  Magnetic skyrmions are nano-sized topologically non-trivial spin textures
that can be moved by external stimuli such as spin currents and internal
stimuli such as spatial gradients of a material parameter. Since the total
energy of a skyrmion depends linearly on most of these parameters, like the
perpendicular magnetic anisotropy, the exchange constant, or the
Dzyaloshinskii-Moriya interaction strength, a skyrmion will move uniformly in a
weak parameter gradient. In this paper, we show that the linear behavior
changes once the gradients are strong enough so that the magnetic profile of a
skyrmion is significantly altered throughout the propagation. In that case, the
skyrmion experiences acceleration and moves along a curved trajectory.
Furthermore, we show that when spin-orbit torques and material parameter
gradients trigger a skyrmion motion, it can move on a straight path along the
current or gradient direction. We discuss the significance of suppressing the
skyrmion Hall effect for spintronic and neuromorphic applications of skyrmions.
Lastly, we extend our discussion and compare it to a gradient generated by the
Dzyaloshinskii-Moriya interaction.
