Interplay between elasticity, ferroelectricity and magnetism at the domain walls of bismuth ferrite

Multiferroic domain walls have recently been proposed as the active element in devices related to spintronics, data storage, and magnetic logic. Among multiferroics, BiFeO₃ is by far the most studied material. Its domain walls have shown rich behaviours that include conductivity in an otherwise insulating crystal, and magnetotransport properties that are markedly different from those of the bulk. In this article we summarize the experimental evidence and the current models used to understand the interplay between elastic, electric, and magnetic properties of the domain walls. Starting from the considera- tion of antiferromagnetic domain structures on a background of ferroelectric domains, and emphasizing pinning effects, we proceed to discuss the microscopic behavior of ferroelectricity and magnetism at the walls. We describe how domain organization in BiFeO₃ is caused by structural transformations, and scrutinize modelling works pinpointing their characteristic features. Finally, we summarize the recent progress and list open questions for future study on BiFeO₃ domain structures.