Odd-even effects are a generic feature of nonlinear physics, as odd- and even-order responses obey distinct symmetry conditions and reflect different aspects of electronic quantum geometry. With profound implications for both fundamental science and transformative applications, nonlinear Hall effects (NLHEs) have garnered intense interest in recent years, yet their odd-even parity remains elusive. Here, we report the observation of NLHE odd-even effects in bilayer graphene by engineering symmetry breaking. We demonstrate that even-order NLHEs necessitate an out-of-plane electric field to break inversion symmetry, whereas odd-order NLHEs require a perpendicular magnetic field to break vertical mirror planes in bilayer graphene. Interestingly, upon applying an out-of-plane magnetic field, we observe a new contribution to even-order NLHEs that increases linearly with field strength. By contrast, the magnetocontribution to odd-order NLHEs is dominated by a higher-order cubic scaling in magnetic field strength. Furthermore, both even- and odd-order NLHEs are strongly enhanced by Landau level formation, and the broken-symmetry Landau levels at filling factors $\nu =\pm 1,\pm 2$ can be clearly distinguished in the NLHE signals. These findings highlight that NLHEs are more sensitive to geometric and topological properties (e.g., Berry curvature hotspots) and symmetry breaking states than linear transport. Our work reveals the odd-even effects of NLHEs in bilayer graphene as well as electric and magnetic control of NLHEs with previously unexplored magnetocontributions, deepening the fundamental understanding of nonlinear transport and opening pathways toward technological advances in nonlinear electronics.

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• Berry curvature
• Hall effect
• Nonlinear optics
• Bilayer graphene
• Electrical transport techniques