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The confinement of the two dimensional electron gas (2DEG), preferentialoccupancy of the Ti 3d orbital and strong spin-orbit coupling at theLaAlO$_3$/SrTiO$_3$ interface play a significant role in its emergingproperties. Here we report a fourfold oscillation in the anisotropic magnetoresistance (AMR) and the observation of planar Hall effect (PHE) at theLaAlO$_3$/SrTiO$_3$ heterointerface. We evaluate the carrier confinementeffects on the AMR and find that the fourfold oscillation appears only for thecase of 2DEG system while it is twofold for the 3D system. As the fourfoldoscillation fits well to the phenomenological model for a cubic symmetrysystem, we attribute this oscillation to the anisotropy in the magneticscattering arising from the interaction of electrons with the localizedmagnetic moments coupled to the crystal symmetry. The AMR behavior is furtherfound to be sensitive to applied gate electric field, emphasizing thesignificance of spin-orbit coupling at the interface. These confinement effectssuggest that the magnetic interactions are predominant at the interface, andthe gate electric field modulation of AMR suggest the possible gate tunablemagnetic interactions in these systems. The observed large PHE furtherindicates that the in plane nature of magnetic ordering arises from thein-plane Ti 3dxy orbitals.

Anisotropic Magneto Resistance and Planar Hall Effect at the  LaAlO$_3$/SrTiO$_3$ Heterointerfaces: Effect of Carrier Confinement on  Magnetic Interactions