Weak Antilocalization and Spin-Orbit Coupling in InAlN/AlN/GaN Heterostructures

Spin-orbit coupling is investigated by magnetotransport and weak antilocalization (WAL) measurements in In$_x$Al$_{1-x}$N/AlN/GaN heterostructures in the carrier density ranges extending from 1.22$\times$10$^{13}$ cm$^{-2}$ to 1.41$\times$10$^{13}$ cm$^{-2}$ and from 1.99$\times$10$^{13}$ cm$^{-2}$ to 2.15$\times$10$^{13}$ cm$^{-2}$. By combining the data from AlGaN/AlN/GaN samples, we find that the spin-orbit field is not a constant at high carrier densities and the electron spin-splitting energies show a deviation from linear behavior with Fermi wavefactor. However, the spin-splitting energies extracted from WAL oscillations, even in this high carrier density regime, were found to be much smaller than the previous reports based on Shubnikov-de Haas (SdH) measurements. We will discuss how the nonuniformities in the carrier density can lead to beating features in SdH oscillations, which can then be misinterpreted as large spin-splitting energies. This finding may resolve the long-standing discrepancy between the WAL and SdH results.