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We investigate coupled spin and heat transport in easy-plane magneticinsulators. These materials display a continuous phase transition betweennormal and condensate states that is controlled by an external magnetic field.Using hydrodynamic equations supplemented by Gross-Pitaevski phenomenology andmagnetoelectric circuit theory, we derive a two-fluid model to describe thedynamics of thermal and condensed magnons, and the appropriate boundaryconditions in a hybrid normal-metal|magnetic-insulator|normal-metalheterostructure. We discuss how the emergent spin superfluidity can beexperimentally probed via a spin Seebeck effect measurement.

Two-Fluid Theory for Spin Superfluidity in Magnetic Insulators