Magnetic vortex near the extended linear magnetic inhomogeneity

In this paper, the problem of a magnetic vortex motion in a field of extended linear inhomogeneity is solved theoretically. The motion parameters are calculated by the method of collective variables (Thiel's equation) with the vortex effective mass and the third-order gyrovector. On the basis of the equation of motion, the influence of the core mass and the third-order gyrovector on the character of the vortex motion as a quasiparticle is analyzed. Using the method of magnetostatic charges, analytical expressions are obtained for the effective potentials where the vortex core is located: (a) near the edge of the magnet or at the boundary of different magnetic phases, (b) near the linear inhomogeneity of local anisotropy (bidirectional and unidirectional). The solution of the equation of motion made it possible to obtain the trajectories of the core in various physical situations. In addition, the paper discusses the features of the Hall effect for vortices/skyrmions, which are provided by the inertial properties and a third-order gyrovector. It is shown that when the core of a linear inhomogeneity crosses a unidirectional anisotropy or the boundary of magnetic phases, a curvature of the trajectory is observed, which is similar to the refraction of light at the boundary of optically dissimilar environment. It is important to note that the introduction of the mass and gyroscopic effect of the third order in the equation of motion showed that the motion of the vortex, even in a homogeneous potential, is not translational. In this case, the trajectory is an overlay of cycloids of different rotation frequencies (analytical expressions are obtained for the frequencies). It is shown that, the introduction of the mass and the gyroscopic term of the third order, the motion of the vortex core cannot be considered translational at least during the time of the transition mode until the stationary mode of motion takes place.

Automated summary

This paper theoretically solves the problem of magnetic vortex motion in a field of extended linear inhomogeneity, calculating the motion parameters with the vortex effective mass and the third-order gyrovector using the method of collective variables. Analytical expressions for the effective potentials near the vortex core's location and the influence of core mass and third-order gyrovector on the vortex motion as a quasiparticle are discussed. The introduction of mass and gyroscopic effect of the third order shows that the motion of the vortex core is not translational, with trajectories overlaying cycloids of different rotation frequencies.