Heat conduction in the system that releases or absorbs latent heat caused by the first-order phase transition gives rise to an intriguing problem. A typical example is seen in the system showing melting and solidification, where the domain boundary between the liquid and solid phase moves with time, known as moving boundary problems. We report in the present paper that a similar moving domain boundary is observed in an all-solid-state system, spinel MnV 2O4, where there is a first-order magnetic phase transition and the transition temperature changes with applied magnetic field. We found that in the sample attached to a heat bath with a constant temperature, thermal current flows (without external heat source) when the magnetic field is increased or decreased, associated with the release or absorption of the latent heat. We also found that the magnitude of the spontaneous heat current depends on the sweep rate of the magnetic field. We show that the experimental results, which have a nonlinear nature, can be reproduced by a simple model and simulation.
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