Surface-induced ferromagnetism and anomalous Hall transport at Hf₂S(0001) and Zr₂S(0001)

Two-dimensional layered electrides possessing anionic excess electrons in the interstitial spaces between cationic layers have attracted much attention due to their promising opportunities in both fundamental research and technological applications. Using first-principles calculations, we predict that the bulk layered electrides Hf₂S and Zr₂S are nonmagnetic with massive Dirac nodal-line (DNL) states arising from Hf-5d/Zr-4d cationic and interlayer anionic electrons. Interestingly, the Hf₂S(0001) and Zr₂S(0001) surface increases the density of states at the Fermi level caused by surface potential, thereby inducing a surface ferromagnetic order via the Stoner instability. The time-reversal symmetry breaking at the surface not only splits the spin components of the DNL states but also generates highly spin-polarized topological surface states having intricate helical spin textures. Consequently, the Hf₂S(0001) and Zr₂S(0001) surface exhibits a large intrinsic anomalous Hall effect originating from the Berry curvature generated by spin-orbit coupling. Our findings offer a playground to investigate the emergence of ferromagnetism and anomalous Hall transport at the surface of nonmagnetic topological electrides.