# Topologically nontrivial magnonic solitons

## TL;DR

This paper explores the formation and classification of topologically nontrivial magnonic solitons in a spin lattice modeled after the Haldane model, revealing thresholds, different classes, and phase separation phenomena.

## Contribution

It introduces the concept of topological magnonic solitons, analyzing their formation, classification, and phase behavior in a nontrivial topological bandgap.

## Key findings

- Soliton formation thresholds depend on anisotropy and interaction strength.
- Multiple classes of topological solitons exist within the same topological phase.
- Solitons can induce phase separation with boundaries between trivial and non-trivial phases.

## Abstract

The intrinsic non-linearities of the spin dynamics in condensed matter systems give rise to a rich phenomenology that can be strongly affected by topology. Here we study formation of magnonic solitons in the topologically nontrivial bandgap of a spin lattice realization of the Haldane model, in both static and dynamic (Floquet) regimes. We consider nonlinearities caused by magnetic crystalline anisotropy and magnon-magnon interactions. We find soliton formation power thresholds as a function of anisotropy coefficient and interaction strength. We predict different classes of topological solitons for the same topological class of the underlying lattice and explain it in terms of a transition from a topologically nontrivial mass to a trivial one. Our findings imply that a soliton can phase-separate, containing boundaries between topologically trivial and non-trivial phases, which is associated with a vanishing spin wave gap.