  We investigate theoretically the spin torque and magnetization dynamic in a
thin ferromagnetic (FM) layer with spatially varying magnetization. The FM
layer is deposited on the surface of a topological insulator (TI). In the limit
of the adiabatic relaxation of electron spin along the magnetization, the
interaction between the exchange interaction and the Rashba-like surface
texture of a TI yields a topological gauge field. Under the gauge field and an
applied current, spin torque is induced according to the direction of the
current. We derived the corresponding effective anisotropy field and hence the
modified Landau-Lifshitz-Gilbert equation, which describes the spin torque and
the magnetization dynamic. In addition, we study the effective field for
exemplary magnetic textures, such as domain wall, skyrmion, and vortex
configurations. The estimated strength of the effective field is comparable to
the switching fields of typical FM materials, and hence can significantly
influence the dynamics of the FM layer.
