# Theory of skyrmion, meron, anti-skyrmion and anti-meron in chiral magnets

## TL;DR

This paper derives exact solutions for skyrmions and merons in chiral magnets, revealing how their sizes depend on magnetic interactions and explaining the stabilization of anti-skyrmions and anti-merons in different symmetry systems.

## Contribution

It provides closed-form solutions for topological structures in chiral magnets and clarifies how material parameters influence their stability and size.

## Key findings

- Skyrmion and meron solutions depend on Dzyaloshinskii-Moriya interaction ratios.
- Anti-skyrmions and anti-merons are stabilized by anisotropic Dzyaloshinskii-Moriya interactions.
- The phase diagram of magnetic phases is constructed based on energy comparisons.

## Abstract

We find closed-form solution of the Euler equation for a chiral magnet in terms of a skyrmion or a meron depending on the relative strengths of magnetic anisotropy and magnetic field. We show that the relevant length scales for these solutions primarily depend on the strengths of Dzyaloshinskii-Moriya interaction through its ratios, respectively, with magnetic field and magnetic anisotropy. We thus unambiguously determine the parameter dependencies on the radius of the topological structures particularly of the skyrmions, showing an excellent agreement with experiments and first-principle studies. An anisotropic Dzyaloshinskii-Moriya interaction suitable for thin films made with $C_{nv}$ symmetric materials is found to stabilize anti-skyrmion and anti-meron, which are prototypical for $D_{2d}$ symmetric systems, depending on the degree of anisotropy. Based on these solutions, we obtain phase diagram by comparing the energies of various collinear and non-collinear competing phases.