We have performed a systematic magneto-optical Kerr spectroscopy study of GaMnAs 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 $sim1.7$ eV. This peak increased in intensity and blue-shifted with Mn doping and further blue-shifted with annealing. Using a 30-band ${bf kcdot p}$ model with antiferromagnetic $s,p$-$d$ exchange interaction, we calculated the dielectric tensor of GaMnAs in the interband transition region, assuming that our samples are in the metallic regime and the impurity band has merged with the valence band. We successfully reproduced the observed spectra without emph{ad hoc} introduction of the optical transitions originated from impurity states in the band gap. These results lead us to conclude that above-bandgap magneto-optical Kerr rotation in ferromagnetic GaMnAs is predominantly determined by interband transitions between the conduction and valence bands.
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