Electronic states and cyclotron resonance inn-type InMnAs

Abstract

We present a theory for electronic and magneto-optical properties of n-type ${\mathrm{In}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ magnetic alloy semiconductors in a high magnetic field $B\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}.$ We use an eight-band Pidgeon-Brown model generalized to include the wave vector ${(k}_{z})$ dependence of the electronic states as well as $s\ensuremath{-}d$ and $p\ensuremath{-}d$ 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 $(x),$ and ${k}_{z}.$ Cyclotron resonance (CR) spectra are computed using Fermi's golden rule and compared with ultrahigh-magnetic-field $(>50$ 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 $s\ensuremath{-}d$ and $p\ensuremath{-}d$ exchange parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}.$ We find that not only $\ensuremath{\alpha}$ but also $\ensuremath{\beta}$ 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 $(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})$ 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.