  The unconventional magnetotransport at the interface between transition-metal
oxides $LaAlO_3$ (LAO) and $SrTiO_3$ (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 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 behaviour. These peculiar features are the
consequences of the anisotropy of both (intra-band and inter-band )
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.
