Ferroelectricity in free standing perovskite-based nanodots: A density functional theory study

TL;DR

This study uses density functional theory to explore ferroelectric and multiferroic states in free-standing perovskite nanodots, revealing how surface termination influences their polar and magnetic properties at the atomic scale.

Contribution

It introduces the cluster tolerance factor (CTF) as a new predictor for polarity in nanodots, extending understanding of ferroelectricity at the nanoscale.

Findings

B-O2 terminated nanodots can exhibit polar ground states.

Surface termination critically affects ferroelectricity in nanodots.

Certain nanodots are both magnetic and polar, indicating multiferroicity.

Abstract

We use density functional theory to investigate the possibility of polar and multiferroic states in free-standing, perovskite-based nanodots at their limit of miniaturization: single unit cell with termination to allow centrosymmetry. 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, regardless of the presence of ferroelectricity in the bulk. These dots all carry a net magnetic moment, except Ca8TiO6. On the other hand, all B-O2 terminated nanodots considered in this study relax to a non-cubic ground state. Rather surprisingly, a subset of these structures (BaTi8O12, BaHf8O12, BaZr8O12, SrTi8O12, CaTi8O12 and KNb8O12) exhibit polar ground states. We propose a new structural parameter, the cluster tolerance factor (CTF), to determine whether a particular combination of A and B will yield a polar ground state in the nanodot geometry, analogous to the Goldschmidt factor in bulk ferroelectrics. We also find that in all polar B-O2 terminated nanodots are also magnetic. The multiferroic state 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.