Spin Hall conductivity, magnetoresistance, and nontrivial topology in BeAu

Topological materials, characterized by various types of band crossings, provide a fertile ground for the emergence of novel topological excitations. While topological electronic excitations have been widely studied, investigations into topological phonons remain relatively limited. Exploring fermionic and bosonic topological properties within a single material opens new avenues for advancing key concepts in condensed matter physics. In this work, we introduce BeAu as a promising candidate that hosts multiple multifold topological excitations in its electronic and phononic band spectra, each protected by specific symmetries. A detailed electronic structure analysis reveals the coexistence of three distinct topological fermions, such as Weyl, Rarita-Schwinger-Weyl, and fourfold fermions, alongside two-dimensional doubly degenerate nodal surface states. Similarly, the phonon dispersion exhibits threefold and fourfold degenerate phonons, as well as two-dimensional nodal surface states. Moreover, BeAu shows a significant spin Hall conductivity, driven by the pronounced spin Berry curvature near degenerate nodes and the spin-orbit coupling-induced band splitting in the electronic band structure. We also investigate the transverse magnetoresistance, observing intriguing behavior under varying magnetic field strengths, suggesting a potential correlation between magnetoresistance and field intensity. Our findings position this material as an exceptional platform for hosting and exploring diverse quasiparticle excitations with significant spin Hall conductivity, making it suitable for applications in spintronic devices.