Microscopic approach to current-driven domain wall dynamics

This review describes in detail the essential techniques used in microscopic theories on spintronics. We have investigated the domain wall dynamics induced by ail electric current, based on the s-d exchange model. The domain wall is treated as rigid anti planar and is described by two collective coordinates: the position and angle of wall magnetization. file 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 oil 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. The effect of conduction electron spin relaxation on the torque and wall dynamics is also studied. (C) 2008 Elsevier B.V. All rights reserved.