Electronic states and cyclotron resonance in n-type InMnAs

We present a theory for electronic and magneto-optical properties of n-type In_1-xMn_xAs magnetic alloy semiconductors in a high magnetic field B‖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 (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-d and p-d exchange parameters α and β. We find that not only α but also β 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 (α-β) 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.