Interface control of emergent ferroic order in Ruddlesden-Popper Sr$_{n+1}$Ti$_n$O$_{3n+1}$

We have discovered from first-principles an unusual polar state in the low n Sr$_{n+1}$Ti$_n$O$_{3n+1}$ Ruddlesden-Popper (RP) layered perovskites in which ferroelectricity is nearly degenerate with antiferroelectricity, a relatively rare form of ferroic order. We show that epitaxial strain plays a key role in tuning the ``perpendicular coherence length'' of the ferroelectric mode, and does not induce ferroelectricity in these low dimensional RP materials as is well known to occur in SrTiO$_3$. These systems present an opportunity to manipulate the coherence length of a ferroic distortion in a controlled way, without disorder or a free surface. [T. Birol, N. A. Benedek, C. J. Fennie, Physical Review Letters, in press]