This chapter delves into the physics of multiferroics, the recent developments of which are discussed here from the viewpoint of the spin current and “emergent electromagnetism” for constrained systems. It presents the three sources of U(1) gauge fields, namely, the Berry phase associated with the noncollinear spin structure, the spin-orbit interaction (SOI), and the usual electromagnetic field. The chapter reviews multiferroic phenomena in noncollinear magnets from this viewpoint and discusses theories of multiferroic behavior of cycloidal helimagnets in terms of the spin current or vector spin chirality. Relativistic SOI leads to a coupling between the spin current and the electric polarization, and hence the ferroelectric and dielectric responses are a new and important probe for the spin states and their dynamical properties. Microscopic theories of the ground state polarization for various electronic configurations, collective modes including the electromagnon, and some predictions including photoinduced chirality switching are discussed with comparison to experimental results.
Arbitrariness of Zwanziger's Parameter in Stochastic Quantization of Non-Abelian Gauge Fields