Evidence of spin–valley coupling in Dirac material BaMnBi ₂ probed by quantum Hall effect and nonlinear Hall effect

Valleytronics is a rapidly advancing field that explores the use of the valley degree of freedom in electronic systems to encode and process information. It relies on electronic states with spin<b>-</b>valley locking, first predicted and observed in monolayer transition metal dichalcogenides like MoS₂. However, very few bulk materials have been reported to host spin<b>-</b>valley locked electronic states. In this work, we present experimental evidence for a predicted, unique spin<b>-</b>valley locked electronic state generated by the Bi zig-zag chains in the layered compound BaMnBi₂. We observed remarkable quantum transport properties in this material, including stacked quantum Hall effect (QHE) and nonlinear Hall effect (NLHE). From the analysis of the QHE, we identified a spin<b>-</b>valley degeneracy of 4, while the NLHE provides supporting evidence for the anticipated valley-contrasted Berry curvature-a typical signature of a spin-valley locked state. This spin<b>-</b>valley locked state contrasts with that observed in the sister compound BaMnSb₂, where the degeneracy is 2. This difference arises from significant variations in their orthorhombic structures and spin-orbital coupling. These findings not only set up a new platform for exploring coupled spin<b>-</b>valley physics in bulk materials but also underscores its potential for valleytronic device applications.