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Magnetic electric effects in ferromagnetic metals are discussed from theviewpoint of effective spin electromagnetic field that couples to conductionelectron spin. The effective field in the adiabatic limit is the spin Berry'sphase in space and time, and it leads to spin motive force (voltage generatedby magnetization dynamics) and topological Hall effect due to spin chirality.Its gauge coupling to spin current describes the spin transfer effect, wheremagnetization structure is driven by an applied spin current. The idea ofeffective gauge field can be extended to include spin relaxation and Rashbaspin-orbit interaction. Voltage generation by the inverse Edelstein effect injunctions is interpreted as due to the electric component of Rashba-inducedspin gauge field. The spin gauge field arising from the Rashba interactionturns out to coincides with troidal moment, and causes asymmetric lightpropagation (directional dichroism) as a result of the Doppler shift. Rashbaconductor without magnetization is shown to be natural metamaterial exhibitingnegative refraction.

Theory of electron transport and magnetization dynamics in metallic ferromagnets