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Effects of electronic correlations in iron and iron pnictides

Effects of electronic correlations in iron and iron pnictides. A. A. Katanin In collaboration with: A. Poteryaev , P. Igoshev , A. Efremov , S. Skornyakov , V. Anisimov. Institute of Metal Physics, Ekaterinburg , Russia.

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Effects of electronic correlations in iron and iron pnictides

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  1. Effects of electronic correlations iniron and iron pnictides A. A. Katanin In collaboration with:A. Poteryaev, P. Igoshev, A. Efremov, S. Skornyakov, V. Anisimov Institute of Metal Physics, Ekaterinburg, Russia Special thanks to Yu. N. Gornostyrev for stimulating discussions

  2. Iron properties a-iron: TC= 1043K, meff=3.13mB Mikhaylushkin, PRL 99, 165505 (2007) g-iron: qCW=-3450K, meff=7.47mB a - bcc,g- fcc,e- hcp agTs=1185 K Arajs. J.Appl.Phys. 31, 986 (1960) Parsons, Phil.Mag. 3, 1174 (1959)

  3. Itinerant approach (Stoner theory) • Large DOS implies ferromagnetism, provided that other magnetic • or charge instabilities are less important • - Too large magnetic transition temperatures, no CW-law • Moriya theory: paramagnons • Reasonable magnetic transition temperatures, CW law • Local moment approaches (e.g. Heisenberg model) • CW law

  4. Rhodes-Wollfarth diagram a-Iron (almost)fulfills Rhodes-Wollfarth criterion (pc/ps 1) • Proposals for iron: • Local moments are formed by eg electrons (Goodenough, 1960) • 95% d-electron localization (Stearns, 1973) • Local moments are formed from the vH singularity eg states(Irkhin, Katsnelson, Trefilov, 1993)

  5. The magnetism of iron a-Iron shows features of both, itinerant (fractional magnetic moment) andlocalized (Curie-Weiss law with large Curie constant) systems • Can one decide unbiasely (ab-initio), which states are localized (if any)? • What is the correct physical picture for decribing local magnetic moments in an itinerant system? • Mixed (Shubins-d(f) • = FM Kondo model) • Local moments(Heisenberg model) • Itinerant (Stoner and Moriya • theory) • How the local moments (if they exist) influence magnetic properties? • What is the similarity and differences between magnetism of a- and g- iron?

  6. Dynamical Mean Field Theory Energy-dependent effective medium theory The self-energy of the embedded atom coincides with that of the solid (lattice model), which is approximated as a k-independent quantity A. Georges et al., RMP 68, 13 (1996)

  7. Spin-polarized LDA+DMFT U = 2.3 eV, J = 0.9 eV Magnetic moment 3.09 (3.13) Critical temperature 1900 K (1043K) Lichtenstein, Katsnelson, Kotliar, PRL 87, 67205 (2001)

  8. a (Bcc) iron: band structure eg t2g t2gи eg states are qualitatively different and weakly hybridized A. Kataninet al., PRB 81, 045117 (2010) Correlations can “decide”,which of them become local

  9. a-iron: orbitally-resolved self-energy Comparison to MIT: Imaginary frequencies Linear for the Fermi liquid Divergent for an insulator t2g states - quasi-particles eg states - non-quasiparticle! Bulla et al., PRB 64, 45103 (2001) A. Kataninet al., PRB 81, 045117 (2010)

  10. Self-energy and spectral functionsat the real frequency axis Real frequencies a-Fe Comparison to MIT: From: Bulla et al., PRB 64, 45103 (2001)

  11. How to see local moments:local spin correlation function Local moments are stable when • Fulfilled at the conventional Mott transition. Can it be fulfilled in the metallic phase ? S(0)S() J=0.9 J=0 t A. Kataninet al., PRB 81, 045117 (2010)

  12. Fourier transform of spin correlation function

  13. Fourier transform of spin correlation function Local moments formed out of eg states do exist in iron!

  14. Which form of one can expect for the system with local moments? • Broaden delta-symbol: g is the dampingof local collective excitations Fora-iron: There is an interval in densities where spin correlation function depends weakly on temperature

  15. Curie law for local susceptibility eg t2g Total local moment p(eg) = 0.56 p(t2g) = 0.45 p(total)=1.22 agrees with the experimental data (known also after A.Liechtenstein, M. Katsnelson, and G. Kotliar, PRL 2001)

  16. Effective model The local moments are coupled via RKKY-type of exchange: RKKY type (similar to s-d Shubin-Vonsovskii model). The theoretical approaches, similar to those fors-d modelcan be used

  17. (fcc) iron TN≈100K • Which physical picture (local moment, itinerant) is suitable to describe g-iron ? • What is the prefered magnetic state for the giron at low T (and why)?

  18. LDA DOS The peak in eg band is shifted by 0.5eV downwards with respect to the Fermi level

  19. (fcc) iron P. A. Igoshevet al., PRB 88, 155120 (2013) More itinerant than a-iron ?

  20. DOS with correlations

  21. Static local susceptibility P. A. Igoshev, A. Efremov, A. Poteryaev, A. K., and V. Anisimov, PRB 88, 155120 (2013)

  22. Dynamic local susceptibility

  23. Size of local moment

  24. Magneticstate:Itinerantpicture QX=(0,0,2) SDW2 Comparison of energies in LDA approachShallcrosset al., PRB 73, 104443 (2006)

  25. Magnetic state: Heisenberg model picture Heisenberg model A. N. Ignatenko, A.A. Katanin, V.Yu.Irkhin, JETP Letters 87, 555 (2008) For stability of (0,0,2p) state one needs J1>0, J2<0.

  26. The polarization bubble, low T LDA LDA+DMFT k m m' k+q T=290К 2p(1,1/2,0) 2p(1/2,1/2,1/2) 2p(1,0,0)

  27. Experimental magnetic structure q = (2p/a) (1, 0.127, 0) Tsunoda, J.Phys.: Cond.Matt. 1, 10427 (1989) Naono and Tsunoda, J.Phys.: Cond.Matt. 16, 7723 (2004)

  28. Fermi surface nesting Colorcoding: red – eg,green – t2g,blue – s+p (0,x,2p) state is supported by the Fermi surface geometry – an evidence for itinerant nature of magnetism

  29. The polarization bubble, high T LDA LDA+DMFT T=1290К

  30. Uniform susceptibility k m' m k 1/ From high-temperature part:

  31. (fcc) iron The experimental value of the Curie constant is reproduced by the theory, although the absolute value of paramagnetic Curie temperature appears too large • Strong frustration! • Nonlocal correlations are important

  32. Magnetic exchange in -iron • The Neel temperature is much larger than the experimental one,similar to the result of the Stoner theory: • Paramagnons • Frustration, i.e. degeneracy of spin susceptibility in different directions

  33. Local spin susceptibility of Ni A. S. Belozerov, I. A. Leonov, and V. I. Anisimov, PRB 2013

  34. Iron pnictideLaFeAsO • Antiferromagnetic fluctuations • Superconductivity • Itinerant system in the normal state Effect of electronic correlations? Possibility of local moment formation?

  35. Density of states Damped qp states Electronic correlations qp states dxz, dyz, dxy states can be more localized No qp states

  36. Local susceptibility

  37. Spin correlation functions • The situation is similar to g-iron, i.e.local moments may exist • at large T only, and, therefore, • seem to have no effect on • superconductivity

  38. Orbital-selective uniform susceptibility Local fluctuations are responsiblefor the part of linear-dependent term in (T) S. L. Skornyakov, A. Katanin, and V. I. Anisimov, PRL ’ 2011

  39. Summary • The peculiarities of electronic properties (flat bands, peaks of density of states)near the FL may lead to the formation of local moments; • Analysis of orbitally-resolved static and dynamic local susceptibilitiesproves to be helpful in classification of different substances regarding the degree of local moment formation In alfa-iron: • The existence of local moments is observed within the LDA+DMFT approach • The formation of local moments is governed by Hundinteraction In gamma-iron: • Local moments are formed at high T>1000K, where this substance exist in nature, but not at low-T (in contrast to alfa-iron); the low-temperature magnetism appears to be more itinerant • Antiferromagnetismis provided by nesting of the Fermi surface

  40. Conclusions • Electronic correlations are important, but, similarly to g-iron,local moments may be formed at large T only • Different orbitals give diverse contribution to magneticproperties • Linear behavior of uniform susceptibility is (at least partly) due to peaks of density of states near the Fermi level In the iron pnictide: Thank you for attention !

  41. Spin correlation functions

  42. Spectral functions Damped qp states qp states No qp states

  43. Effective model and diagram technique (similar to s-d Shubin-Vonsovskii model). Treat eg electrons within DMFT and t2g electrons perturbatively Simplest way is to decouple an interaction and integrate out t2g electrons “bare” quadratic term quartic interaction Kind of boson (“4”) model, containing both, itinerant and local moment degrees of freedom

  44. Diagram technique: perspective

  45. The dynamic susceptibility “Moriya” correction bare bare RKKY Influence of itinerant electrons on local moment degrees of freedom Exchange integrals and magnetic properties can be extracted

  46. Two different approaches to magnetism of transition metals(and explaining Curie-Weiss behavior): • Itinerant (Stoner, Moriya, …) • Local moment (Heisenberg, …) Local moments in transition metals Since they are (good) metals, at first glance no ‘true’ local moments are formed • However, under some conditions the formation • of (orbital-selective) local moments is possible: • Weak hybridization between different states (e.g. • t2g and eg) • Presence of Hund exchange interaction • Specific shape of the density of states Can one unify these approaches (one band: Moriya, degenerate bands: Hubbard, …) More importantly: what is the ‘adequate’ (‘appropriate’) effective model, describing magnetic properties of transition metals ?

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