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

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..)

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

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

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, (2001)] and by MC simulations [Sato et al. Jap J Appl Phys 44(30), L948 (2005)] Kinetics not considered so-far

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

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

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

Diffusion of Mn 0 along a 0.81 eV

Diffusion of Mn 0 along a – global maximum Off Tetrahedral site, steric hindrance

Diffusion of Mn 0 along a –local minimum I Just below N plane, slightly off centre of hexagonal channel

Diffusion of Mn 0 along a –local maximum ΔE global min – local max: 120 meV

Diffusion of Mn 0 along a – Global minimum s p dαdα Σ dβdβ DOS arb units 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.

Diffusion of Mn 0 along a – local minimum II

Diffusion of Mn 0 along c 1.94 eV

Diffusion of Mn 0 along c – global minimum Very similar to global min along a

Diffusion of Mn 0 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

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 T c ’s The groundstate interstitial site of Mn in GaN has been identified. Under exptl. conditions only stable in neutral charge state. Exhibits spin polarisation.