Spin Torque and Force due to Current for General Spin Textures

Abstract

The nonadiabatic correction to spin transfer torque arising from fast-varying spin texture is calculated treating the conductions electron fully quantum mechanically. The torque is nonlocal in space, and is shown to be equivalent to a force (due to momentum transfer) acting on the center of mass of the texture. Another kind of force exists in the adiabatic regime, and it is identified to be of topological origin. These forces are shown to be the counter-reactions of electric transport properties, resistivity and the Hall effect.