# Tunable multi-magnon Floquet topological edge states

## TL;DR

This paper demonstrates that periodic modulation of the Dzyaloshinskii-Moriya interaction in a 2D magnon insulator can induce topological phase transitions, creating controllable, robust edge states with potential applications in magnonic devices.

## Contribution

It introduces a method to induce and control topological edge states in a magnon insulator via time-modulated DMI, including multi-magnon states.

## Key findings

- Periodic DMI modulation induces topological phase transitions.
- Edge states are composed of single-magnon and two-magnon bound states.
- Chirality of edge states can be controlled by the phase of the drive.

## Abstract

We show that periodically time-modulating the Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional magnon insulator may induce a topological phase transition that results in the presence of robust edge modes. To this end, we study a square lattice of spins interacting via an XXZ Heisenberg model with a ferromagnetic longitudinal coupling and antiferromagnetic transverse coupling, as well as the aforementioned time-modulated DMI. The topologically protected edge states of this system are composed of coherent superpositions of single-magnon excitations and two magnon bound states. Furthermore, we show that the chirality of the edge states can be controlled by adjusting the relative phase for the drive on the DMI associated with nearest neighbors in the x and y directions.