Domains and domain walls in multiferroics

Abstract Multiferroics are gathering solid-state matter in which several types of orders are simultaneously allowed, as ferroelectricity, ferromagnetism (or antiferromagnetism), ferroelasticity, or ferrotoroidicity. Among all, the ferroelectric/ferromagnetic couple is the most intensively studied because of potential applications in novel low-power magnetoelectric devices. Switching of one order thanks to the other necessarily proceeds via the nucleation and growth of coupled domains. This review is an introduction to the basics of ferroelectric/ferromagnetic domain formation and to the recent microscopy techniques devoted to domains imaging, providing new insights into the archetypal multiferroic domain morphologies. Some relevant examples are also given to illustrate some of the unexpected properties of domain walls, as well as the way these domain walls can be manipulated altogether thanks to various types of magnetoelectric coupling.