# Self-Focusing Skyrmion Racetracks in Ferrimagnets

## TL;DR

This paper proposes a theoretical framework where inhomogeneous ferrimagnetic films near the angular momentum compensation point can guide skyrmions along self-focusing racetracks, enabling controlled skyrmion motion.

## Contribution

It introduces the concept of using lines of zero angular momentum as self-focusing racetracks for skyrmions in ferrimagnets, with derived equations of motion and trajectory analysis.

## Key findings

- Skyrmions can follow snake trajectories in nonuniform angular momentum density.
- The equations of motion unify ferromagnetic and antiferromagnetic limits.
- Self-focusing racetracks can be engineered using angular momentum profiles.

## Abstract

We theoretically study the dynamics of ferrimagnetic skyrmions in inhomogeneous metallic films close to the angular momentum compensation point. In particular, it is shown that the line of the vanishing angular momentum can be utilized as a self-focusing racetrack for skyrmions. To that end, we begin by deriving the equations of motion for the dynamics of collinear ferrimagnets in the presence of a charge current. The obtained equations of motion reduce to those of ferromagnets and antiferromagnets at two special limits. In the collective coordinate approach, a skyrmion behaves as a massive charged particle moving in a viscous medium subjected to a magnetic field. Analogous to the snake orbits of electrons in a nonuniform magnetic field, we show that a ferrimagnet with the nonuniform angular momentum density can exhibit snake trajectories of skyrmions, which can be utilized as racetracks for skyrmions.