Spin-magnetophonon level splitting in semimagnetic quantum wells

Spin-magnetophonon level splitting in a quantum well made of a semimagnetic wide gap semiconductor is considered. The semimagnetic semiconductors are characterized by a large effective $g$ factor. The resonance conditions $\hbar\omega_{\rm LO}=\mu_BgB$ for the spin flip between two Zeeman levels due to interaction with longitudinal optical phonons can be achieved sweeping magnetic field $B$. This condition is studied in quantum wells. It is shown that it leads to a level splitting that is dependent on the electron-phonon coupling strength as well as on the spin-orbit interaction in this structure. We treat in detail the Rashba model for the spin-orbit interaction assuming that the quantum well lacks inversion symmetry and briefly discuss other models. The resonant transmission and reflection of light by the well is suggested as a suitable experimental probe of the level splitting.