Hydrodynamic theory of spin waves in spin glasses and other systems with noncollinear spin orientations

The hydrodynamic theory of spin waves is extended to a magnetic system such as a spin glass or a crystal with helical spin order, in which there are equilibrium magnetizations on different sites, with spin directions that are not collinear. If the total magnetization is zero and if the interactions are assumed to be isotropic in spin space, one predicts well-defined spin waves at small wave vectors k⃗, with a linear dispersion relation, and three polarizations for each value of k⃗. The hydrodynamic assumption of a finite spin-stiffness constant may be questionable, however, for the spin glass. Nonzero magnetization is discussed briefly.