Observation of out-of-plane spin-polarization in bulk 3R-MoS$_2$

Transition metal dichalcogenide of noncentrosymmetric 3R-type structure, 3R-MoS$_2$, is investigated by spin- and angle-resolved photoemission spectroscopy. The top of valence bands of 3R-MoS$_2$ at the Brillouin zone corners ($K$- and $K'$-points) are found to show huge spin splitting with $z$-oriented (Zeeman-type) spin-polarization, in contrast to the nearly spin-degenerate centrosymmetric 2H-MoS$_2$. The observed spin-polarizations reach $P_z \sim\pm 1$ at $\overline{K}$- and $\overline{K'}$-points, corresponding well with the relativistic first-principles band calculations. It provides the direct evidence of spin-valley coupling realized through the broken inversion symmetry and the strong spin-orbit interaction of Mo $4d$-orbitals, leading to the spin-valley polarized state in MoS$_2$.