Electronic states and cyclotron resonance in n-type InMnAs

We present a theory for electronic and magneto-optical properties of n-type ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ magnetic alloy semiconductors in a high magnetic field $B\Vert \mathrm{ẑ}.$ We use an eight-band Pidgeon-Brown model generalized to include the wave vector ${(k}_z)$ dependence of the electronic states as well as $s-d$ and $p-d$ exchange interactions with localized Mn d electrons. Calculated conduction-band Landau levels exhibit effective masses and g factors that are strongly dependent on temperature, magnetic field, Mn concentration $\mathrm{}\left(x\right),$ and $k_z.$ Cyclotron resonance (CR) spectra are computed using Fermi’s golden rule and compared with ultrahigh-magnetic-field $(>\mathrm{}50\mathrm{}$ T) CR experiments, which show that the electron CR peak position is sensitive to x. Detailed comparison between theory and experiment allowed us to extract the $s-d$ and $p-d$ exchange parameters $\alpha$ and $\beta .$ We find that not only $\alpha$ but also $\beta$ affects the electron mass because of the strong interband coupling in this narrow-gap semiconductor. In addition, we derive analytical expressions for effective masses and g factors within the eight-band model. Results indicates that $\left(\alpha -\beta \right)$ is the crucial parameter that determines the exchange interaction correction to the cyclotron masses. These findings should be useful for designing novel devices based on ferromagnetic semiconductors.