Ensemble spin relaxation of shallow donor qubits in ZnO

Abstract

We present an experimental and theoretical study of the longitudinal electron spin relaxation (${T}_{1}$) of shallow donors in the direct band-gap semiconductor ZnO. ${T}_{1}$ is measured via resonant excitation of the Ga donor-bound exciton. ${T}_{1}$ exhibits an inverse-power dependence on magnetic field ${T}_{1}\ensuremath{\propto}{B}^{\ensuremath{-}n}$, with $4\ensuremath{\le}n\ensuremath{\le}5$, over a field range of 1.75 T to 7 T. We derive an analytic expression for the donor spin-relaxation rate due to spin-orbit (admixture mechanism) and electron-phonon (piezoelectric) coupling for the wurtzite crystal symmetry. Excellent quantitative agreement is found between experiment and theory suggesting the admixture spin-orbit mechanism is the dominant contribution to ${T}_{1}$ in the measured magnetic field range. Temperature and excitation-energy dependent measurements indicate a donor density dependent interaction may contribute to small deviations between experiment and theory. The longest ${T}_{1}$ measured is 480 ms at 1.75 T with increasing ${T}_{1}$ at smaller fields theoretically expected. This work highlights the extremely long longitudinal spin-relaxation time for ZnO donors due to their small spin-orbit coupling.