  We present a first-principles scheme for computing the magnetoelectric
response of multiferroics. We apply our method to BiFeO3 (BFO) and related
compounds in which Fe is substituted by other magnetic species. We show that
under certain relevant conditions -- i.e., in absence of incommensurate spin
modulation, as in BFO thin films and some BFO-based solid solutions -- these
materials display a large linear magnetoelectric response. Our calculations
reveal the atomistic origin of the coupling and allow us to identify the most
promising strategies to enhance it.
