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

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