Fig. 6: Theoretical magnetic textures of CrBr₃ multilayers.

We analyze the measured magnetoconductance background in terms of the theoretically predicted evolution of magnetic textures in a CrBr₃ moiré interface under an applied out-of-plane magnetic field H. The magnetoconductance is expected to follow closely the magnetic field dependence of the square of the magnetization³⁰, δG ~ (δM)². a Visualization of magnetic textures at selected applied magnetic fields, labeled by I, II, and III. The textures are represented by the z-component of the local magnetization (M^z); yellow dashed line represents the moiré unit cell; black circles represent the boundary between ferromagnetic and antiferromagnetic interlayer Heisenberg exchange. b Visualization of the spin orientation in the two layers at three points in the moiré unit cell AA, AB, and M’ (another monoclinic stacking at the midpoint between two neighboring AA regions). c, Plot of the magnetoconductance background δG_bg and of δM², as a function of H (quantities are normalized to 1 at 1 T, to enable their comparison). Both δM and δG_bg increase smoothly at first, up to the critical field for the spin-flip transition at the AA-stacked region at \(\mu\)₀H_⊥ ~ 0.2 T (I → II; pink shaded region). A second smooth increase then occurs with the antiferromagnetic domains near the M’-stacked region that are further reduced in size, up to a second critical field \(\mu\)₀H_⊥ ~ 0.5–0.7 T associated with a spin flop-transition (II → III; blues shaded region). The two theoretical curves for biaxial strain have 1% strain, spin stiffness is 1.4 meV, and anisotropy is 0.01 meV and 0.02 meV, respectively. The two curves with uniaxial strain have 1% and 3% strain, respectively, the spin stiffness is 10 meV, and anisotropy is 0.01 meV. The overall evolution is the same irrespective of these details and reproduces qualitatively the evolution of the background magnetoconductance.