One-LO-phonon resonant Raman scattering in wide-gap diluted magnetic semiconductors.

Abstract

The efficiency of resonant Raman scattering by LO phonons in wide-gap diluted magnetic semiconductors is investigated near the ${\mathit{E}}_{0}$ gap in external magnetic fields with ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te as an example. A theoretical model for the absolute Raman-scattering efficiency (RSE) in zinc-blende-type semiconductors, taking into account Wannier-Mott excitons as intermediate electronic states, is given for the special case of Zeeman-split conduction and valence bands. Neglecting Landau quantization this Zeeman splitting arises from the exchange interaction between band electrons and localized magnetic moments of ${\mathrm{Mn}}^{2+}$ ions. Deformation-potential (DP) and Fr\"ohlich (F) interactions for the exciton--one-phonon coupling are both taken into account. The Zeeman splitting and exciton states are considered in the framework of the envelope-function approximation using a parabolic model for the conduction and valence bands. Explicit expressions for the RSE as a function of the laser frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{L}}$ and of the external magnetic field B are given. Conditions for double resonance are discussed and selection rules are deduced for different scattering configurations. Absolute Raman intensities for scattering by LO phonons via DP and F exciton-phonon interaction in ${\mathrm{Cd}}_{0.8}$${\mathrm{Mn}}_{0.2}$Te have been measured in the Faraday configuration with external magnetic fields B=0--4 T. Quantitative comparison between experiment and theory shows that (a) an inhomogeneous broadening of the excitonic states due to the random distribution of Cd and Mn atoms has to be taken into account and (b) the measured RSE in the DP scattering configurations is strongly influenced by depolarization of the scattered light near resonance.