Spin Hall effect in a spin-1 chiral semimetal
Ke Tang, Yong-Chang Lau, Kenji Nawa, Zhenchao Wen, Qingyi Xiang, Hiroaki Sukegawa, Takeshi Seki, Yoshio Miura, Koki Takanashi, Seiji Mitani
Abstract
The spin-1 chiral semimetal is a state of quantum matter hosting unconventional chiral fermions that extend beyond the common Dirac and Weyl fermions. B20-type CoSi is a prototypal material that accommodates such an exotic quasiparticle. To date, the spin-transport properties in the spin-1 chiral semimetals have not been thoroughly explored. In this work, we fabricated B20-CoSi thin films on sapphire $c$-plane substrates by magnetron sputtering and studied the spin Hall effect (SHE) by combining experiments and first-principles calculations. The SHE of CoSi was investigated using CoSi/CoFeB/MgO heterostructures via spin Hall magnetoresistance and harmonic Hall measurements. First-principles calculations yield an intrinsic spin Hall conductivity (SHC) at the Fermi level that is consistent with the experiments and reveal its unique Fermi-energy dependence. Unlike the Dirac and Weyl fermion-mediated Hall conductivities that exhibit a peaklike structure centering around the topological node, SHC of B20-CoSi is odd and crosses zero at the node with two antisymmetric local extrema of opposite sign situated below and above in energy. Hybridization between Co $d$-Si $p$ orbitals and spin-orbit coupling are essential for the SHC, despite the small (\ensuremath{\sim}1%) weight of the Si $p$ orbital near the Fermi level. This work expands the horizon of topological spintronics and highlights the importance of Fermi-level tuning in order to fully exploit the topology of spin-1 chiral fermions for spin-current generation.