Universal dynamics far from equilibrium in Heisenberg ferromagnets

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, which results in a strong momentum-dependent magnon-magnon scattering amplitude and absence of collisions between magnons and the condensate. 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 the analytic scaling solution, 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 thin-layered ferromagnets such as Yttrium Iron Garnet.