Electronic structure of ferromagnetic Ga$_{1-x}$Mn$_{x}$As probed by infrared to visible magneto-optical spectroscopy

We present a study of the electronic band structure of ferromagnetic Ga$_{1-x}$Mn$_{x}$As determined from the spin dependent optical transitions that are manifested in the Faraday and Kerr spectra in the infrared to visible range (100-2000 meV). The data are compared to predictions from conventional mean field p-d exchange model. The spin-split band structure is probed as function of the exchange interaction strength and carrier concentration by exploring a series of optimally annealed Ga$_{1-x}$Mn$_{x}$As films with a broad range of magnetic doping (x=0.01- 0.14)~ and Curie temperatures (up to 190K). Large shifts in the magneto-optical spectra are observed with varying Mn concentration, consistent with valence band models (Acbas et al., Phys. Rev. Lett. 103, 137201 (2009)).