Robust Zeeman-type band splitting in sliding ferroelectrics

Here, we perform density functional theory calculations complemented by symmetry analysis to unveil the evolution of ferroelectricity during sliding and the behavior of Zeeman splitting along the transition path. While the evolution of the out-of-plane component of the electric polarization vector resembles the conventional ferroelectric transition, switching between positive and negative values, we observe significant in-plane components parallel to the sliding direction, reaching their maximum at the intermediate state.

Moreover, we demonstrate that the R-stacked bilayers exhibit substantial Zeeman-type band splitting, akin to monolayers, which persists throughout the transition path, being allowed by the lack of inversion symmetry. Further analysis of different stacking configurations generated by sliding along various directions confirms that the Zeeman effect in MX2, primarily arising from the polarity of prismatic ligand coordination of the metal atom, is remarkably robust and completely governs the spin polarization of bands, independently of the sliding direction.

This resilience promises to maintain robust spin transport in vdW heterostructures based on MX2 bilayers, opening new opportunities for ferroelectric spintronics.