Local thermomagnonic torques in two-fluid spin dynamics

We develop a general phenomenology describing the interplay between coherent and incoherent dynamics in ferromagnetic insulators. Using the Onsager reciprocity and Neumann's principle, we derive expressions for the local thermomagnonic torques exerted by thermal magnons on the order-parameter dynamics and the reciprocal pumping processes, which are in close analogy to the spin-transfer torque and the spin pumping at metallic interfaces. Our formalism is applicable to general long-wavelength dynamics and, although here we explicitly focus on ferromagnetic insulators possessing U(1) symmetry, our approach can be easily extended to other classes of magnetic materials. As an illustrative example, we apply our theory to investigate a domain wall floating over a spin superfluid, whose dynamics are triggered thermally at the system's edge. Our results demonstrate that the local pumping of coherent spin dynamics by a thermal magnon gas offers an alternative route - with no need for conducting components and thus devoid of ohmic losses - for the control and manipulation of topological solitons.