Nonvolatile manipulation of magnetic orderings in two-dimensional (2D) van der Waals (vdW) materials presents a promising avenue for advanced spintronic applications. Bilayer ${\mathrm{CrI}}_3$ (BL-${\mathrm{CrI}}_3$) exhibits an interlayer antiferromagnetic (AFM) ground state, distinct from the interlayer ferromagnetic (FM) ordering of its bulk counterpart, making it a compelling system for studying the magnetic phase transition. While integrating BL-${\mathrm{CrI}}_3$ with a ferroelectric layer like $\alpha \text{−}{\mathrm{In}}_2{\mathrm{Se}}_3$ has been proposed as a strategy to modulate these transitions, prior computational studies have yielded conflicting results. Here, we systematically investigate BL-${\mathrm{CrI}}_3/\alpha \text{−}{\mathrm{In}}_2{\mathrm{Se}}_3$ heterostructures using first-principles calculations, examining the effects of lattice strain, spin-orbit coupling (SOC), and electric polarization on magnetic stability. Our findings reveal that larger in-plane lattice constants favor the AFM state, while SOC promotes FM ordering. Notably, a bilayer ${\mathrm{In}}_2{\mathrm{Se}}_3$ substrate proves highly effective in achieving nonvolatile magnetic ground-state reversal. These results decipher the critical roles of strain, SOC and electric polarization in the manipulation of magnetism in 2D materials and provide essential insights for designing 2D vdW heterostructures with robust magnetoelectric properties.

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• Magnetic coupling
• Magnetic interactions
• Magnetic order
• First-principles calculations