Title: Spin caloritronics as a probe of nonunitary superconductors

Abstract: Superconducting spintronics focuses on the interplay between superconductivity and magnetism and has sparked significant interest in nonunitary superconductors as a platform for novel magneto-superconducting phenomena. However, a direct test for nonunitary superconductors is currently absent, and their identification is challenging. In this paper, we demonstrate that spin current driven by the thermal gradient sensitively probes the nature of the condensate in nonunitary superconductors. We should note that the spin polarization of the condensate in the momentum space induces the spin-Seebeck effect, and the spin-dependent chirality (spin-chirality) of the condensate induces the spin-Nernst effect in nonunitary superconductors. Notably, the nonvanishing spin-Seebeck effect provides a smoking gun evidence of nonunitary superconductivity in materials because it reflects the spin polarization of the Cooper pairs in the momentum space, irrespective of whether the net pair spin magnetization vanishes. Our results position the spin caloritronics phenomena as a definitive probe of nonunitary superconductors.