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The epitaxial atomistic interfaces of two insulating oxides, LaAlO$_3$(LAO)/SrTiO$_3$ (STO), have attracted great interest owing to rich emergentphenomena \cite{hwang12:nmat,coey13:mrs,ohtomo04:} such as interfacemetallicity \cite{ohtomo04:,nakagawa06:}, thickness dependent insulator-metaltransition \cite{huijben06:nmat}, superconductivity \cite{N.Reyren08312007},ferromagnetism \cite{brinkman.07:natmat}, and even their coexistence\cite{bert11:nphys,li11:nphys,dikin11:prl}. However, the physics origin offerromagnetic ordering in the $n$-type LAO/STO interface is in debate. Here wepropose that the polar distortion of La atom can ignite the ferromagnetism atthe interface even without oxygen vacancy. The induced hybridization between La$d_{z^2}$ and O $p_{x,y}$ states can mediate double-exchange like interactionbetween Ti $d_{xy}$ electrons. We further suggest that the structural andelectrical modification of the outermost surface of LAO or switching thepolarization direction of ferroelectric overlayers on LAO/STO can promote suchLa displacement.

La displacement driven Double-exchange like mediation in Titanium $d_{xy}$ ferromagnetism at the LaAlO$_3$/SrTiO$_3$