Electrical control of noncollinear magnetism in VAl2S4 van der Waals structures

computational methods; cohesive energy, elastic constants, AIMD results and phonon dispersion spectrum of VAl2S4 monolayer; total energy of monolayer and bilayer VAl2S4 with different magnetic states; schematic of V-3d orbitals splitting; possible magnetic state, MAE, and band structure for VAl2S4 monolayer; structure of PE-IM and PE-I patterns; energy distribution for possible bilayer patterns; energy barrier along Path-I for VAl2S4 bilayer at equilibrium and decreased interlayer distance; energy difference ∆E_(DD-UU) of FE-Ⅰ state with vertical external electric field.