Instability of magnetic skyrmion strings induced by longitudinal spin currents

One of the fascinating aspects of two-dimensional topological spin textures, so-called magnetic skyrmions, is their interplay with spin currents. It is well established that spin-transfer torques exerted by in-plane spin currents give rise to a motion of magnetic skyrmions resulting in a skyrmion Hall effect. In films of finite thickness or in three-dimensional bulk samples the skyrmions extend in the third direction forming a string. This string is aligned with the applied magnetic field and nonreciprocal spin waves can propagate along skyrmion strings. In this work, we investigate the influence of spin currents that flow parallel to the skyrmion string. We show that, remarkably, such a current component immediately destabilizes the string in a clean system. This instability is caused by the longitudinal current leading to the emission of translational Goldstone modes with finite wavevectors along the string, in contrast to the transversal current that couples only to the Goldstone mode with zero momentum. As a result, helix-shaped deformations develop, whose amplitudes grow with time and eventually break the string. Employing an analytical stability analysis complemented by micromagnetic simulations, we demonstrate that both a single string and skyrmion string lattice are destabilized by this mechanism.