First-Principles Approach to Lattice-Mediated Magnetoelectric Effects*

I will present a microscopic theory of the magnetoelectric response of an insulator, and derive from it an analytical expression for the lattice-mediated part of the effect. As I will show, such a result provides us with distinct hints at strategies to increase the magnitude of the response, as well as with a convenient method for performing first-principles calculations. I will illustrate the usefulness of the proposed approach with applications to Cr$_{2}$O$_{3}$, a model magnetoelectric crystal, and BiFeO$_{3}$ and related compounds, the best studied, and arguably most technologically promising, family of multiferroics. \newline \newline Ref.: J. I\~{n}iguez, Phys. Rev. Lett. 101, 117201 (2008).