Dynamics of magnetic skyrmions under temperature gradients

We expand the Zhang–Li spin-transfer torque [Phys. Rev. Lett. 93, 127204 (2004)] to finite temperatures by the scattering amplitude. Considering various factors, including the adiabatic and diabatic effects of electrons and magnons, entropy equivalent field, thermal dipole field, thermal activation, magnetic-anisotropy gradient, and diffusion, we answer a recent question both experimentally and theoretically controversial: Will skyrmions move to the hot or cold region under thermal gradients?