Magnetoresistance of two-dimensional and three-dimensional electron gas in LaAlO₃/SrTiO₃ heterostructures: Influence of magnetic ordering, interface scattering, and dimensionality

Magnetoresistance (MR) anisotropy in LaAlO₃/SrTiO₃ interfaces is compared between samples prepared in high-oxygen partial-pressure (P_O2) of 10^-4 mbar exhibiting quasi-two-dimensional (quasi-2D) electron gas and low P_O2 of 10^-6 mbar exhibiting 3D conductivity. While the 3D interfaces show positive MR for all temperatures, the quasi-2D interfaces show negative MR below 30 K, suggesting the presence of magnetic centers in the quasi-2D system. Interestingly, a linear relation between MR and applied magnetic fields was observed in the 3D interfaces for an in-plane field, while in the quasi-2D interfaces for an out-of-plane field, demonstrating the dominant effect of the interface and substrate's vicinal step scattering, respectively. Furthermore, the MR with the out-of-plane field is always larger compared to the MR with in-plane field, suggesting lower dissipation of electrons from interface than defect scattering. Our study demonstrates that MR can be used to distinguish the dimensionality of the charge transport and various (defect, magnetic center, and interface boundary) scattering processes in this system.