The nonlinear Hall effect has emerged as an essential field in condensed matter physics for its connection with the properties of quantum geometry and its potential application in electronic devices. However, when the nonlinear Hall current scales quadratically with a single driving electric field, it is difficult to regulate the direction of the Hall response by reversing the driving electric field. This limitation hinders the practical implementation of nonlinear Hall effect in logic memory applications. Here, we establish a symmetry-based framework for the nonvolatile control of the nonlinear Hall effect through ferroelectric switching in two-dimensional ferroelectric materials. We prove that ferroelectric switching reverses the effective spin-orbit field, thereby reversing the sign of the Berry curvature dipole and, consequently, the nonlinear Hall conductivity. Using symmetry analysis and tight-binding models, we identify 18 layer groups that allow a ferroelectric switchable nonlinear Hall effect driven by Berry curvature dipole. By first-principles calculations we demonstrate that the monolayer $\alpha \text{−}\mathrm{Bi}$ and ${\mathrm{NbOI}}_2$ are ideal platforms to verify our proposed switchable mechanism. Our results provide a generalized framework for the nonvolatile control of nonlinear Hall effect, paving the way for its potential application in logical storage through assisting in the detection of two-dimensional ferroelectric polarization states.

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• Anomalous Hall effect
• Electrical conductivity
• Ferroelectricity
• 2-dimensional systems
• First-principles calculations
• Tight-binding model
• Wannier function methods