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Predicting and Understanding Correlated Electron Materials: A Computational Approach

Kristjan Haule. Predicting and Understanding Correlated Electron Materials: A Computational Approach. Collaborators: J.H. Shim & G. Kotliar. Standard theory of solids (Landau Fermi liquid, Density Functional Theory) Complex correlated matter -> standard theory fails LDA+DMFT and its strengths

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Predicting and Understanding Correlated Electron Materials: A Computational Approach

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  1. Kristjan Haule Predicting and Understanding Correlated Electron Materials: A Computational Approach Collaborators: J.H. Shim & G. Kotliar

  2. Standard theory of solids (Landau Fermi liquid, Density Functional Theory) Complex correlated matter -> standard theory fails LDA+DMFT and its strengths Detailed comparison of LDA+DMFT results with experiments for a heavy fermion material CeIrIn5 Local Ce 4f - spectra and comparison to AIPES) Momentum resolved spectra and comparison to ARPES Optical conductivity and its connection to hybridization gaps Fermi surface in DMFT Sensitivity to substitution of transition metal ion: difference between CeIrIn5, CeCoIn5 and CeRhIn5 Outline • References: • KH, J.H. Shim, and G. Kotliar, Phys. Rev. Lett 100, 226402 (2008) • J.H. Shim, KH, and G. Kotliar, Science 318, 1618 (2007). • J.H. Shim, KH, and G. Kotliar, Nature 446, 513 (2007).

  3. Rigid band Well defined quasiparticles-> Rigid bands with long lifetime Standard theory of solids- Fermi liquid theory Excitation spectrum of a fermion system has the same structure as the excitation spectrum of a perfect Fermi gas. One to one correspondence between the interacting system and Fermi gas Lev Davidovich Landau Nobel laureate 1962 fundamentals

  4. Walter Kohn, Nobel laureate 1998 M L K Becomes quantitative/predictive Kohn-Hohenberg-Sham (1964): One-to-one mapping between the interacting system in the ground state and Kohn-Sham system of non-interacting particles. Band Theory: electrons as waves: Rigid band picture: En(k) versus k All “complexity” hidden in the XC functional

  5. M. Van Schilfgarde Standard theory at work Very powerful quantitative tools were developed: DFT(LDA,LSDA,GGA) ,GW • Predictions: • total energies, • stability of crystal phases • optical transitions

  6. Transition metal oxides transition metal ion Oxygen Complex electronic matter Cage of 6 oxygen atoms (octahedra) Transition metal inside Transition metal ions Rare earth ions Build a microscopic crystal with this building block Actinides

  7. V Oxygen V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Metal insulator transition VO2 Coating – smart window Above 29º reflects heat, Manning T. D. & Parkin I. P. J. Mater. Chem. ,14. Article (2004).

  8. Mn Oxygen V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature399, 560 (1999) Albert Fert and Peter Grünberg Nobel Laureate 2007 Colossal magnetoresistance LaMnO3+doping+layering Hard disk device Giant magnetoresistance

  9. Co Oxygen V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature399, 560 (1999) Co: Giant thermopower Y. Wang et.al., Nature 423, 425 (2003) Giant thermopower NaxCo2O4 Electronic refrigeration

  10. Ni,Ru Oxygen V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature399, 560 (1999) Co: Giant thermopower Ni: Electronic crystallization Y. Wang et.al., Nature 423, 425 (2003) J. Tranquada et.al., PRL 73, 1003 (1993) Ru: Electronic nematic R.A. Borzi et.al., Science 315, 214 (2007) Electronic crystallization/nematic La2NiO4.125 Electronic crystal

  11. Cu Oxygen V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature399, 560 (1999) Co: Giant thermopower Ni: Electronic crystallization Y. Wang et.al., Nature 423, 425 (2003) J. Tranquada et.al., PRL 73, 1003 (1993) Ru: Electronic nematic R.A. Borzi et.al., Science 315, 214 (2007) Cu: High temperature superconductor Bednorz&Muller, Z Phys. 64, 189(1986) High temperature superconductivity layering+doping Nobel Laureate 1987

  12. As Fe Fe high temperature superconductors Tetrahedral cage (rather than octahedral) Smaller c, perfect angle • Hosono et.a.., Tokyo, JACS • X.H. Chen, et.al., Beijing,arXiv: 0803.3790 • Zhi-An Ren, Beijing, arXiv: 0803.4283 • Zhi-An Ren, Beijing, arXiv: 0804.2053.

  13. CeXIn5 X In Ce In Ce In CeCoIn5 CeIrIn5 CeCoIn5 CeRhIn5 Heavy fermion materials (115) AFM SC SC AFM+SC Ce atom in cage of 12 In atoms • Properties can be tuned (substitution, • pressure, magnetic field) between • antiferromagnetism • superconductivity • quantum critical point

  14. Strong correlation – Standard theory of solids fails • The electronic matter in these materials has tremendous potential for applications (large response to small stimuli, variety of responses,…) • But it involves strong electronic interactions and has proved extremely difficult to understand • Need for new methods and techniques which can deal with strong electronic correlations

  15. Coherent+incoherent spectra Rigid band Why does it fail? • 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.

  16. New concepts, new techniques….. 1B HB model (DMFT): DMFT can describe Mott transition: Bright future! Dynamical Mean Field Theory the simplest approach which can describe the physics of strong correlations ->the spectral weight transfer ->Mott transition ->local moments and itinerant bands, heavy quasiparticles

  17. Weiss mean field theory for spin systems Exact in the limit of large z Dynamical mean field theory (DMFT) for the electronic problem exact in the limit of large z Classical problem of spin in a magnetic field Problem of a quantum impurity (atom in a fermionic band) Space fluctuations are ignored, time fluctuations are treated exactly DMFT in a Nutt shell

  18. DMFT multiband& multiplets D DMFT + electronic structure method Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated orbitals (s,p): use LDA or GW For correlated orbitals (f or d): add all local diagrams by solving QIM (G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).

  19. Luttinger Ward functional NCA OCA SUNCA General impurity solvers: a diagrammatic real axis solver K.H., J Kroha & P. Woelfle, Phys. Rev. B 64, 155111 (2001) General impurity problem Sum most important diagrams

  20. An exact impurity solver, continuous time QMC - expansion in terms of hybridization K.H. Phys. Rev. B 75, 155113 (2007) K.H. Phys. Rev. B 75, 155113 (2007) ; P Werner, PRL (2007); N. Rubtsov PRB 72, 35122 (2005). General impurity problem Diagrammatic expansion in terms of hybridization D +Metropolis sampling over the diagrams • Exact method: samples all diagrams! • Allows correct treatment of multiplets

  21. DMFT+LMTO package http://www.physics.rutgers.edu/~haule/download.html To be available at Database of materials

  22. How to compute spectroscopic quantities (single particle spectra, optical conductivity phonon dispersion…) from first principles? How to relate various experiments into a unifying picture. DMFT maybe simplest approach to meet this challenge for correlated materials Basic questions to address

  23. ? A(w) w k Issues in complex electronic matter • Electronic properties are a strong function of temperature, • pressure, doping • Electronic states are developing in a nontrivial way in (w,k) space • (rigid band picture does not apply) One example of a “heavy fermion” system, Ce-115’s: • How does the crossover from localized moments • to itinerant q.p. happen? • Where in momentum space q.p. appear and how?

  24. ALM in DMFT Schweitzer& Czycholl,1991 Crossover scale ~50K • High temperature • Ce-4f local moments • Low temperature – • Itinerant heavy bands Coherence crossover in experiment out of plane in-plane

  25. Temperature dependence of the localCe-4f spectra A(w) – number of available states per energy A(k,w) – number of available states per momentum per energy ACe-4f(w) CeIrIn5 • At 300K, only Hubbard bands • At low T, very narrow q.p. peak • (width ~3meV) • SO coupling splits q.p.: +-0.28eV SO • Redistribution of weight up to very high • frequency J. H. Shim, KH, and G. Kotliar Science 318, 1618 (2007).

  26. 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 pointed out by NPF 2004 Crossover around 50K

  27. Anomalous Hall coefficient Consistency with the phenomenological approach of NPF Fraction of itinerant heavy fluid +const m* of the heavy fluid Remarkable agreement with Y. Yang & D. Pines Phys. Rev. Lett. 100, 096404 (2008).

  28. Angle integrated photoemission vs DMFT Experiment at T=10K Maybe surface sensitive at 122eV ARPES Fujimori, 2006

  29. Angle integrated photoemission vs DMFT • Nice agreement for the • Hubbard band position • SO split qp peak • Hard to see narrow resonance • in ARPES since very little weight • of q.p. is below Ef Lower Hubbard band ARPES Fujimori, Phys. Rev. B 73, 224517 (2006).

  30. Momentum resolved Ce-4f spectra Af(w,k) Hybridization gap q.p. band Fingerprint of spd’s due to hybridization scattering rate~100meV SO Ce In In Not much weight T=10K T=300K

  31. w k first mid-IR peak at 250 cm-1 CeCoIn5 Optical conductivity F.P. Mena & D.Van der Marel, 2005 Typical heavy fermion at low T: no visible Drude peak no sharp hybridization gap Narrow Drude peak (narrow q.p. band) Hybridization gap second mid IR peak at 600 cm-1 Interband transitions across hybridization gap -> mid IR peak E.J. Singley & D.N Basov, 2002

  32. Optical conductivity in LDA+DMFT • 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

  33. 10K In eV Ce In Multiple hybridization gaps non-f spectra 300K • Larger gap due to hybridization with out of plane In • Smaller gap due to hybridization with in-plane In

  34. M X M G X X M M X Fermi surface change with T Big change-> from small hole like to large electron like LDA+DMFT (400 K) LDA+DMFT (10 K) LDA e1 g h h g

  35. Ce In In X 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

  36. Magnetism in CeRhIn5 CeRhIn5 is most localized -> susceptible to long range magnetic order • Commensurate AFM stable below ~3K • Moment has mainly G-7 symmetry: • moment lies in the ab plane • Moment is ~1mB • In exp: • AFM stable below 3.8K, but is spiral • Q=(1/2,1/2,0.298)a • For B>3T, Q=(1/2,1/2,1/4)b • Moment in plane! • Moment 0.26a,b, 0.59b, 0.75cmB , 0.79 mBd a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000) b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007) c) Bao W et al, Phys. Rev. B 62 R14621 (2000) d) J. Thompson & T. Park, (2008)

  37. Conclusions • Complex correlated matter holds a great promise for future technological materials • There is a lack of tools for describing complex correlated matter from first principles • Many aspect of complex matter physics are well described by DMFT • We have shown one such example: heavy fermion materials CeXIn5 • Temperature crossover • Spectral weight redistribution in momentum and frequency • Sensitivity to chemical substitution

  38. Thank you!

  39. As Fe,Ni As,P La,Sm,Ce Fe O Iron superconductors, structure • 2D square lattice of Fe • Fe - magnetic moment • As-similar then O in cuprates But As not in plane! Perfect tetrahedra 109.47°

  40. Kink in resistivity What is the glue? KH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)): Phonons give Tc<1K L. Boeri, O. V. Dolgov, A. A. Golubov arXiv:0803.2703 (PRL, 101, 026403 (2008)): l<0.21, Tc<0.8K Not conventional superconductors! Y. Kamihara et.al., J. Am. Chem. Soc. 130, 3296 (2008). Huge spin susceptibility (50 x Pauli)

  41. Signatures of moments CaFe2As2 and Ca0.5Na0.5Fe2As2 Doped LaOFeAs Susceptibility 50xlarger than Pauli LDA Large restivity in normal state T. Nomura et.al., 0804.3569

  42. LDA value J~0.35 gives correct order of Magnitude for both c and r. Importance of Hund’s coupling LaO1-0.1F0.1FeAs Hubbard U is not the “relevant” parameter. The Hund’s coupling brings correlations! Specific heat within LDA+DMFT for LaO1-0.1F0.1FeAs at U=4eV For J=0 there is negligible mass enhancement at U~W! The coupling between the Fe magnetic moment and the mean-field medium (As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling! KH, G. Kotliar, cond/mat 0803.1279

  43. Structural transition SDW not noticed Structural transition & SDW superconductivity superconductivity Very unusual Common features of the parent c. SmOFeAs CaFe2As2 and Ca0.5Na0.5Fe2As2 Enormous normal state resistivities!

  44. electron doped R O1-xFx FeAs hole doped (not electron doped) (Ba1-xKx)Fe2As2 (Tc=38K, x~0.4), Marianne Rotter et.al., arXiv:0805.4630 Ba or Ca FeAs layer FeSe1-0.08, (Tc=27K @ 1.48GPa), Yoshikazu Mizuguchi et.al., arXiv: 0807.4315 No arsenic ! A. Kreyssig, arXiv:0807.3032 Bond angle seems to matter most. Perfect tetrahedra (109.47° ) -> higher Tc Variety of materials CaFe2As2, (Tc=12K @ 5.5GPa), Milton S. Torikachvili, arXiv:0807.0616v2 Li1-xFeAs, (Tc=18K), X.C.Wang et.al., arXiv:0806.4688 BaFeAs2 (Tc=?) J.H. Shim, KH, G. Kotliar, arXiv: 0809.0041

  45. SmFeAsO1-xFx S.C. Riggs et.al., arXiv: 0806.4011 Phase diagrams SmFeAsO magneto-transport experiments • muon spin rotation A. J. Drew et.al., arXiv:0807.4876. Very similar to cuprates, log(T) insulator due to impurities

  46. CaFe2As2 under pressure Volume collapse A. Kreyssig et.al, arXiv: 0807.3032 Phase diagrams CaFe2As2 Stoichiometric compound

  47. Structural transition SDW not noticed Structural transition & SDW superconductivity superconductivity Very unusual Common features of the parent c. SmOFeAs CaFe2As2 and Ca0.5Na0.5Fe2As2 Enormous normal state resistivities!

  48. magnetic Tetragonal->Orth. R. Klingeler et.al., arXiv:0808.0708v1 Magnetic and structural PT LaOFeAs arXiv:0806.3304v1 Clarina de la Cruz, Nature 453, 899 (2008). In single crystals of 122 seems TM and TS close or the same

  49. side view top view SDW temperature and magnetic moment vary strongly between compounds: LaFeAsO: TSDW~140K μ~0.3-0.4μB (a) NdFeAsO: TSDW~1.96K μ~0.9μB/Fe (b) BaFe2As2: T0~TSDW~100K μ~0.9μB/Fe (c) SrFe2As2: T0~TSDW~205K μ~1.01μB/Fe (d) (a) Clarina de la Cruz et.al, Nature 453, 899 (2008). But Iron Fe2+ has 6 electrons, [Ar] 3d6 4s0 and spin S=2. (b) Jan-Willem G. Bo, et.al., arXiv:0806.1450 (c) Huang, Q. et al., arXiv:0806.2776 (d) K. Kaneko et.al., arXiv: 0807.2608 Why is not μ larger? Why it varies so much? Fe magnetism ? Weak structural distortion ~150 K: from tetragonal to orthorombic SDW (stripe AFM) at lower T Neutrons by: Clarina de la Cruz et.al, Nature 453, 899 (2008).

  50. Itinerancy & Frustration The undoped compound is metal (although very bad one ~1mWcm), hence moment is partially screened Magnetic exchange interaction is very frustrated (Qimiao Si, Elihu Abrahams, arXiv:0804.2480) Exchange interactions are such that J2~J1/2, very strong frustration, (KH, G. Kotliar, arXiv: 0805.0722) For the doped compound, LDA structural optimization fails for non-magnetic state! (It is very good if magnetism is assumed) For non-magnetic state, LDA predicts 1.34Å shorter FeAs distance (10.39 instead of 11.73). One of the largest failures of LDA. Paramagnetic state must have (fluctuating) magnetic moments not captured in LDA T. Yildirim, arXiv: 0807.3936

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