Fig. 4: Electric field effects on interlayer magnetic coupling.

a The change of E_ex as a function of Ɛ_z for different vdW magnetic bilayers. A positive value of Ɛ_z indicates the out-of-plane direction pointing from MnX₂ (X = S, Se, Te) to CrI₃ layer. b The nearly linear relation between ΔE_ex/ΔƐ_z and P_ex. Without loss of generality, here we take ΔE_ex/ΔƐ_z = [E_ex(Ɛ_z = 0.1) − E_ex(Ɛ_z = − 0.1)]/0.2. The gray line indicates the linear fitting of the calculation results. c E_ex as a function of Ɛ_z for CrI₃/MnSe₂ bilayer without and with an in-plane biaxial tensile strain of 1%. d Comparison between charge transfer and spin-electric-potential mechanism in the CrI₃/MnSe₂.