Exploring Spin Hall Conductivity and Tunable Magnetoresistance in the Rare-Earth Topological Antiferromagnetic Dirac Semimetal GdCuSn

Magnetic topological materials, driven by their nontrivial electronic structures, can give rise to exotic physical properties such as spin Hall conductivity and large magnetoresistance (LMR), holding promise for technological advancements that could revolutionize data storage technologies and magnetic sensors. In this study, we investigate the structural, magnetic, electronic, and dynamical properties of the equiatomic (1:1:1) rare-earth intermetallic compound GdCuSn using first-principles calculations. GdCuSn is found to exhibit a C-type antiferromagnetic ground state and its Néel temperature is estimated by correlating various spin configurations with the Heisenberg spin model within the mean-field approximation. The electronic band structure reveals the presence of a nodal surface along the kz = π plane, protected by a combination of time-reversal symmetry and nonsymmorphic 2-fold screw-rotation symmetry. This unique noncentrosymmetric magnetic system exhibits Dirac points, which are rare due to the breaking of both inversion symmetry and time-reversal symmetry. Additionally, a large spin Hall effect is induced by the spin Berry curvature, which further enhances the spin transport properties of the system. Furthermore, we explore the longitudinal and transverse magnetoresistance behaviors of GdCuSn under varying magnetic fields and correlate magnetoresistance with Fermi surface topology. Phonon dispersion calculations confirm dynamical stability and identify a nodal surface on the kz = π plane in the bulk Brillouin zone of the phononic spectra. This comprehensive investigation highlights the intricate connections among magnetism, topology, and transport properties in rare earth-based intermetallic compound, suggesting potential applications in spintronic devices based on antiferromagnets.