Effective gauge field theory of spintronics

The aim of this paper is to present a comprehensive theory of spintronics phenomena based on the concept of effective gauge field, the spin gauge field. An effective gauge field generally arises when we change a basis to describe system and describes low energy properties of the system. In the case of ferromagnetic metals we consider, it arises from structures of localized spin (magnetization) and couples to spin current of conduction electron. The first half of the paper is devoted to quantum mechanical arguments and phenomenology. We show that the spin gauge field has adiabatic and nonadiabatic (off-diagonal) components, consisting an SU(2) gauge field. The adiabatic component gives rise to spin Berry's phase, topological Hall effect and spin motive force, while nonadiabatic components are essential for spin-transfer torque and spin pumping effects by inducing nonequilibrium spin accumulation. In the latter part of the paper, field theoretic approaches are described. Dynamics of localized spins in the presence of applied spin-polarized current is studied in a microscopic viewpoint, and current-driven domain wall motion is discussed. Recent developments on interface spin-orbit interaction is also mentioned.