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We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state without magnetic fields. The spin Seebeck effect originates from spin-split collective excitation modes although the ground state does not exhibit any magnetic orderings. This peculiar phenomenon is inherent in the excitonic insulating state, whose order parameter is time-reversal odd and yields a spin splitting for the collective excitation modes. We also find that the spin current is strongly enhanced and its direction is inverted in the vicinity of the phase transition to another magnetically ordered phase. We suggest that the present phenomenon is possibly observed in perovskite cobaltites with the GdFeO$_3$-type lattice distortion.
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