Macroscopic dynamics of ferromagnetic smectic-A

We derive the macroscopic dynamic equations for ferromagnetic smectic-A liquid crystals for which the spontaneous magnetization is parallel to the layer normal of the layering. As additional macroscopic variables when compared to simple fluids, we have the layer displacement u, familiar from smectic liquid crystals, and the magnetization density M. We find a number of reversible and dissipative cross-coupling terms to the additional macroscopic variables and discuss possible experiments to detect them. Among other effects, we point out that the velocity of first sound becomes anisotropic due to the influence of the modulus of the magnetization, while the magnitude of the velocity of second sound is modified. As for the static behavior, we find cross-coupling terms between the magnitude of the magnetization, on the one hand, and layer compression as well as osmotic pressure, on the other hand. In addition, we point out that as a dissipative effect, temperature gradients can induce gradients in the magnetization parallel to the layer normal, mediated by layer compressions.