First-principles approach to lattice-mediated magnetoelectric effects

I will present a first-principles scheme for the computation of the magnetoelectric (ME) response of magnetic insulators. The method focuses on the \textit{lattice-mediated} part of the magnetic response to an electric field, which can be expected to be the dominant contribution in materials displaying a strong coupling, thus avoiding the technical difficulties associated to the treatment of a purely electronic ME effect. I will describe results of calcultions for Cr$_{2}$O$_{3}$ and other model magnetoelectric compounds.