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Fig.S1 The the stacking energy ($\triangle E$,$\triangle E=E^{stacking}-E^{AF-stacking}$) for the bilayer Janus GdBrI system with different stacking orders. Fig.S2 Electronic band structures of bilayer Janus GdBrI for AF-stacking order (a,b) and AE-stacking order (c,d) with magnetization orientations along the +x and +y directions, respectively, accounting for SOC. The Fermi level is set to zero. Fig.S3 The orbital-resolves density of states of Gd-d for bilayer Janus GdBrI for AD-stacking order without SOC, under the application of biaxial tensile strain +5%.