  In heterostructures of LaAlO3 (LAO) and SrTiO3 (STO), two nonmagnetic
insulators, various forms of magnetism have been observed [1-7], which may [8,
9] or may not [10] arise from interface charge carriers that migrate from the
LAO to the interface in an electronic reconstruction [11]. We image the
magnetic landscape [5] in a series of n-type samples of varying LAO thickness.
We find ferromagnetic patches that appear only above a critical thickness,
similar to that for conductivity [12]. Consequently we conclude that an
interface reconstruction is necessary for the formation of magnetism. We
observe no change in ferromagnetism with gate voltage, and detect
ferromagnetism in a non-conducting p-type sample, indicating that the carriers
at the interface do not need to be itinerant to generate magnetism. The fact
that the ferromagnetism appears in isolated patches whose density varies
greatly between samples strongly suggests that disorder or local strain induce
magnetism in a population of the interface carriers.
