Extended Hydrodynamics of Planar Heisenberg Ferromagnetic Systems
Access to hydro and quasi-hydro regimes in magnetic systems is steadily increasing with the advances in fabrication of clean materials, and motivates study of hydrodynamics beyond conventional regimes and probe non-equilibrium transport. We employ the framework of extended irreversible thermodynamics which includes dynamical dissipative currents as quasi-hydro variables, and effect the modified hydrodynamic equations suitable to describe planar Heisenberg ferromagnetic systems in both paramagnetic and ferromagnetic phases. We show that the new transport coefficients and relaxation time scales introduced by quasi-hydro variables can engineer diverse combination of dispersion relations and provide control over the nature of hydrodynamic modes. For instance, we can change the diffusive energy mode into propagating one in multiple ways, including by tuning the relaxation time of magnetization current.