Qing-Lian Xu ^a, Zhen-Gang Zhu ^a,b,c,∗, Gang Su ^b,c,d,∗

^a School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

^b Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, College of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

^c CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China

^d Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

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.