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Tunable spin-orbit interaction (SOI) is an important feature for futurespin-based devices. In the presence of a magnetic field, SOI induces anasymmetry in the energy bands, which can produce non-linear transport effects($V\sim I^2$). Here, we focus on such effects to study the role of SOI in the(111) LaTiO$_3$/SrTiO$_3$ interface. This system is a convenient platform forunderstanding the role of SOI since it exhibits a single-band Hall-responsethrough the entire gate-voltage range studied. We report a pronounced rise inthe non-linear resistance at a critical in-plane field $H_{cr}$. This risedisappears with a small out-of-plane field. We explain these results byconsidering the location of the Dirac point formed at the crossing of thespin-split energy bands. An in-plane magnetic field pushes this point outsideof the Fermi surface, and consequently changes the symmetry of the Fermicontours and intensifies the non-linear transport. An out-of-plane magneticfield opens a gap at the Dirac point, thereby significantly diminishing thenon-linear effects. We propose that magnetoresistance effects previouslyreported in interfaces with SOI could be comprehended within our suggestedscenario.

Enhanced Non-linear Response by Manipulating the Dirac Point in the (111) LaTiO$_3$/SrTiO$_3$ Interface