Unexpectedly Large Electronic Contribution to Linear Magnetoelectricity

We show that the electronic part of the linear magnetoelectric response, usually omitted in first-principles studies, can be comparable in magnitude to that mediated by polar lattice distortions, even in strong magnetoelectrics. Using a self-consistent response to a Zeeman field for noncollinear spins, we show how polarization emerges in magnetoelectrics through both electronic and lattice contributions--analogous to the high- and low-frequency responses of dielectrics. The approach we use is computationally simple, and can be used to study linear and nonlinear responses to magnetic fields.