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Half-metallic ferromagnets: an overview of the theory

Half-metallic ferromagnets: an overview of the theory. Introduction Model systems: Zinc-blende pnictides and chalcogenides (CrAs etc) Surfaces and interfaces Spin-orbit coupling Magnon excitations and Curie temperature. Phivos Mavropoulos. Introduction: Definition & properties. Examples :

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Half-metallic ferromagnets: an overview of the theory

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  1. Half-metallic ferromagnets:an overview of the theory • Introduction • Model systems: Zinc-blende pnictides and chalcogenides (CrAs etc) • Surfaces and interfaces • Spin-orbit coupling • Magnon excitations and Curie temperature Phivos Mavropoulos

  2. Introduction: Definition & properties • Examples: • Heusler alloys (NiMnSb etc) • (de Groot et al, PRL 1983) • Diluted Magnetic Semiconductors • Zinc-blende pnictides and • chalcogenides (CrAs etc) • Some manganites (eg LSMO) What is a half-metallic ferromagnet? Spin-polarised material showing 100% polarisation at EF • Relevance to spintronics: • Conductance through only one spin channel • Possibility for 100% spin-polarised current, 100% spin injection etc.

  3. Example: Heusler alloys Slater-Pauling behaviour in Heusler alloys(I. Galanakis, P.H. Dederichs) Full Heusler Half Heusler • Total magn. Moment per unit cell is integer in half-metallic systems.

  4. Model system: Zinc-blende CrAs First created by Akinaga et al (JJAP 2000) Tetrahedral environment: p-d hybridisation

  5. Variation of lattice constant a(GaP)<a(GaAs)<a(InAs) • Generally, compression or expansion drives EF out of the gap. Galanakis and Mavropoulos, PRB (2003)

  6. Surfaces can be half-metallic Galanakis, PRB (2002); Galanakis and Mavropoulos, PRB (2003)

  7. Interfaces with semiconductors CrAs/GaAs and CrSb/InAs (001) multilayers Alternating monolayers: …Cr/As/Cr/As/Ga/As/Ga/As… periodically repeated • Half-metallic property preserved throughout the multilayers. • Explanation: Coherent growth allows bonding-antibonding • splitting at the interface Mavropoulos, Galanakis, and Dederichs, JPCM (2004)

  8. NiMnSb Surface/Interface Minority DOS at Fermi level, atomic layer-resolved(Results: M. Lezaic) Interface (001) with InP Surfaces (001) Heusler alloys lose half-metallicity at the surfaces and interfaces with semiconductors. Other results: De Groot, Galanakis

  9. What destroys the gap? Structural causes: • Defects, impurity bands • Surface & interface states Electronic structure revisited: • Spin-orbit coupling • Non-quasiparticle states • Spin excitations at T>0

  10. Some nonzero DOS in the “gap” is unavoidable

  11. Spin-orbit coupling: states in the gap Mavropoulos et al, PRB (2004) Result agrees with FLAPW calculations of M. Lezaic

  12. Conclusion: Heavy elements increase SO coupling → Polarisation decreases

  13. Non-quasiparticle states DMFT+LDA calculation NiMnSb Chioncel, Katsnelson, de Groot, and Lichtenstein, PRB 68, 144425 (2003) DOS starts exactly at EF • Non-quasiparticle states first predicted by the Hubbard model. • Nonzero DOS starts at the Fermi level. • Irkhin and Katsnelson, Physics-Uspekhi (1994)

  14. What happens at T>0 ? Magnon excitations will reduce the spin polarisation long before Tc Approximation: Frozen magnons as spin spirals. Type 1: cone-like spiral Type 2: flat spiral Calculations with FLAPW can give the dispersion E(q). Excitation energy of the magnon: E(q)-E(0).

  15. Frozen magnon results NiMnSb Dispersion Relation E(q) DOS appears within gap • Average polarisation P(T) can be found by: • Monte Carlo simulation • Bose-Einstein statistics + magnon energies Results: M. Lezaic

  16. Estimation of Curie temperature Mean field approximation: Total energy calculations in Ferromagnetic state and Disordered Local Moment state (CPA) Mapping to Heisenberg model gives: Application also to DMS by Sato & Dederichs Results: M. Lezaic, with Akai KKR-CPA code • Mean-field approximation gives systematically too high Tc

  17. Curie Temperature (2) More realistic approach: Monte Carlo method. Mn-Mn exchange interaction: Impurity-in-CPA Calculate Heisenberg exchange constants within LDA and feed them into a MC program. CPA medium Jij Mn 2 Mn 1 • Possibilities for calculation of Jij : • Frozen magnons, J(q), and Brillouin Zone integration. • Lichtenstein’s “Magnetic Force Theorem” (Green function method) Method already applied to diluted magnetic semiconductors by Sato & Dederichs

  18. Outlook • Ground state properties are fairly well understood. • Systematic calculations on systems with defects are needed: • CPA method for averaging • Impurity-in-bulk method for isolated impurities & their interactions • Calculation of Curie temperature. • Open problem: Spin polarisation at T>0: How and when does half-metallic property stop?

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