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

The confinement of the two dimensional electron gas (2DEG), preferential occupancy of the Ti 3d orbital and strong spin-orbit coupling at the LaAlO$_3$/SrTiO$_3$ interface play a significant role in its emerging properties. Here we report a fourfold oscillation in the anisotropic magneto resistance (AMR) and the observation of planar Hall effect (PHE) at the LaAlO$_3$/SrTiO$_3$ heterointerface. We evaluate the carrier confinement effects on the AMR and find that the fourfold oscillation appears only for the case of 2DEG system while it is twofold for the 3D system. As the fourfold oscillation fits well to the phenomenological model for a cubic symmetry system, we attribute this oscillation to the anisotropy in the magnetic scattering arising from the interaction of electrons with the localized magnetic moments coupled to the crystal symmetry. The AMR behavior is further found to be sensitive to applied gate electric field, emphasizing the significance of spin-orbit coupling at the interface. These confinement effects suggest that the magnetic interactions are predominant at the interface, and the gate electric field modulation of AMR suggest the possible gate tunable magnetic interactions in these systems. The observed large PHE further indicates that the in plane nature of magnetic ordering arises from the in-plane Ti 3dxy orbitals.