Combined first-principles and Boltzmann transport theory methodology for studying magnetotransport in magnetic materials

Unusual magnetotransport behaviors, such as temperature-dependent negative magnetoresistance (MR) and bowtie-shaped MR, have puzzled us for a long time. Although several mechanisms have been proposed to explain these phenomena, the absence of comprehensive quantitative calculations has made these explanations less convincing. In our work, we introduce a methodology to study magnetotransport behaviors in magnetic materials. This approach integrates the anomalous Hall conductivity induced by the Berry curvature, with a multiband ordinary conductivity tensor, employing a combination of first-principles calculations and semiclassical Boltzmann transport theory. Our method also incorporates the temperature dependence of the relaxation time and the anomalous Hall conductivity, as well as the field dependence of the anomalous Hall conductivity. We initially test this approach on models, obtaining distinct behaviors of magnetoresistance and Hall resistivity across several types of magnetic materials, and then apply it to a Weyl semimetal Co_{3}Sn_{2}S_{2}. The results, which align well with experimental observations in terms of magnetic field and temperature dependencies, demonstrate the efficacy of our approach. This methodology provides a comprehensive and efficient means to understand the underlying mechanisms of the unusual complex behaviors observed in magnetotransport measurements in magnetic materials.