Spin-orbit interaction in ZnO/Mg$_x$Zn$_{1-x}$O heterojunctions probed by electron spin resonance spectroscopy

The spin–orbit interaction in a series of ZnO/Mg$_x$Zn$_{1-x}$O heterojunctions containing a two-dimensional electron system with a wurtzite structure has been studied in detail. The spin–orbit coupling constants have been determined from the analysis of the modification of the single-particle $g$-factor caused by the spin–orbit interaction in the quantum Hall effect regime. The $g$-factor has been measured with high accuracy by the electron paramagnetic resonance technique in wide ranges of magnetic fields and electromagnetic frequencies. The spin–orbit coupling constants have been determined for a series of samples with different Mg concentrations, which has allowed us to obtain the dependence of the spin–orbit coupling constant on the two-dimensional electron density $n$. The measured spin–orbit coupling constant is in the range of $0.5$–$0.8$ meV Å and quite weakly depends on $n$. The coefficients specifying the linear and cubic contributions to the spin–orbit interaction determined from the approximation of the experimental data are $\alpha_0 = 0.48$ meV Å and $\gamma=0.12$ eV Å$^3$, respectively. These values are correlated with results obtained by other research groups.