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?

Spin-polarised material showing

100% polarisation at EF

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)

Relevance to spintronics:•Conductance through only one spin channel•Possibility for 100% spin-polarised current, 100% spin injection etc.

Example: Heusler alloysSlater-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 CrAsTetrahedral environment: p-d hybridisation

First created by Akinaga et al (JJAP 2000)

Variation of lattice constanta(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 semiconductorsCrAs/GaAs and CrSb/InAs (001) multilayers

•Half-metallic property preserved throughout the multilayers.

•Explanation: Coherent growth allows bonding-antibonding splitting at the interface

Alternating monolayers:

…Cr/As/Cr/As/Ga/As/Ga/As…

periodically repeated

Mavropoulos, Galanakis, and Dederichs, JPCM (2004)

NiMnSb Surface/Interface

Heusler alloys lose half-metallicity at the surfaces and interfaces with semiconductors.

Minority DOS at Fermi level, atomic layer-resolved (Results: M. Lezaic)

Interface (001) with InPSurfaces (001)

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 NiMnSbChioncel, 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

DOS appearswithin gap

DispersionRelation E(q)

NiMnSb

Average polarisation P(T) can be found by:1. Monte Carlo simulation2. Bose-Einstein statistics + magnon energies

Results: M. Lezaic

Estimation of Curie temperatureMaterial 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

Mean field approximation:

Total energy calculations in

Ferromagnetic state and

Disordered Local Moment state (CPA)

Mapping to Heisenberg model gives:

DLMFMCB EETk 3

2

•Mean-field approximation gives systematically too high Tc

Results: M. Lezaic, with Akai KKR-CPA code

Application also to DMS by Sato & Dederichs

Curie Temperature (2)

Mn-Mn exchange interaction:Impurity-in-CPA

JijMn 1 Mn 2

CPA medium

More realistic approach: Monte Carlo method.

Calculate Heisenberg exchange constantswithin LDA and feed them into a MC program.

Method already applied to diluted magnetic semiconductors by Sato & Dederichs

Possibilities for calculation of Jij :

1. Frozen magnons, J(q), and Brillouin Zone integration.

2. Lichtenstein’s “Magnetic Force Theorem” (Green function method)

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?