Ensemble spin relaxation of shallow donor qubits in ZnO

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 $T_1\propto B^{-n}$, with $4\leq n\leq 5$, 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.