Complex field-, temperature-, and angle-dependent Hall effects from intrinsic Fermi surface revealed by first-principles calculations

The Hall effect, ever intriguing since its discovery, has spurred the exploration of its phenomena, intensified by advances in topology and novel materials. Differentiating the ordinary Hall effect from extraordinary properties like the anomalous Hall effect (AHE) is challenging, especially in materials with topological origins. In our study, we leverage semiclassical Boltzmann transport theory and first-principles calculations within the relaxation time approximation to analyze Hall effects comprehensively. We have found that the complex magnetic field dependence of ordinary Hall effect, including the sign reversals, appearing of plateau and nonlinearity, can be understood and reproduced by our approach both for multiband models and realistic topological materials of ZrSiS and ${\mathrm{PtTe}}_{2}$. The Hall resistivity versus temperature and magnetic fields can be well scaled, similar to Kohler's rule for longitudinal resistivity. This methodology can also accurately model the angular dependent Hall effects such as planar Hall effects of bismuth. These findings indicate that the dependencies of various Hall effects and magnetoresistance on magnetic fields are mainly determined by the details of Fermi surface and the relaxation time. The intrinsic Fermi surface determines the carriers' density, type, and velocity, while the later is mostly influenced by extrinsic factors, such as quality of sample with defects, impurities, and domains. This insight might simplify the understanding of several seemingly complex transport phenomena in nonmagnetic materials, with no need for hypotheses of other sophisticated mechanisms, such as magnetization-induced AHE, Lifshitz transition-induced changes in carrier type, exotic orders like charge density wave, or some delicate scattering of carriers with chiral or nonreciprocal dependence. In order for the completeness of the discussion of Berry curvature, we also discussed the Hall effects when the Berry curvature is considered in the magnetic materials.