Multiferroic ground states in free standing perovskite-based nanodots: a density functional theory study

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-O 2 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 K 8 NbO 6 ), regardless of the presence of ferroelectricity in the bulk. In contrast, all the B–O 2 terminated nanodots considered relax to a non-cubic ground state. Rather surprisingly, all of these structures exhibit polar ground states (except NaNb 8 O 12 ). 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 Ca 8 TiO 6 ) and all polar B–O 2 terminated nanodots are magnetic, where none show magnetism in the bulk. As with bulk systems, multiferroicity in the B–O 2 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.