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Using field effect devices with side gates, we modulate the 2 dimensionalelectron gas hosted at the LaAlO$_3$/SrTiO$_3$ interface to study thetemperature and doping evolution of the magnetotransport. The analysis of thedata reveals different transport regimes depending on the interplay between thedifferent (elastic, inelastic, and spin-orbit) scattering times and theirtemperature dependencies. We find that the spin-orbit interaction stronglyaffects the low temperature transport in the normal state in a very largeregion of the phase diagram, extending beyond the superconducting dome.

Weak-localization and spin-orbit interaction in side-gate field effect devices at the LaAlO$_3$/SrTiO$_3$ interface