Crystalline electric field and intrinsic anomalous Hall effect in the antiferromagnetic topological semimetal TbPdSb

The multifunctional properties of $RTX$ ($R$ = lanthanide element, $T$ = Pd, Pt, and $X$ = Sb, Bi) half-Heusler compounds have attracted substantial attention for both fundamental research and potential applications. Within this series, we have investigated the electronic structure and physical properties of the TbPdSb single crystal, which crystallizes in the hexagonal structure with space group $P{6}_{3}mc$ (No. 186). The field and temperature dependence of the magnetization data reveal a strong magnetocrystalline anisotropy, and magnetic susceptibility for $B\ensuremath{\parallel} c$ shows two broad humps at $\ensuremath{\sim}14$ and 125 K due to the presence of the crystal electric field (CEF) effect. The magnetic susceptibility data are well explained by the CEF analysis based on the point charge model, suggesting the $J$ = 6 multiplet of the ${\mathrm{Tb}}^{3+}$ ion splits into one singlet and six doublets with an overall splitting of $\ensuremath{\sim}431$ K. The transverse magnetoresistance (MR) displays a crossover at the critical field $B{}^{*}$ from semiclassical ${B}^{2}$ dependence at low field to unsaturated linear $B$ dependence at high field up to 50 K. The critical field $B{}^{*}$ is proportional to the quadratic temperature dependence, which confirms the existences of Dirac fermions. The longitudinal MR also exhibits a rapid increase at low fields and a nonsaturating behavior with ${B}^{2}$ dependence at high fields. The Hall resistivity data suggest that electrical transport in TbPdSb is governed by the predominance of hole-type charge carriers. We have observed a large anomalous Hall conductivity of $\ensuremath{\sim}1620 {\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ at 2 K and 3 T. Our Hall data analysis shows that the anomalous Hall effect in TbPdSb likely originates from the Berry curvature due to spin textures. The extensive first-principles calculations characterize TbPdSb as a topologically nontrivial nodal-line semimetal, showcasing the robustness of its Dirac points in the presence of the spin-orbit coupling effect. These findings offer valuable insights into its electronic and magnetic properties, unveiling its distinctive behavior at a fundamental level.