Magnetic and ferroelectric phase diagram of twisted CrI₃

Stacking orders are found to be able to strongly influence the interlayer magnetic interactions and ferroelectricity in van der Waals materials. Twist engineering is an effective strategy to integrate the properties from different stacking orders into a single material. Here, we peform a systematically study on the twisted CrI3, where the structural reconstruction is included. The variation of interlayer interaction lead to magnetic competition at the region with weak interaction, which has been reported a promising platform for achieving magnetic bubbles and merons. We find that the formation and density of magnetic bubble arrays strongly relative to twisted angle and number of stacking layers. Structural reconstruction compresses the space for antiferromagnetic domians and inhibits the formatin of magnetic bubbles in twisted bilayer CrI3, while the magnetic bubbles survive in twisted double-multilayer CrI3. On the other hand, twisted CrI3 with twist angles close to 60° present both magnetic bubble arrays and moire ferroelectricity. Our results highlight the potential to create moire magnetism and ferroelectricity in twisted magnetic materials, and may find application in high-density multiferroic memory storage.