Magnetic field effects on spin-flip processes in semimagnetic quantum wells

Abstract

We report results of calculations on the spin-flip scattering rate of heavy holes and excitons in semimagnetic quantum wells in an external magnetic field due to the $sp\text{\ensuremath{-}}d$ exchange interaction. Numerical estimates are given for the example of $\mathrm{CdMnTe}$ quantum wells with magnetic wells and nonmagnetic barriers. Due to a giant spin splitting induced by the magnetic field in a semimagnetic quantum well, the heavy hole at zero momentum contributes significantly to spin-flip scattering processes, in marked contrast to the zero-field case. For single (free) heavy holes, the spin-flip scattering rate shows a fast increase with magnetic field which turns to saturation at fields exceeding $1\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The larger the thickness of a quantum well, the stronger is such an acceleration of the heavy-hole spin relaxation. Still the maximum values of the scattering rate (on the order of ${10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$) are largest for narrow wells. For the exciton-bound carriers (electron and holes), the electron-hole correlation effects get important, particularly, in the presence of an external magnetic field. As a result, the scattering rate for the spin-flip transitions within the states of the (heavy-hole) bright exciton, shows a pronounced maximum at low fields $(\ensuremath{\lesssim}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{T})$. The scattering rate saturates at moderate fields of about $2\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ at a magnitude on the order of a few tens of picoseconds.