Energetic Couplings in Ferroics

International audience; Ferroics include diverse degrees of freedom (such as structural distortions and magnetic moments) among which cross couplings occur, rendering a large variety of interesting phenomena. Determining such couplings, based on symmetry analysis, is not only important to interpret observed phenomena but can also result in novel predictions to be then experimentally checked. Often, such energetic couplings are difficult to construct without a deep knowledge of group theoretical symmetry principles. In the present review, a crash course towards the derivation of energetic couplings, without using much the group theoretical language, is provided. Rather, the present approach relies on a graphical technique and suitable symbolic language, which naturally yields some known couplings (resulting in, e.g., spin/dipole canting, magnetically driven polarization and antipolar/antiferroelectric states). This review also reports and discusses other symmetry-allowed energetic terms, including some leading to the occurrence of an electric polarization in a variety of materials, and "exotic" ones that generate complex phases and phenomena in, e.g., nanostructures and heterostructures.