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We investigate the effect of PbTiO3 on the LaAlO\(_3\)/SrTiO\(_3\) hetero-structure by density functional theory, where the asymmetry sandwich not only forms a quasi-two dimensional electron gas but also reveals a ferromagnetic state in the TiO\(_2\) interfaces. It is found out that magnetic moments of TiO\(_2\) interface layers are around 0.18 \(\mu_B\) while they are mostly negligible in the pure LaAlO\(_3\)/SrTiO\(_3\) system. Even though magnetic moments are mainly produced by Ti t2g orbitals, oxygen plays a key role in the formation of the ferromagnetic state since polar distortions primarily occur in oxygen positions of the SrTiO\(_3\) and PbTiO\(_3\) sides in opposite directions.

Magnetism in the Interfaces of the Sandwiched PbTiO\(_3\)/LaAlO\(_3\)/SrTiO\(_3\) Hetero-structure