Electric Field-Induced Skyrmion Crystals via Charged Monopoles in   Insulating Helimagets
  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. 
Haruki Watanabe, Ashvin Vishwanath
cond-mat.str-el hep-th