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Layered antiferromagnetism is the spatial arrangement of ferromagnetic layers with antiferromagnetic interlayer coupling. Recently, the van der Waals magnet, chromium triiodide (CrI 3 ), emerged as the first layered antiferromagnetic insulator in its few-layer form 1 , opening up ample opportunities for novel device functionalities 2-7 . Here, we discovered an emergent nonreciprocal second order nonlinear optical effect in bilayer CrI 3 . The observed second harmonic generation (SHG) is giant: several orders of magnitude larger than known magnetization induced SHG 8-11 and comparable to SHG in the best 2D nonlinear optical materials studied so far 12-15 (e.g. MoS 2 ). We showed that while the parent lattice of bilayer CrI 3 is centrosymmetric and thus does not contribute to the SHG signal, the observed nonreciprocal SHG originates purely from the layered antiferromagnetic order, which breaks both spatial inversion and time reversal symmetries. Furthermore, polarization-resolved measurements revealed the underlying C 2h symmetry, and thus monoclinic stacking order in CrI 3 bilayers, providing crucial structural information for the microscopic origin of layered antiferromagnetism 16-20 . Our results highlight SHG as a highly sensitive probe that can reveal subtle magnetic order and open novel nonlinear and nonreciprocal optical device possibilities based on 2D magnets.

Controlling the crystal structure is a powerful approach for manipulating the fundamental properties of solids. Unique to two-dimensional (2D) van der Waals materials, the control can be achieved by modifying the stacking order through rotation and translation between the layers. Here, we report the first observation of stacking dependent interlayer magnetism in the 2D magnetic semiconductor, chromium tribromide (CrBr 3 ), enabled by the successful growth of its monolayer and bilayer through molecular beam epitaxy. Using in situ spin-polarized scanning tunneling microscopy and spectroscopy, we directly correlated the atomic lattice structure with observed magnetic order. We demonstrated that while individual CrBr 3 monolayer is ferromagnetic, the interlayer coupling in bilayer depends strongly on the stacking order and can be either ferromagnetic or antiferromagnetic. Our observations provide direct experimental evidence for exploring the stacking dependent layered magnetism, and pave the way for manipulating 2D magnetism with unique layer twist angle control.