Hall effect and hole densities in Ga1−xMnxAs

By studying the Hall effect in a series of low resistivity ${\mathrm{Ga}}_{\text{1−x}}{\mathrm{Mn}}_x\mathrm{As}$ samples, accurate values for the hole density $\mathrm{p,}$ Mn concentration $\mathrm{x,}$ and Curie temperature $T_C$ are obtained over the range $\text{0.015⩽x⩽0.08.}$ The hole density corresponds to 90% of the Mn concentration at low $\mathrm{x,}$ and has a maximum value of ${\text{1.0×10}}^{27}$ ${\mathrm{m}}^{\text{−3}}$ when $T_C\text{=125\hspace{0.17em}}\mathrm{K}.$ These data allow the first meaningful comparison of mean field predicted Curie temperatures with experiment over a wide range of $\mathrm{x.}$ The theory is in qualitative agreement with experiment, but overestimates $T_C$ at large $x$ and underestimates $T_C$ at low $\mathrm{x.}$