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

Introduction: Definition & properties What is a half-metallic ferromagnet? 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) 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.

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.

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

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)

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

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)

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

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

Some nonzero DOS in the “gap” is unavoidable

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

Conclusion: Heavy elements increase SO coupling → Polarisation decreases

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)

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).

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

Estimation of Curie temperature Mean field approximation: Total energy calculations in Ferromagnetic state and Disordered Local Moment state (CPA) Mapping to Heisenberg model gives: Material Tc (MF) Tc (Exp) CoMnSb 848 490 NiMnSb 1391 730 PdMnSb 922 500 PtMnSb 986 582 Co2MnGe 1966 905 Co2MnAl 1333 693 Co2MnGa 721 694 Co2MnSi 2059 985 Application also to DMS by Sato & Dederichs Results: M. Lezaic, with Akai KKR-CPA code Mean-field approximation gives systematically too high Tc

Mn-Mn exchange interaction: 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 1 Mn 2 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

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?