# Universal prethermal dynamics in Heisenberg ferromagnets

## TL;DR

This paper investigates the universal non-equilibrium dynamics of magnons in Heisenberg ferromagnets, revealing a new universality class with distinct scaling exponents due to SU(2) symmetry, supported by kinetic theory and applicable to experiments.

## Contribution

It introduces a new universality class of far-from-equilibrium magnon dynamics in Heisenberg ferromagnets, characterized by unique scaling exponents derived from the system's SU(2) symmetry.

## Key findings

- Universal scaling in momentum and time of magnon distribution.
- Distinct exponents from those in Bose-Einstein condensates.
- Robustness of scaling across different initial conditions.

## Abstract

We study the universal far from equilibrium dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal scaling in momentum and time of the quasiparticle distribution function, with the universal exponents distinct from those recently observed in Bose-Einstein condensates. This new universality class originates from the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude. We compute the universal exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with microwave pumping of magnons. We compare our numerical results with analytic estimates of the scaling exponents and demonstrate the robustness of the scaling to variations in the initial conditions. Our predictions can be tested in quench experiments of spin systems in optical lattices and pump-probe experiments in ferromagnetic insulators such as yttrium iron garnet.