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We construct the hydrodynamic theory for spin 1/2 Bose gases at arbitrarytemperatures. This theory describes the coupling between the magnetization, andthe normal and superfluid components of the gas. In particular, our theorycontains the geometric forces on the particles that arise from their spin'sadiabatic following of the magnetization texture. The phenomenologicalparameters of the hydrodynamic theory are calculated in the Bogoliubovapproximation and using the Boltzmann equation in the relaxation-timeapproximation. We consider the topological Hall effect due to the presence of askyrmion, and show that this effect manifests itself in the collective modes ofthe system. The dissipative coupling between the magnetization and the normalcomponent is shown to give rise to magnetization relaxation that is fourthorder in spatial gradients of the magnetization direction.

Magnetization relaxation and geometric forces in a Bose ferromagnet