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The emergence of magnetism in otherwise nonmagnetic compounds and itsunderlying mechanisms have become the subject of intense research. Here wedemonstrate that the nonmagnetic oxygen vacancies are responsible for anunconventional magnetic state common for titanate interfaces and surfaces.Using an effective multiorbital modelling, we find that the presence oflocalized vacancies leads to an interplay of ferromagnetic order in theitinerant t2g band and complex magnetic oscillations in theorbitally-reconstructed eg-band, which can be tuned by gate fields at oxideinterfaces. The magnetic phase diagram includes highly fragmented regions ofstable and phase-separated magnetic states forming beyond nonzero criticaldefect concentrations.

Emerging magnetism and electronic phase separation at titanate interfaces