The reversal of the anomalous Hall effect (AHE) via low-power ferroelectric (FE) switching has recently attracted significant interest. However, a general symmetry-based design principle for such control remains absent. Here, we establish effective symmetry criteria for FE-switchable AHE in two-dimensional (2D) multiferroics without altering the magnetic configuration. By analyzing the transformation properties of Berry curvature under magnetic space group (MSG) symmetry operations associated with FE switching, we show that FE-switchable AHE in 2D multiferroics requires the following conditions (i) The MSG of the FE phase contains none of the symmetry operations belonging to the Berry curvature reversing set $S=\{T,2_{\parallel },n_{001}T,PT,m_{\perp },m_{001}T,S_{n}T\}$, thereby allowing a nonzero AHE. (ii) The MSG of the paraelectric phase contains at least one symmetry operation that not only belongs to the set $S$, but also maps the two symmetry-related FE states onto each other by reversing the FE polarization, thereby ensuring the simultaneous switching of both FE polarization and AHE. These criteria are validated by first-principles calculations in the in-plane FE VOBrI and out-of-plane FE ${\mathrm{Co}}_2{\mathrm{NF}}_2$ single layers, and further confirmed using a modified Kane–Mele model. Our results provide a practical symmetry-based guideline for designing and screening 2D multiferroics with FE-switchable AHE and Chern number $C$.

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• Anomalous Hall effect
• Ferroelectricity
• Magnetism
• Quantum anomalous Hall effect
• 2-dimensional systems
• Symmetries
• First-principles calculations
• Tight-binding model
• Wannier function methods