# Instantons in Chiral Magnets

## TL;DR

This paper systematically constructs and analyzes instanton solutions in one-dimensional anti-ferromagnetic chiral magnets, revealing diverse soliton behaviors across different phases and mapping models with Dzyaloshinskii-Moriya interaction to simpler forms.

## Contribution

It provides a comprehensive construction of instantons in chiral magnets and explores their properties across various phases, including phase diagrams and mappings to related models.

## Key findings

- Instantons manifest as domain walls, bions, dislocations, and isolated solitons.
- Phase diagram includes easy-axis, helical, and tricritical points with distinct instanton behaviors.
- Models with Dzyaloshinskii-Moriya interaction can be mapped to simpler models without it.

## Abstract

We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the $O(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.