Identification of spin effects in the anomalous Righi-Leduc effect in ferromagnetic metals

The emerging of spin caloritronics leads to a series of new spin-thermal related effects, such as spin Seebeck effect (SSE), spin Nernst effect (SNE) and their corresponding inverse effects. Anomalous Righi-Leduc effect (ARLE) describes that a transverse temperature gradient can be induced by a longitudinal heat flow in ferromagnets. The driving force and the response of the ARLE are all involved with heat. It is curious if spin effects mediate the heat transport and provide extra influence. In this work, we investigate the ARLE and the interplay between the heat current, charge current, and spin current via linear response theory. We identified that spin effects do have clear roles in heat transport, which can be confirmed by phase shifts of voltage output varying with the direction of magnetization. Our formulas fit the experimental data very well. Moreover, we discuss more configuration of magnetization which is expected to be tested in the future. It should be emphasized that the present formalism including spin effects is out of the theory based on magnon transport, which may be conspicuous in the devices within the spin diffusion length.