Tunable spin-valley coupling in layered polar Dirac metals

In non-centrosymmetric metals, spin-orbit coupling (SOC) induces momentum-dependent spin polarization at the Fermi surfaces. This is exemplified by valley-contrasting in monolayer transition metal dichalcogenides (TMDCs) with in-plane inversion asymmetry. However, valley configuration of massive Dirac fermions TMDCs fixed graphene-like structure, which limits variety spin-valley coupling. Here, we show that layered polar BaMn$X_2$ ($X =$Bi, Sb) hosts tunable spin-valley-coupled fermions, originate from distorted $X$ square net lattice polarization. We found spite larger SOC, BaMnBi$_2$ has approximately one-tenth distortion BaMnSb$_2$, a different spin-polarized valleys theoretically predicted. was experimentally observed as clear difference Shubnikov-de Haas oscillation high fields between two materials. The chemically makes it promising material for various spin-valleytronic devices.