Two-dimensional multiferroic RuClF/AgBiP 2 S 6 van der Waals heterostructures with valley splitting properties and controllable magnetic anisotropy.

The investigation of new properties in two-dimensional (2D) multiferroic heterostructures is significant. In this work, the electronic properties and magnetic anisotropy energies (MAEs) of 2D multiferroic RuClF/AgBiP 2 S 6 van der Waals (vdW) heterostructures are systematically studied by first principles calculations based on density functional theory (DFT). The Hubbard on-site Coulomb parameter ( U ) of Ru atoms is necessary to account for the strong correlation among the three-dimensional electrons of Ru. RuClF/AgBiP 2 S 6 heterostructures in different polarizations (RuClF/AgBiP 2 S 6 -P↑ and RuClF/AgBiP 2 S 6 -P↓) are ferromagnetic semiconductors with stable structures. Valley polarizations are present in the band structures of RuClF/AgBiP 2 S 6 heterostructures with spin-orbit coupling (SOC), the valley splitting energies of which are 279 meV and 263 meV, respectively. The MAEs of RuClF/AgBiP 2 S 6 heterostructures indicate perpendicular magnetic anisotropy (PMA), which are primarily attributed to the differences in matrix elements within Ru (d yz , d z 2 ) orbitals. In addition, valley splittings and MAEs of RuClF/AgBiP 2 S 6 heterostructures are modified at different biaxial strains. Specifically, the highest valley splittings are 283 meV and 287 meV at ε = 2%, while they disappear at ε = -6%. The PMA of RuClF/AgBiP 2 S 6 -P↑ is gradually decreased at biaxial strains of -6% to 2%, and MAE is transformed into in-plane magnetic anisotropy (IMA) at ε = 4%. RuClF/AgBiP 2 S 6 -P↓ maintains PMA at different strains. The study of non-volatile electrical control of valley splitting phenomena in multiferroic RuClF/AgBiP 2 S 6 heterostructures is crucial in the field of valleytronic devices, which has important theoretical significance.