  Two-dimensional electron gas due to semiconductor interfaces can have high
mobility and exhibits superconductivity, magnetism, and other exotic properties
that are unexpected in constituent bulk materials. We study crystal structures,
electronic states, and magnetism of short-period (BTO)$_m$/(GTO)$_2$ ($m$=2 and
4) superlattices consisting of ferroelectric BaTiO$_3$ (BTO) and ferrimagnetic
insulating polar GdTiO$_3$ (GTO) by first principles calculations. Our
investigation shows that the middle Ti-O monolayer in the GTO layer becomes
metallic because the ferroelectricity in the insulating BTO layer induces an
inhomogeneous electric field against the polarity-produced electric field in
the GTO layer and thus differentially changes the d energy levels of the three
Ti-O monolayers related with the GTO layer. Through avoiding electron
reconstruction, the ferroelectric polarization also makes the electronic states
and magnetism of two interfacial Ti-O monolayers become substantially different
from those in the GTO/SrTiO$_3$ superlattices without ferroelectricity. Such
superlattices are interesting for potential spintronics applications because of
their unique asymmetrical two-dimensional electron-gas properties and possible
useful spin-orbit effects.
