Hydrodynamic Theory of Spin Waves

A hydrodynamic theory of spin waves is developed for certain magnetic systems in analogy with the derivation of two-fluid hydrodynamics for liquid helium. The systems considered are "isotropic" and "planar" ferromagnets and antiferromagnets. In each system, low-frequency spin waves are predicted to exist at long wavelengths for any temperature below the transition to the paramagnetic phase. The real part of the frequency is given exactly in terms of thermodynamic quantities. The damping rate is proportional to the square of the real part of the frequency in each case, and hence is negligible in the long-wavelength limit, compared to the real part. These results for the damping rates are new, and disagree with previous microscopic calculations for the Heisenberg ferromagnet and antiferromagnet. An experiment using neutron diffraction is proposed to test the hydrodynamic theory in the almost isotropic antiferromagnet RbMn${\mathrm{F}}_3$. The assumptions necessary to derive the hydrodynamic theory are discussed in detail, as are the limits of validity of the theory, and the applicability of the results to real systems.