Magnetization textures in twisted bilayer CrX_{3} (X=Br, I)

Motivated by the recent experimental demonstration of stacking dependent interlayer magnetic interaction [T. Song et al., Nat. Mater. 18, 1298 (2019)1476-112210.1038/s41563-019-0505-2; T. Li et al., Nat. Mater. 18, 1303 (2019)1476-112210.1038/s41563-019-0506-1; W. Chen et al., Science 366, 983 (2019)SCIEAS0036-807510.1126/science.aav1937], we investigate the magnetization textures and the control possibilities in the moiré pattern formed of twisted bilayer two-dimensional (2D) magnets CrX_{3} (X=Br, I). We find that the stacking dependent interlayer magnetic interaction results in the formation of periodic magnetization domains in a long-period moiré pattern. Magnetization textures with various topological numbers can be constructed, depending on the winding of the textures around the domain walls. A uniform external magnetic field competes with the lateral modulated interlayer magnetic interaction and can be utilized to tune the magnetization textures.