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Using first-principles calculations based on the density functional theory,we show a strong strain dependence of magnetic order in(LaMnO$_{3}$)$_n$/(SrMnO$_{3}$)$_{2n}$ (001) superlattices with $n=1,2$. Theepitaxial strain lifts the degeneracy of Mn $e_{g}$ orbitals, thus inducing aninherent orbital order, which in turn strongly affects the ferromagnetic doubleexchange of itinerant $e_{g}$ electrons, competing with the antiferromagneticsuperexchange of localized $t_{2g}$ electrons. For the case of tensile straininduced by SrTiO$_3$ (001) substrate, we find that the ground state is A-typeantiferromagnetic and $d_{x^2-y^2}$ orbital ordered, which is in excellentagreement with recent experiments [S. J. May {\it et al.}, Nature Materials{\bf 8}, 892 (2009)]. Instead, for the case of compressive strain induced byLaAlO$_3$ (001) substrate, we predict that the ground state is C-typeantiferromagnetic and $d_{3z^2-r^2}$ orbital ordered.

Strain-engineered magnetic order in (LaMnO$_{3}$)$_n$/(SrMnO$_{3}$)$_{2n}$ superlattices