Ab initio study of the diffusion of Mn through GaN

1. Ab initio study of the diffusion of Mn through GaN Johann von Pezold Atomistic Simulation Group Department of Materials Science University of Cambridge

2. Dilute Magnetic Semiconductors (DMS) Host semiconductor + magnetic dopant Ferromagnetic coupling Spin and Charge D o F (Spintronics) Novel devices (e.g. spin FET, spin LED, magnetic recording ..)

3. GaN – based DMS • III-Vs well established – (opto)-electronic devices • (Ga,Mn)As, but TC ~ 110 K • Dietl et al.: RT ferromagnetism of (Ga,Mn)N predicted [Science 287 (2000) 1019] • huge research effort, both theoretical and experimental • TC ≥ RT confirmed • TC 10 – 940 K reported

4. Mn d-states Mn d-states DOS (Mn0.0156Ga0.9844)As DOS (Mn0.0156Ga0.9844)N Mechanism of Ferromagnetism in DMS Mean field approach (Dietl et al.) • FM due to Zener p/d exchange interaction • Large carrier density essential (~ 1020 cm-3). Kulatov et al., Phys Rev B 66, 045203 (2002) • Strong p-d hybridisation for (Mn,Ga)As, not for (Mn,Ga)N

5. FM coupling in (Mn,Ga)N (Sato et al.) • localisation of d states  strong, short- ranged (NN) exchange interaction (double exchange mechanism) • Mn atoms need to form (nano) clusters for FM coupling • Significant driving force for clustering observed by LDA/ASA calculations [van Schilfgaarde et al. Phys. Rev. B 63, 233205 (2001)] and by MC simulations [Sato et al. Jap J Appl Phys 44(30), L948 (2005)] • Kinetics not considered so-far

6. Diffusion through GaN 2 obvious diffusion channels along c along a/b

7. Method • 2x2x2 supercell of GaN (32 atoms) • Mn constrained along c/a to sample PES, 32 configurations • Four host atoms furthest away from Mn fully constrained – avoid relaxation to GS • Full geometry optimisation for every configuration • CASTEP, ultrasoft PSPs, nlcc for Ga

8. 0.137 eV Charge State of Mni • +4, +3, +2,+1, 0, -1 and -2 charge states were considered • Only +1 charge state was found to be more stable than neutral Mni (under extremely electron deficient conditions) GaN tends to be intrinsically n-type and hence the +1 charge state is unlikely to be realised Diffusion study for Mn0

9. Diffusion of Mn0 along a 0.81 eV

10. Diffusion of Mn0 along a – global maximum • Off Tetrahedral site, steric hindrance

11. Diffusion of Mn0 along a –local minimum I • Just below N plane, slightly off centre of hexagonal channel

12. Diffusion of Mn0 along a –local maximum ΔE global min – local max: 120 meV

13. Σ p dα s DOS arb units dβ Diffusion of Mn0 along a – Global minimum strong N-Mn interaction; Mn off centre of hexagonal channel DOS similar to that observed for subst Mn (impurity states in gap), broadening due to smaller supercell.

14. Diffusion of Mn0 along a – local minimum II

15. Diffusion of Mn0 along c 1.94 eV

16. Diffusion of Mn0 along c – global minimum • Very similar to global min along a

17. Diffusion of Mn0 along c – global maximum • Mn-Ga interaction clearly very unfavourable • very significant lattice relaxation • again Mn relaxes away from the centre of the hexagonal channel

18. Conclusion • Anisotropic diffusion constants for the diffusion of Mn along a (0.81 eV) and c (1.94 eV) directions of GaN have been found. • Diffusion driven by favourable Mn-N interaction and unfavourable Ga-Mn interaction • The calculated diffusion barriers may explain the scatter in experimentally observed Tc’s • The groundstate interstitial site of Mn in GaN has been identified. Under exptl. conditions only stable in neutral charge state. Exhibits spin polarisation.