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

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.