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We study the coupled magnon energy transport and collective magnetization dynamics in ferromagnets with magnetic textures. By constructing a phenomenological theory based on irreversible thermodynamics, we describe motion of domain walls by thermal gradients and generation of heat flows by magnetization dynamics. From microscopic description based on magnon kinetics, we estimate the transport coefficients and analyze the feasibility of energy-related applications in insulating ferromagnets, such as yttrium iron garnet and europium oxide.

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