  We theoretically study magnetoelectric effects in a heterostructure of a
generic band insulator and a ferromagnet. In contrast to the kinetic
magnetoelectric effect in metals, referred to as the Edelstein effect or the
inverse spin galvanic effect, our mechanism relies on virtual interband
transitions between the valence and conduction bands and therefore immune to
disorder or impurity scattering. By calculating electric field-induced
magnetization by the linear response theory, we reveal that the magnetoelectric
effect shows up without specific parameter choices. The magnetoelectric effect
qualitatively varies by changing the direction of the magnetic moment in the
ferromagnet: the response is diagonal for the out-of-plane moment, whereas it
is off-diagonal for the inplane moment. We also find out that in optical
frequencies, the magnetoelectric signal can be drastically enhanced via
interband resonant excitations. Finally, we estimate the magnitude of the
magnetoelectric effect for a hybrid halide perovskite semiconductor as an
example of the band insulator and compare it with other magnetoelectric
materials. We underscore that our mechanism is quite general and widely
expectable, only requiring the Rashba spin-orbit coupling and exchange
coupling. Our result could potentially offer a promising method of Joule
heating-free electric manipulation of magnetic moments in spintronic devices.
