A measurement of the hole density in the ferromagnetic semiconductor ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ 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 ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ 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.

• Received 8 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.033202