# Anharmonic Collective Oscillations in Isotropic Spin Systems and their Spectroscopic Signatures

## TL;DR

This paper reveals that isotropic spin systems can exhibit soft quartic spin modes leading to a temperature-dependent spin-wave gap, expanding the understanding of spin dynamics and suggesting new spectroscopic signatures.

## Contribution

It introduces a theoretical framework for soft spin modes in isotropic systems with no fine-tuning, supported by numerical simulations and phenomenological analysis.

## Key findings

- Quartic potentials induce a temperature-dependent spin-wave gap.
- Numerical models show gap growth with temperature in spiral spin states.
- Predictions can be tested via inelastic neutron scattering experiments.

## Abstract

Spin waves are the fundamental excitations in magnetically ordered spin systems and are ubiquitously observed in magnetic materials. However, the standard understanding of spin waves as collective spin oscillations in an effective harmonic potential does not consider the possibility of soft modes, such as those due to an effective quartic potential. In this work, we show that such quartic potentials arise under very general conditions in a broad class of isotropic spin systems without a fine-tuning of the interaction parameters. Considering models with spin spiral ground states in two and three spatial dimensions, we numerically demonstrate that quartic amplitude spin oscillations produce a fluctuation-induced spin-wave gap which grows with temperature according to a characteristic power-law. In conjunction with a phenomenological theory, the present work provides a general theoretical framework for describing soft spin modes, extending the previously discussed spin dynamics in the presence of order-by-disorder, and highlighting the important role of finite-size effects. Our predictions of a temperature-dependent gap in spiral spin systems could be tested in inelastic neutron scattering experiments, providing direct spectroscopic evidence for thermal effects arising from soft spin modes in magnetic materials.