Dzyaloshinskii–Moriya-like interaction in ferroelectrics and antiferroelectrics

The Dzyaloshinskii–Moriya interaction (DMI) between two magnetic moments mi and mj is of the form $${\rm{D}}_{ij} \cdot ({\rm{m}}_i \times {\rm{m}}_j)$$ . It originates from spin–orbit coupling, and is at the heart of fascinating phenomena involving non-collinear magnetism, such as magnetic topological defects (for example, skyrmions) as well as spin–orbit torques and magnetically driven ferroelectricity, that are of significant fundamental and technological interest. In sharp contrast, its electric counterpart, which is an electric DMI characterized by its $${{\bf{D}}}_{ij}^{\prime}$$ strength and describing an interaction between two polar displacements ui and uj, has rarely been considered, despite the striking possibility that it could also generate new features associated with non-collinear patterns of electric dipoles. Here we report first-principles simulations combined with group theoretical symmetry analysis which not only demonstrate that electric DMI does exist and has a one-to-one correspondence with its magnetic analogue, but also reveals a physical source for it. These findings can be used to explain and/or design phenomena of possible technological importance in ferroelectrics and multiferroics. The Dzyaloshinskii–Moriya interaction (DMI) enables coupling of magnetic spins and is responsible for non-collinear phenomena such as skyrmions. Here, using first-principles simulations and group theory analysis, it is demonstrated that an electric DMI exists and is analogous to the magnetic DMI.