Ferromagnetism and its evolution during long-term annealing in (Ga,Mn)As

A combined first-principles total energy Monte Carlo method is used to study the Curie temperature $T_{\mathrm{C}}$ and its evolution in (Ga,Mn)As. The inter- and intra-cluster magnetic interactions are treated separately in a modified Heisenberg Hamiltonian. We find for random Mn distributions (mimicking as-grown samples) a $T_{\mathrm{C}}$ maximum at the Mn concentration of 6%. During annealing we show that a slow clustering process of substitutional Mn atoms takes place and reduces $T_{\mathrm{C}}$. Our calculated temporal evolution of $T_{\mathrm{C}}$ during annealing agrees closely with experiment.

Figure 1

(a) Exchange coefficient $J$ in Eq. (1) for the effective local ${\mathrm{Mn}}_{\mathrm{Ga}}$ concentrations $\xi$ of 0.03 (full line), 0.06 (dashed line), and 0.08 (dotted line). (b) First-principles spin-flip energies $\Delta E_{\mathrm{DFT}}$ vs spin-flip energies $\Delta E_H$ calculated with the modified Heisenberg Hamiltonian of Eq. (1). Closed and open squares are calculated for $x=0.03$ and 0.06, respectively.

Figure 2

Calculated Curie temperatures $T_{\mathrm{C}}$ for random ${\mathrm{Mn}}_{\mathrm{Ga}}$ configurations (closed squares), and for regular ordered monomer lattices (open squares). The lines are only to guide the eye. The dashed (continuous) line in the inset shows the distribution of the intercluster distances for the regular ordered monomer lattice (the fully random ${\mathrm{Mn}}_{\mathrm{Ga}}$ configuration) at $x=0.06$. The vertical arrow shows the maximum of $J$ in Fig. 2a.

Figure 3

Calculated Curie temperatures $T_{\mathrm{C}}$ at the annealing temperatures of 250 and $300°\mathrm{C}$ as a function of annealing time at $x=0.05$. The inset shows the behavior of the magnetization order parameter $m$ on temperature $T$.