Two-dimensional antiferromagnetic (AFM) valley materials attract significant attention due to their combined valley polarization and magnetic order. However, the achievement of the anomalous valley Hall effect (AVHE) still faces challenges of spin degeneracy and difficulty in controlling valley polarization. In this study, through theoretical research of the H-functionalized MXene bilayer ${\mathrm{Cr}}_2{\mathrm{CH}}_2$ system, a different mechanism for regulating AVHE by interlayer slip or an applied electric field is proposed. The study finds that the AB stacking exhibits an AFM ground state and intrinsic ferroelectricity, and that reversal of the polarization can switch the layer contribution of valley polarization, enabling nonvolatile electrical control of the AVHE. This work provides a feasible strategy and design principles for developing electrically writable and readable memory devices based on AFM valley materials.

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• First-principles calculations
• Magnetism
• Spin-orbit coupling
• Valleytronics