Abstract
We use density functional theory to investigate the possibility of polar and multiferroic states in free-standing, perovskite-based nanodots at the atomic limit of miniaturization: single unit cells with terminations which allow centro-symmetry. We consider both A-O and B-O2 terminations for three families of nanodots: (i) A = Ba with B = Ti, Zr, and Hf; (ii) A = Ca and Sr with B = Ti; and (iii) A = Na and K with B = Nb. We find all A–O terminated dots to be non-polar and to exhibit cubic symmetry (except for K8NbO6), regardless of the presence of ferroelectricity in the bulk. In contrast, all the B–O2 terminated nanodots considered relax to a non-cubic ground state. Rather surprisingly, all of these structures exhibit polar ground states (except NaNb8O12). We propose a new structural parameter, the cluster tolerance factor (CTF), to determine whether a particular chemistry will result in a polar ground state nanodot, analogous to the Goldschmidt factor for bulk ferroelectrics. In addition, we find that all A–O terminated (except Ca8TiO6) and all polar B–O2 terminated nanodots are magnetic, where none show magnetism in the bulk. As with bulk systems, multiferroicity in the B–O2 terminated dots originates from separation between spin density in peripheral B atoms and polarity primarily caused by the off-center central A atom. Our findings stress that surface termination plays a crucial role in determining whether ferroelectricity is completely suppressed in perovskite-based materials at their limit of miniaturization.
