Abstract

Magnetic skyrmions are widely discussed 2D topological solitons found in films of numerous chiral magnets. Here we consider skyrmions in 3D bulk magnets. In this case, the skyrmion core penetrates the magnet volume forming a topological string-like object analogous to the vortex strings in water or in the atmosphere. In equilibrium, the skyrmion string is a static straight line oriented along the applied magnetic field. In general, the position of the string can be defined by the coordinate- and time-dependent first moment of topological charge calculated for the continuously stacked horizontal cross-sections perpendicular to the applied magnetic field. We demonstrate that in the limit of low energies, the skyrmion string dynamics is captured by a non-linear Schrödinger equation (NLSE) of focusing type. Two classes of non-linear periodic waves (so-called dc- and cn-waves) are analytically predicted to exist for the skyrmion string, that is numerically verified with full-scale micromagnetic simulations. The separatrix soliton solution just corresponds to the solitary wave found previously [1]. A breather solution of NLSE, namely Ma breather, was also confirmed for the skyrmion string by means of the micromagnetic simulations.

In addition, we discuss the influence of a spin-polarized current flowing along the skyrmion string, and we show that such a current destabilizes the string. For the ideally clean system, an infinitesimal current is sufficient for the string destabilization. While the finite threshold current is needed in presence of the defects. Our finding of spin-current-induced instability applies to an isolated skyrmion string as well as to a skyrmion string lattice [2].

References:
[1] V. Kravchuk, U. Rößler, J. van den Brink, M. Garst, PRB, 102, 220408(R) (2020).
[2] S. Okumura, V. Kravchuk and M. Garst, in preparation