Spin-Orbit Interaction in GaN / Alx Ga

Fundamental aspects of spin-orbit interaction in commercially relevant $\mathrm{Ga}\mathrm{N}$/${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ heterostructures hosting two-dimensional electron systems are extensively studied by electron spin resonance (ESR). This unprecedentedly accurate experimental technique allows access to the fine details of coupling between the spin degree of freedom and the quantized orbital motion of an electron in the quantum Hall regime through the precise measurement of the electron $g$-factor. Filling-factor-dependent changes of the $g$-factor value in strong magnetic fields allow extraction of the Rashba spin-orbit interaction constant $\ensuremath{\alpha}$ in various $\mathrm{Ga}\mathrm{N}$/${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ heterojunctions with electron sheet densities in the range $0.8--5.2\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. Despite three significantly different approaches used to tune the electron density, the extracted value of $\ensuremath{\alpha}$ is on the order of $5.3\ifmmode\pm\else\textpm\fi{}0.4$ meV $\text{\AA{}}$ for all experimental realizations. This striking finding can be explained by assuming that the spin-orbit interaction is of bulk origin. Theoretical calculations confirm this observation, as the bulk cubic in-plane wave-vector term of the spin-orbit interaction compensates the rising contribution due to the change in the quantum well shape. Finally, the value of $\ensuremath{\alpha}$ is cross-checked and confirmed by weak antilocalization measurements in the longitudinal magnetoresistance at substantially lower magnetic field values compared to the ESR approach. The presented experimental findings provide knowledge for estimating the true scales of spin-orbit interaction in GaN-based spintronic devices.