We performed a systematic magneto-optical Kerr spectroscopy study of Ga${}_{1\ensuremath{-}x}$Mn${}_{x}$As with varying Mn densities as a function of temperature, magnetic field, and photon energy. Unlike previous studies, the magnetization easy axis was perpendicular to the sample surface, allowing us to take remanent polar Kerr spectra in the absence of an external magnetic field. The remanent Kerr angle strongly depended on the photon energy, exhibiting a large positive peak at $~1.7$ eV. This peak increased in intensity and blueshifted with Mn doping and further blueshifted with annealing. Using a 30-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model with antiferromagnetic $s,p$-$d$ exchange interaction, we calculated the dielectric tensor of Ga${}_{1\ensuremath{-}x}$Mn${}_{x}$As in the interband transition region, assuming that our samples are in the metallic regime and the impurity band has merged with the valence band. Our modeling successfully reproduces the observed spectra.
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