LaAlO$_3$/SrTiO$_3$: a tale of two magnetisms

This book chapter reviews the experimental evidence for magnetic phenomena at the LaAlO3/SrTiO3 interface. We argue that essentially all of the signatures of magnetism can be sorted into two distinct categories: (1) magnetic phases (e.g., ferromagnetic or Kondo) involving local magnetic moments and their coupling to itinerant electrons; (2) metamagnetic effects that are mediated by attractive electron-electron interactions that do not involve local moments. We review possible candidates for the local moments that give rise to the ferromagnetic phases and focus on arguments for one potential source: oxygen vacancies. For the metamagnetic transport signatures, band-structure effects (e.g., Lifshitz transition) and strong attractive electron-electron interaction can help consolidate disparate experimental findings.