Spin torques and anomalous velocity in spin textures induced by fastelectron injection from topological ferromagnets: The role of gauge fields.

A new method for analyzing magnetization dynamics in spin textures under the influence of fast electron
injection from topological ferromagnetic sources such as Dirac half metals has been proposed. These electrons,
traveling at a velocity v with a non-negligible value of v/c (where c is the speed of light), generate
a non-equilibrium magnetization density in the spin-texture region, which is related to an electric dipole
moment via relativistic interactions. When this resulting dipole moment interacts with gauge fields in the
spin-texture region, an effective field is created that produces spin torques. These torques, like spin-orbit
torques that occur when electrons are injected from a heavy metal into a ferromagnet, can display both
damping-like and anti-damping-like properties. Finally, we demonstrate that such an interaction between
the dipole moment and the gauge field introduces an anomalous velocity that can contribute to transverse
electrical conductivity in the spin texture in a way comparable to the topological Hall effect.