High Curie temperatures at low compensation in the ferromagnetic semiconductor (Ga,Mn)As

We investigate the relationship between the Curie temperature $T_C$ and the carrier density $p$ in the ferromagnetic semiconductor (Ga,Mn)As. Carrier densities are extracted from analysis of the Hall resistance at low temperatures and high magnetic fields. Results are found to be consistent with ion channeling measurements when performed on the same samples. We find that both $T_C$ and the electrical conductivity increase monotonically with increasing $p$, and take their largest values when $p$ is comparable to the concentration of substitutional Mn acceptors. This is inconsistent with models in which the Fermi level is located within a narrow isolated impurity band.

Figure 1

Resistivity versus temperature for (Ga,Mn)As films with $x_{\mathrm{total}}$ $=$ 12$\%$, as-grown and after annealing at 180 °C, with and without H codoping.

Figure 2

(a) $R_{xx}$ and (b) $R_{xy}$ versus magnetic field $B$ measured at 2 K, for a H-doped and annealed (Ga,Mn)As film with $x_{\mathrm{total}}$ $=$ 12$\%$. The magnetic field is applied perpendicular to the film. Symbols in (b) are fits to $R_{xy}$ with exponent $n$ $=$ 0 ($C$ $=$ 24.4 Ω), $n$ $=$ 1 ($C$ $=$ 0.0053), and $n$ $=$ 2 ($C$ $=$ 1.2 × 10${}^{-6}$ Ω${}^{-1}$), respectively. The inset of (b) shows the full range of $R_{xy}$ on sweeping the magnetic field from negative to positive values.

Figure 3

(a) $T_C$ versus hole density obtained from high-field Hall measurements, for three different (Ga,Mn)As films. (b) Electrical conductivity at room temperature (open symbols) and low temperature (filled symbols) for (Ga,Mn)As films with $x_{\mathrm{total}}$ $=$ 12$\%$, with (squares) and without (circles) H codoping. In both (a) and (b), the hole density for each sample is varied by a series of short annealing steps.

Figure 4

$T_C/x_{\mathrm{eff}}$ versus $p/N_{\mathrm{eff}}$. Blue squares correspond to samples where hole density $p$ is obtained from high-field Hall measurements. Gray circles correspond to samples from Ref. 11, where $p$ is obtained from ion channeling measurements. Red stars correspond to samples from Ref. 17, where $p$ is obtained from ion channeling measurements. The green line is the prediction of the microscopic calculation of Ref. 7.