Longitudinal spin relaxation time of donor-bound electrons in a CdTe quantum well

Abstract

We study the magnetic-field dependence of the longitudinal spin relaxation time ${T}_{1}$ of donor-bound electrons placed in the middle of an 8-nm CdTe quantum well with different doping concentrations in the range from $1\ifmmode\times\else\texttimes\fi{}{10}^{9}$ to $2.9\ifmmode\times\else\texttimes\fi{}{10}^{11}$ $\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ and at low temperature. We use an extended photoinduced Faraday rotation technique, which expands the usual domain of the measured decays from tens of ns to $\ensuremath{\mu}\mathrm{s}$. As in high-purity bulk semiconductors, a maximum relaxation time of around ${T}_{1}\ensuremath{\sim}10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ is observed for a residually doped sample at low magnetic field of $B=0.08\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. For higher doping concentrations, the magnetic-field dependence of ${T}_{1}$ shows a nonmonotonic behavior: first a rapid increase, followed by a plateau or a decrease of ${T}_{1}$. The fast increase of ${T}_{1}$ at low magnetic fields is explained by the inhibition of the mechanisms identified at zero field---hyperfine and anisotropic exchange interactions---while the behavior at high magnetic field can be succesfully explained by a mechanism proposed by Lyubinskiy and associated to electron hops [I. S. Lyubinskiy, JETP Lett. 88, 814 (2008)]. A good agreement between experiment and theory is found for samples below the metal-insulator transition, when Dresselhaus terms of spin-orbit coupling are considered to be the dominant ones in the Hamiltonian describing the system.