Generalized Fourier law and anomalous Righi-Leduc effect in a ferromagnet

Spin caloritronics brings us new spin-thermal related effects, such as spin Seebeck effect, spin Nernst effect and their inverse effects. It is time to revisit the thermoelectric effects in ferromagnets by considering them. In this paper, a generalized Fourier law is derived and an anomalous Righi-Leduc effect is proposed for a ferromagnet when a temperature gradient is applied. A full description including particle current, spin current and heat current is necessarily taken into account and gives rise to novel contributions to the Righi-Leduc coefficient. This may shed more light on the spin caloritronics in ferromagnets.