Low-temperature ferromagnetism in (Ga, Mn)N: Ab initio calculations

The magnetic properties of dilute magnetic semiconductors (DMSs) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. By using the Korringa–Kohn–Rostoker coherent-potential approximation (KKR-CPA) method within the local-density approximation, the electronic structure of (Ga, Mn)N and (Ga, Mn)As is calculated. Effective exchange coupling constants $J_{ij}$’s are determined by embedding two Mn impurities at sites $i$ and $j$ in the CPA medium and using the $J_{ij}$ formula of Liechtenstein et al. [J. Magn. Magn. Mater. 67, 65 (1987)]. It is found that the range of the exchange interaction in (Ga, Mn)N, being dominated by the double exchange mechanism, is very short ranged due to the exponential decay of the impurity wave function in the gap. On the other hand, in (Ga, Mn)As, where $p\text{−}d$ exchange mechanism dominates, the interaction range is weaker but long ranged, because the extended valence hole states mediate the ferromagnetic interaction. Curie temperatures ($T_{\mathrm{C}}$’s) of DMSs are calculated by using the mean-field approximation (MFA), the random-phase approximation, and the, in principle exact, Monte Carlo method. It is found that the $T_{\mathrm{C}}$ values of (Ga, Mn)N are very low since, due to the short-ranged interaction, percolation of the ferromagnetic coupling is difficult to achieve for small concentrations. The MFA strongly overestimates $T_{\mathrm{C}}$. Even in (Ga, Mn)As, where the exchange interaction is longer ranged, the percolation effect is still important and the MFA overestimates $T_{\mathrm{C}}$ by about 50%–100%.

Figure 1

Calculated exchange interaction $J_{ij}$ in (a) (Ga, Mn)N and (b) (Ga, Mn)As as a function of distance.

Figure 2

Curie temperatures of nearest-neighbor Heisenberg model in fcc structure. $T_{\mathrm{C}}$’s are calculated by the mean-field approximation (solid line), the random-phase approximation (dotted line), and the Monte Carlo simulation (crosses). The percolation threshold is 0.20 for the fcc structure.

Figure 3

Curie temperatures of (a) (Ga, Mn)N and (b) (Ga, Mn)As calculated by the MFA (solid lines), the RPA (dotted lines), and the MCS (filled squares). For the MCS, the exchange interactions up to 15th shell are taken into account.