We report a detailed analysis of magneto-transport properties of top- and back-gated LaAlO$_3$/SrTiO$_3$ heterostructures. Efficient modulation in magneto-resistance, carrier density, and mobility of the two-dimensional electron liquid present at the interface is achieved by sweeping top and back gate voltages. Analyzing those changes with respect to the carrier density tuning, we observe that the back gate strongly modifies the electron mobility while the top gate mainly varies the carrier density. The evolution of the spin-orbit interaction is also followed as a function of top and back gating.
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