Onset of Ferromagnetism in Low-Doped ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$

We develop a quantitatively predictive theory for impurity-band ferromagnetism in the low-doping regime of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$. We compare it with measurements of a series of samples whose compositions span the transition from paramagnetic insulating to ferromagnetic conducting behavior. The theoretical Curie temperatures depend sensitively on the local fluctuations in the Mn-hole binding energy, which originate from Mn disorder and As antisite defects. The experimentally determined hopping energy is an excellent predictor of the Curie temperature, in agreement with the theory.

Figure 1

(a) Model taking into account an energy difference $\Delta E$ between the two Mn-hole states. (b) Ferromagnetic interaction energy for Mn-Mn pairs separated by 17 Å. Line between the two Mn is along the [221] direction, with sample magnetization along [001] (nearest to $\Delta E=0$, or red) or [100] (next, or blue), or along the [100] direction, with sample magnetization along [001] (next, or orange) or [100] (farthest from $\Delta E=0$, or green). (c) $T_c$ as a function of $T_0$ for several averaged values of $2J(0)S^2$ for 17 Å pairs.

Figure 2

Temperature dependence of the resistivity (open symbols) and the magnetization (closed symbols) along the [100] crystalline direction of as-grown ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ epilayers grown in rotated mode for $x=0.03$ and 0.015.

Figure 3

Resistivity from 25 K to 80 K for $x=0.015$ nonrotated samples. The straight lines are the fits performed in this temperature range as discussed in the text. (b) The full temperature range $T=2–300\mathrm{K}$ for all FM samples from the $x=0.015$ series, where a noticeable deflection appears near $T_c$ and separates the curve into two segments.

Figure 4

Curie temperature of nonrotated ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ samples with $x=0.0075$, 0.01, 0.0125, and 0.015 plotted as a function of (a) carrier concentration at 300 K (b) conductivity at 25 K, and (c) hopping energy at $T_c$.