Semiclassical theory of anisotropic transport at LaAlO3/SrTiO3 interfaces under an in-plane magnetic field

The unconventional magnetotransport at the interface between transition-metal oxides ${\mathrm{LaAlO}}₃$ ($\mathrm{LAO}$) and ${\mathrm{SrTiO}}₃$ ($\mathrm{STO}$) is frequently related to mobile electrons interacting with localized magnetic moments. However, nature and properties of magnetism at this interface are not well understood so far. In this paper, we focus on transport effects driven by spin-orbit coupling and intentionally neglect possible strong correlations. The electrical resistivity tensor is calculated as a function of the magnitude and orientation of an external magnetic field parallel to the interface. The semiclassical Boltzmann equation is solved numerically for the two-dimensional system of spin-orbit coupled electrons accelerated by an electric field and scattered by spatially correlated impurities. At temperatures of a few Kelvin and densities such that the chemical potential crosses the second pair of spin-orbit split bands, we find a strongly anisotropic modulation of the (negative) magnetoresistance above $10\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, characterized by multiple maxima and minima away from the crystalline axes. Along with the drop of the magnetoresistance, an abrupt enhancement of the transverse resistivity occurs. The angular modulation of the latter considerably deviates from a (low-field) sinusoidal dependence to a (high-field) step-like behavior. These peculiar features are the consequences of the anisotropy of both intraband and interband scattering amplitudes in the Brillouin zone when the relevant energy scales in the system---chemical potential, spin-orbit interaction, and Zeeman energy---are all comparable to each other. The theory provides good qualitative agreement with experimental data in the literature.