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This review describes in detail the essential techniques used in microscopic theories on spintronics. We have investigated the domain wall dynamics induced by electric current based on the $s$-$d$ exchange model. The domain wall is treated as rigid and planar and is described by two collective coordinates: the position and angle of wall magnetization. The effect of conduction electrons on the domain wall dynamics is calculated in the case of slowly varying spin structure (close to the adiabatic limit) by use of a gauge transformation. The spin-transfer torque and force on the wall are expressed by Feynman diagrams and calculated systematically using non-equilibrium Green's functions, treating electrons fully quantum mechanically. The wall dynamics is discussed based on two coupled equations of motion derived for two collective coordinates. The force is related to electron transport properties, resistivity, and the Hall effect. Effect of conduction electron spin relaxation on the torque and wall dynamics is also studied.Comment: manucript accepted to Phys. Re

A self-contained theory of the domain wall dynamics in ferromagnets under finite electric current is presented. The current has two effects: one is momentum transfer, which is proportional to the charge current and wall resistivity (rho(w)); the other is spin transfer, proportional to spin current. For thick walls, as in metallic wires, the latter dominates and the threshold current for wall motion is determined by the hard-axis magnetic anisotropy, except for the case of very strong pinning. For thin walls, as in nanocontacts and magnetic semiconductors, the momentum-transfer effect dominates, and the threshold current is proportional to V(0)/rho(w), V0 being the pinning potential.

A magnetic vortex is a curling magnetic structure realized in a ferromagnetic disk, which is a promising candidate for a memory cell for future non-volatile data-storage devices. Thus, an understanding of the stability and dynamical behaviour of the magnetic vortex is a major requirement for developing magnetic data-storage technology. Since the publication of experimental proof for the existence of a nanometre-scale core with out-of-plane magnetization in a magnetic vortex, the dynamics of vortices have been investigated intensively. However, a way to electrically control the core magnetization, which is a key for constructing a vortex-core memory, has been lacking. Here, we demonstrate the electrical switching of the core magnetization by using the current-driven resonant dynamics of the vortex; the core switching is triggered by a strong dynamic field that is produced locally by a rotational core motion at a high speed of several hundred metres per second. Efficient switching of the vortex core without magnetic-field application is achieved owing to resonance. This opens up the potentiality of a simple magnetic disk as a building block for spintronic devices such as a memory cell where the bit data is stored as the direction of the nanometre-scale core magnetization.

Effects of conduction electrons on magnetization dynamics, represented by spin torques, are calculated microscopically in the first order in spatial gradient and time derivative of magnetization. Special attention is paid to the so-called $\beta$-term and the Gilbert damping, $\alpha$, in the presence of electrons' spin-relaxation processes, which are modeled by quenched magnetic (and spin-orbit) impurities. The obtained results such as $\alpha \ne \beta$ hold for localized as well as itinerant ferromagnetism.Comment: 4 page