# Coarsening dynamics of an isotropic ferromagnetic superfluid

## TL;DR

This paper studies the coarsening dynamics of a ferromagnetic superfluid with isotropic symmetry, revealing diffusive domain growth, vortex annihilation, and a transition to anisotropic order under small magnetic fields.

## Contribution

It introduces the analysis of phase ordering and vortex dynamics in an isotropic ferromagnetic superfluid, highlighting the effects of magnetic fields on symmetry and scaling behavior.

## Key findings

- Domains grow as t^{1/2} indicating diffusive coarsening
- Vortices annihilate over time but some persist in small groups
- Small magnetic fields induce a transition from isotropic to anisotropic order

## Abstract

In zero magnetic field the ground state manifold of a ferromagnetic spin-1 condensate is SO(3) and exhibits $\mathbb{Z}_2$ vortices as topological defects. We investigate the phase ordering dynamics of this system after being quenched into this ferromagnetic phase from a zero temperature unmagnetized phase. Following the quench, we observe the ordering of both magnetic and gauge domains. We find that these domains grow diffusively, i.e. with domain size $L(t)\sim t^{1/2}$, and exhibit dynamic scale invariance. The coarsening dynamics progresses as $\mathbb{Z}_2$ vortices annihilate, however we find that at finite energy a number of these vortices persist in small clumps without influencing magnetic or gauge order. We consider the influence of a small non-zero magnetic field, which reduces the ground state symmetry, and show that this sets a critical length scale such that when the domains reach this size the system dynamically transitions in order parameter and scaling behaviour from an isotropic to an anisotropic ferromagnetic superfluid.