An introduction to the use of representation analysis for studying magnetoelectrics and multiferroics

This lecture is an introduction to the theory of representations applied to the study of magnetoelectric and multiferroic materials. It is intended for students or newcomers in the field and explains the key concepts required to understand phenomenologically the coupling between magnetic phase transitions in crystals and dielectric properties. Symmetry properties of some prototypal magnetoelectrics and multiferroics are analysed, including the treatment of incommensurate spin-driven ferroelectrics. It is deliberately written with a minimal use of mathematical formulation or a strict group theoretical approach