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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 : - PowerPoint PPT Presentation
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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?
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