (2008)

  27. Orbitally resolved DOS

  28. DMFT “STM” URu2Si2 T=20 K Ru Si Si U Fano lineshape: q~1.24, G~6.8meV, very similar to exp Davis

  29. Lattice response

  30. Localization Delocalization in Actinides Mott Transition d Pu a a Modern understanding of this phenomenaDMFT. 17

  31. Total Energy as a function of volume for Pu Moment is first reduced by orbital spin moment compensation. The remaining moment is screened by the spd and f electrons The f electron in d-phase is only slightly more localized than in the a-phase which has larger spectral weight in the quasiparticle peak and smaller weight in the Hubbard bands (Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu.

  32. Localization Delocalization in Actinides Mott Transition d Pu a a Modern understanding of this phenomenaDMFT. 17

  33. 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, Heffner et al. (2006)): d Pu is non magnetic. No static or fluctuating moments. Susceptibility, specific heat in a field, neutron quasielastic and inelastic scattering, muon spin resonance… • Paramagnetic LDA underestimates Volume of dPu. • Thermodynamic and transport properties similar to strongly correlated materials. • Plutonium: correlated paramagnetic metal.

  34. DMFT Phonons in fcc d-Pu ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et.al, Science, 22 August 2003)

  35. K.Haule J. Shim and GK Nature 446, 513 (2007)Trends in Actinides alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=7.15 F0=4.5,F2=8.11 Curium has large magnetic moment and orders antiferromagneticallyPu does is non magnetic.

  36. Havela et. al. Phys. Rev. B 68, 085101 (2003) Photoemission

  37. What is the valence in the late actinides ? Plutonium has an unusual form of MIXED VALENCE

  38. Finding the f occupancyTobin et. al. PRB 72, 085109 2005 K. Moore and G. VanDerLaan RMP (2009). Shim et. al. Europhysics Lett (2009) LDA results DMFT results

  39. Localization delocalization of f electrons in compounds. • Pu Chalcogenides [PuSe, PuS, PuTe]: Pauli susceptibility, small gap in transport. • Pu Pnictides [PuP, PuAs, PuSb], order magnetically. • Simple cubic NaCl structure • Going from pnictides to chalcogenides tunes the degree of localization of the f electron. Earlier work Shick et. al. Pourovski et. al.

  40. LDA+DMFT C. Yee Expts. T. Rurakiewicz et. al. PRB 70, 205103

  41. PuTe: a 5f mixed valent semi-conductor PuSb: a local moment metal

  42. Summary • Correlated Electron Systems. Huge Phase Space. Fundamental questions. Promising applications. • DMFT reference frame to think about electrons in solids. Quasiparticles Hubbard bands. Compare with the standard model. • Many succesful applications, some examples illustrating a) the concepts, b) the role of realistic modelling, and c) the connection between theory and experiment and the role of theoretical spectroscopy. 28

  43. Conclusion: • DMFT provides a surprisingly accurate description of f electron systems. • It’s physical content at very low temperatures is that of a heavy Fermi liquid in common with other methods but asymptotia is hardly reached (and relevant). Complete description of the crossover. • Variety and Universality.

  44. Outlook • “Locality “ as an alternative to Perturbation Theory. • Needed: progress in implementation. e.g. full solution of DMFT equations on a plaquette, robust GW+DMFT …………. • Fluctuation around DMFT. • Interfaces, junctions, heterostructures……….. • Motterials, Materials,……. • Towards rational material design with correlated electrons systems http://www.kitp.ucsb.edu/activities/auto/?id=970 28

  45. Looking for moments. Pu under (negative ) pressure. C Marianetti, K Haule GK and M. Fluss Phys. Rev. Lett. 101, 056403 (2008)

  46. Conclusion: some general comments. DMFT approach. Can now start from the material. Can start from high energies, high temperatures, where the method (I believe ) is essentially exact, far from critical points, provided that one starts from the right “reference frame”. Spectral “fingerprints” and their chemical origin. Still need better tools to analyze and solve the DMFT equations. Still need simpler approaches to rationalize simpler limit. Validates some aspects of slave boson mean field theories, modifies quantitatively and sometimes qualitatively the answers.

  47. At lower temperatures, one has to study different broken symmetry states. At lower temperatures, one has to study different broken symmetry states. Compare free energies, draw phase diagram Beyond DMFT: Write effective low energy theories that match the different regions of the phase diagram. Close contact with experiments. Many materials are being tried, methods are being refined Contemplating material design using correlated electron systems.

  48. Buildup of coherence in single impurity case Very slow crossover! coherent spectral weight TK T T* Buildup of coherence coherence peak scattering rate Slow crossover compared to AIM Crossover around 50K

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