Robust Zeeman-type band splitting in sliding ferroelectrics

Transition metal dichalcogenides are known for their intriguing spin-valley effects, which can be harnessed through proximity in van der Waals heterostructures. Their hexagonal monolayers exhibit significant Zeeman band splitting of valence bands, reaching up to several hundred meV and giving rise to spin textures that yield long spin lifetimes. However, this effect is suppressed in the hexagonal bilayers due to inversion symmetry. The recent discovery of sliding ferroelectricity in ${MX}_{2}$ bilayers ($M=\mathrm{Mo}$, W; $X=\mathrm{S}$, Se) opens a pathway for the electrical control of the spin properties in these materials. While substantial Zeeman splitting is found in the rhombohedral structure, its behavior during the ferroelectric transition remains unclear. In this paper, we explore different stacking configurations of ${MX}_{2}$ bilayers by sliding and demonstrate, using density functional theory calculations and symmetry analysis, that the Zeeman effect completely dominates the spin polarization of bands throughout the structural transition. This promises to maintain robust spin transport in polar ${MX}_{2}$ bilayers, opening potential avenues for ferroelectric spintronics.