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Abstract
We present the first systematic {\em ab initio} study of anti-ferrodistortive (AFD) order in Ruddlesden-Popper (RP) phases of strontium titanate, Sr$_{1+n}$Ti$_n$O$_{3n+1}$, as a function of both compressive epitaxial strain and phase number $n$. We find all RP phases to exhibit AFD order under a significant range of strains, recovering the bulk AFD order as $\sim 1/n^2$. A Ginzburg-Landau Hamiltonian generalized to include inter-octahedral interactions reproduces our {\em ab initio} results well, opening a pathway to understanding other nanostructured perovskite systems.
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