Trends in (LaMnO$_3$)$_n$/(SrTiO$_3$)$_m$ superlattices with varying layer thicknesses

We investigate the thickness dependence of the structural, electronic, and magnetic properties of (LaMnO$_3$)$_n$/(SrTiO$_3$)$_m$ ($n$, $m$ = 2, 4, 6, 8) superlattices using density functional theory. The structure relaxation turns out to be highly sensitive to the onsite Coulomb interaction. In contrast to bulk SrTiO$_3$, strongly distorted O octahedra are observed in the SrTiO$_3$ layers with a systematic off centering of the Ti atoms. The systems favour ferromagnetic spin ordering rather than the antiferromagnetic spin ordering of bulk LaMnO$_3$ and all show half-metallicity, while a systematic reduction of the minority spin band gaps as a function of the LaMnO$_3$ and SrTiO$_3$ layer thicknesses originates from modifications of the Ti $d_{xy}$ states.