  Electrons propagating in a magnetically ordered medium experience an
additional gauge field associated with the Berry phase of their spin following
the local magnetic texture. In contrast to the usual electromagnetic field,
this gauge field admits monopole excitations, corresponding to hedgehog defects
of the magnetic order. In an insulator, these hedgehogs carry a well-defined
electric charge allowing for them to be controlled by electric fields. One
particularly robust mechanism that contributes to the charge is the orbital
magnetoelectric effect, captured by a $\theta$ angle, which leads to a charge
of $e\theta/2\pi$ on hedgehogs. This is a direct consequence of the Witten
effect for magnetic monopoles in a $\theta$ medium. A physical consequence is
that external electric fields can induce skyrmion crystal phases in insulating
helimagnets.
