$LaAlO_3/SrTiO_3$--A Tale of Two Magnetisms

Ten years since the first report of magnetism by Brinkman et al.\footnote{A. Brinkman \textit{et al.}, Nat. Mater. \textbf{6}, 493 (2007)}, a unified picture of magnetism at the two-dimensional electron system (2DES) between $LaAlO_3/SrTiO_3$ is still lacking. The understanding is further hindered by the complex interplay of magnetism and many other aspects of this system: multi-band superconductivity, quantum paraelectricity, multiferroicity, to name but a few. We argue that the reported magnetic signatures in this system can come from two principal origins\footnote{Y. Pai \textit{et al.}, arXiv:1610.00789)}: (1) a ferromagnetic long-range order resulting from local magnetic moments mediated by itinerant electrons, and (2) metamagnetic phenomena associated with electron pairing without superconductivity \footnote{G. Cheng \textit{et al.}, Nature \textbf{521}, 196 (2015)} . Finally, we discuss possible experimental tests of this framework.