We report a magnetotransport study of spin relaxation in 1.4-21.2 nm epitaxial SrIrO$_3$ thin films coherently strained on SrTiO$_3$ substrates. Fully charge compensated semimetallic transport has been observed in SrIrO$_3$ films thicker than 1.6 nm, where the charge mobility at 10 K increases from 45 cm$^2$/Vs to 150 cm$^2$/Vs with decreasing film thickness. In the two-dimensional regime, the charge dephasing and spin-orbit scattering lengths extracted from the weak localization/anti-localization effects show power-law dependence on temperature, pointing to the important role of electron-electron interaction. The spin-orbit scattering time $\tau_\text{ so}$ exhibits an Elliott-Yafet mechanism dominated quasi-linear dependence on the momentum relaxation time $\tau_\text{ p}$. Ultrathin films approaching the critical thickness of metal-insulator transition show an abrupt enhancement in $\tau_\text{ so}$, with the corresponding $\tau_\text{ so}/\tau_\text{ p}$ about 7.6 times of the value for thicker films. A likely origin for such unusual enhancement is the onset of strong electron correlation, which leads to charge gap formation and suppresses spin scattering.
Categories: cond-mat.str-el cond-mat.mes-hall