Spectroscopic determination of hole density in the ferromagnetic semiconductor Ga_1-xMn_xAs

A measurement of the hole density in the ferromagnetic semiconductor Ga_1-xMn_xAs is notoriously difficult using standard transport techniques due to the dominance of the anomalous Hall effect. Here we report a spectroscopic measurement of the hole density in four Ga_1-xMn_xAs samples (x = 0, 0.038, 0.061, and 0.083) at room temperature using a Raman-scattering intensity analysis of the coupled plasmon-LO-phonon mode and the unscreened LO phonon. The unscreened LO-phonon frequency linearly decreases as the Mn concentration increases up to 8.3%. The hole density determined from the Raman scattering shows a monotonic increase with increasing x for x≤0.083, exhibiting a direct correlation to the observed T_c. The optical technique reported here provides an unambiguous means of determining the hole density in this important class of "spintronic" semiconductor materials.