1. 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

2. 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.

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, (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 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

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:
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

17. 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

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?