The Berry curvature dipole induced by symmetry breaking plays a pivotal role in electronic transport properties and nonlinear responses, such as the nonlinear Hall effect and circular photogalvanic effect. The study of the Berry curvature dipole is often explored in time-reversal symmetric systems, but it should not be limited to such materials. Here, we predicted that the ferroelectricity in monolayer ${\mathrm{CrNBr}}_2$ produces the Berry curvature dipole, leading to the nonlinear Hall effect and circular photogalvanic current. The linear anomalous Hall effect and circularly polarized optical absorption, governed by spin-orbit coupling, are independent of ferroelectric polarization and exhibit extremely small conductance. In contrast, multiferroic monolayer ${\mathrm{CrNBr}}_2$ achieves a large nonlinear Hall conductivity ($\sim 1e^3/\hslash \mathrm{e}{\mathrm{V}}^{-1}$ at 30 K) and circular photogalvanic current, despite its suppression at high temperatures from phonon scattering. The coupling between the ferroelectric polarization and the Berry curvature dipoles (intraband for nonlinear Hall conductance and interband for circular photogalvanic current) allows for nonvolatile switching of these effects, presenting substantial promise for nanoelectronic and optoelectronic devices.

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• Anomalous Hall effect
• Berry curvature
• Ferroelectricity
• First-principles calculations