Goldstone mode of the broken helix in U(1) magnet EuIn2As2

TL;DR

This study investigates how strain and magnetic fields influence the Goldstone mode in the broken helix phase of EuIn₂As₂, revealing the relationship between magnetic symmetry and spin-wave dynamics using optical polarimetry.

Contribution

It provides the first detailed analysis of the Goldstone mode response to external perturbations in EuIn₂As₂, linking symmetry considerations to observable frequency scaling.

Findings

Goldstone mode frequency depends linearly on magnetic field when dominant.

Nearly uniform spin precession observed only under strong magnetic field.

Mode frequency scaling aligns with symmetry-based predictions near zero field.

Abstract

Goldstone modes acquire a frequency gap in the presence of perturbations that break the underlying continuous symmetry. Here, we study the response of a spin-based Goldstone mode to strain and magnetic field in the broken helix, a multi-$\textbf{Q}$ phase of EuIn$_2$As$_2$. Optical polarimetry with spatial and temporal resolution allows us to access information about both the structure and frequency of optically excited spin-wave modes under different strain conditions. We observe nearly uniform spin precession characteristic of a Goldstone mode only when magnetic field dominates over strain. In this regime, the frequency depends linearly on the applied field. A symmetry analysis for predicting the mode frequency near zero field demonstrates that the observed scaling is of the lowest allowed order. This work thus demonstrates the connections between magnetic symmetries and the frequency dependence of the Goldstone mode in an external field, and illustrates the power of our technique for studying the dynamics of complex magnets.