$SU(N)$ spin-phonon simulations of Floquet dynamics in spin $S > 1/2$ Mott insulators

TL;DR

This paper develops a novel $SU(N)$ spin-phonon simulation method to explore Floquet dynamics in spin-1 Mott insulators, revealing complex non-equilibrium phenomena driven by phonons and Floquet engineering.

Contribution

It introduces a generalized $SU(N)$ Monte Carlo and molecular dynamics technique for simulating spin-phonon coupled systems with spin $S > 1/2$, applied to a relevant spin-1 Mott insulator model.

Findings

Discovery of phonon-induced magnetization in quadrupolar phases

Strengthening of Néel order and gapping of spin waves via Floquet anisotropy

Observation of non-equilibrium phase transitions and Floquet spin wave copies

Abstract

The dynamics of magnetic moments coupled to phonons is of great interest for understanding spin transport in solids as well as for our ability to control magnetism via tailored phonon modes. For spin $S > 1/2$, spin-orbit coupling permits an unusual linear coupling of phonons to quadrupolar moments, so that phonons act as a dynamical transverse field for the spins. Here, we develop a generalized $SU(N)$ spin-phonon Monte Carlo and molecular dynamics technique to simulate the equilibrium and nonequilibrium properties of such spin-orbital-phonon coupled Mott insulators, and apply it to a spin-1 model with competing XY antiferromagnet (AFM) and quadrupolar paramagnet (QPM) phases which is relevant to the Mott insulator $\rm{Ba_2FeSi_2O_7}$. We uncover a rich variety of dynamical phenomena in this system induced by linear or chiral phonon drives, including the generation of a uniform magnetization in the QPM and AFM, strengthening of N\'eel order and gapping of the AFM Nambu-Goldstone mode by Floquet-Ising anisotropy, a non-equilibrium QPM to AFM transition, and creation of Floquet copies of transverse and longitudinal spin waves. Our work is relevant for driven spin-1 magnets, such as $\rm{Ba_2FeSi_2O_7}$, and we highlight broader implications for nonequilibrium multipolar magnetism.