Ferroelectric Switching Pathways and Domain Structure of SrBi$_2$(Ta,Nb)$_2$O$_9$ from First Principles

Several families of layered perovskite oxide ferroelectrics exhibit a coupling between polarization and structural order parameters, such as octahedral rotation distortions. This coupling provides opportunities for novel electric field-based manipulation of material properties, and also stabilizes complex domain patterns and domain wall vortices. Amongst layered perovskites with such coupled orders, the Aurivillius-phase oxides SrBi$_2B_2$O$_9$ ($B$=Ta, Nb) are well-known for their excellent room temperature ferroelectric performance. This work combines group theoretic analysis with density functional theory calculations to examine the ferroelectric switching processes of SrBi$_2B_2$O$_9$. Low-energy two-step ferroelectric switching paths are identified, with polarization reversal facilitated by structural order parameter rotations. Analysis of the domain structure reveals how the relative energetics of the coupled order parameters translates into a network of several distinct domain wall types linked by domain wall vortex structures. Comparisons are made between the ferroelectric switching and domain structure of SrBi$_2B_2$O$_9$ and those of the layered $n$=2 Ruddlesden-Popper hybrid improper ferroelectrics. The results provide new insight into how ferroelectric properties may be optimized by engineering the complex crystal structures of Aurivllius-phase oxides.