Surfing the waves of the Fermi sea: apparent violation of the Mott relation in a noncentrosymmetric kagome ferromagnet

A number of magnetic Weyl semimetals with large anomalous Hall coefficient (AHC) and large anomalous Nernst coefficient (ANC) have recently been discovered and adapted for various electronic and thermoelectric applications. The well known Mott relation establishes that the ANC is proportional to the energy derivative of the AHC, and is commonly used to inform doping strategies to adjust the Fermi level and tune these two quantities. However, in some materials, the AHC and ANC peak at the same doping level, leading to an apparent violation of the Mott relation. This occurs because of the failure of the rigid band approximation, which assumes a fixed band structure and a linear relationship between the Fermi energy and doping, neglecting disorder or changes in magnetism that might affect the electronic structure in a real material. Using a minimal lattice model with two Weyl points and a doping-dependent Zeeman splitting, we show that for tilted Weyl points, changes in the Zeeman splitting move the Weyl points both in energy and momentum space, leading to non-linear changes in AHC and ANC. With this model we show how the proximity of the paramagnetic phase in UCo_0.8Ru_0.2Al leads the AHC and ANC to peak at the same doping level. We also discuss how doping-dependent measurements of the AHC and ANC in magnetic semimetals can be used as a kind of spectroscopy to identify the energy and momentum space location of Weyl points.