  Multi-orbital physics in quasi-two-dimensional electron gases (q2DEGs)
triggers unique phenomena not observed in bulk materials, such as
unconventional superconductivity and magnetism. Here, we investigate the
mechanism of orbital selective switching of the spin-polarization in the oxide
q2DEG formed at the (001) interface between the LaAlO$_{3}$, EuTiO$_{3}$ and
SrTiO$_{3}$ band insulators. By using density functional theory calculations,
transport, magnetic and x-ray spectroscopy measurements, we find that the
filling of titanium-bands with 3d$_{xz,yz}$ orbital character in the EuTiO3
layer and at the interface with SrTiO$_{3}$ induces an antiferromagnetic to
ferromagnetic switching of the exchange interaction between Eu-4f$^{7}$
magnetic moments. The results explain the observation of the carrier density
dependent ferromagnetic correlations and anomalous Hall effect in this q2DEG,
and demonstrate how combined theoretical and experimental approaches can lead
to a deeper understanding of novel electronic phases and serve as a guide for
the materials design for advanced electronic applications.
