A strategy to drive skyrmion motion by a combination of an anisotropy gradient and spin Hall effect has recently been demonstrated. Here, we study the fundamental properties of this type of motion by combining micromagnetic simulations and a generalized Thiele equation. We find that the anisotropy gradient drives the skyrmion mainly along the direction perpendicular to the gradient, due to the conservative part of the torque. There is some slower motion along the direction parallel to the anisotropy gradient due to damping torque. When an appropriate spin Hall torque is added, the skyrmion velocity in the direction of the anisotropy gradient can be enhanced. This motion gives rise to acceleration of the skyrmion as this moves to regions of varying anisotropy. This phenomenon should be taken into account in experiments for the correct evaluation of the skyrmion velocity. We employ a Thiele like formalism and derive expressions for the velocity and the acceleration of the skyrmion that match very well with micromagnetic simulation results.
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