  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.
