Electronic structure and carrier dynamics of the ferromagnetic semiconductor ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$

Infrared spectroscopy is used to study the doping and temperature dependence of the intragap absorption in the ferromagnetic semiconductor ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As},$ from a paramagnetic, $x=0.017\mathrm{}$ sample to a heavily doped, $x=0.079\mathrm{}$ sample. Transmission and reflectance measurements coupled with a Kramers-Kronig analysis allow us to determine the optical constants of the thin films. All ferromagnetic samples show a broad absorption resonance near 200 meV, within the GaAs band gap. We present a critical analysis of possible origins of this feature, including a Mn-induced impurity band and intervalence band transitions. The overall magnitude of the real part of the frequency dependent conductivity grows with increasing Mn doping, and reaches a maximum in the $x=0.052\mathrm{}$ sample where $T_C$ saturates at the highest value $\left(\sim 70\mathrm{K}\right)$ for the series. We observe spectroscopic signatures of compensation and track its impact on the electronic and magnetic state across the Mn phase diagram. The temperature dependence of the far infrared spectrum reveals a significant decrease in the effective mass of itinerant carriers in the ferromagnetic state. A simple scaling relation between changes in the mass and the sample magnetization suggest that the itinerant carriers play a key role in producing the ferromagnetism in this system.