  We present a theory for electronic and magneto-optical properties of n-type
In(1-x)Mn(x)As magnetic alloy semiconductors in a high magnetic field, B. We
use an 8-band Pidgeon-Brown model generalized to include the wavevector (Kz)
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 Kz. 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 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 the effective masses and g
facors within the 8-band model. Results indicate that (alpha - beta) is the
crucial parameter that determines the exchange interaction correction to the
cyclotron masses. These findings sould be useful for designing novel devices
based on ferromagnetic semiconductors.
