  We demonstrate that the electronic contribution to the linear magnetoelectric
response, usually omitted in first-principles studies, can be comparable in
magnitude to that mediated by lattice distortions, even for materials in which
responses are strong. Using a self-consistent Zeeman response to an applied
magnetic field for noncollinear electron spins, we show how electric
polarization emerges in linear magnetoelectrics through both electronic- and
lattice-mediated components -- in analogy with the high- and low-frequency
dielectric response to an electric field. The approach we use is conceptually
and computationally simple, and can be applied to study both linear and
non-linear responses to magnetic fields.
