Supplement 1

Band structures of monolayer GdF2 with the SOC effect in the FM ground state at the HSE06 level in Fig.S1; plane-averaged electrostatic potentials of monolayer GdF2 and Sc2CO2 in Fig.S2; DOS diagram of GdF2/Sc2CO2 multiferroic heterojunction in Fig.S3; band structures and the variation curves of valley splitting of GdF2/Sc2CO2 multiferroic heterojunction under different U values in Fig.S4; band structure and variation curves of valley splitting of GdF2/Sc2CO2 multiferroic heterojunctions with different biaxial strains under PBE+U method in Fig.S5-S7; optimized lattice constant, interlayer distance, minimum distance between F and O atom and binding energy of the GdF2/Sc2CO2 vdW heterostructures in Table.S1; the energy difference between ferromagnetic and antiferromagnetic configurations of GdF2/Sc2CO2 multiferroic heterostructure under different polarization directions in Table.S2.