As a crucial information carrier in condensed matter physics and next-generation information devices, the valley degree of freedom has made the realization of its polarization modulation and effective induction of the anomalous valley Hall effect a core research direction in the field of valleytronics. However, relevant studies on achieving this effect in two-dimensional double-transition-metal MXenes antiferromagnetic systems remain scarce. Based on first-principles calculations, we systematically investigate the valley-related electronic structure and transport properties of double-transition-metal MXene ${\mathrm{HfCr}}_2{\mathrm{C}}_2{\mathrm{H}}_2$. It is found that the ${\mathrm{HfCr}}_2{\mathrm{C}}_2{\mathrm{H}}_2$ can lift the valley degeneracy at the edges of the conduction and valence bands, resulting in valley splittings of 63.3 meV and 16.1 meV, respectively. Importantly, the nonzero Berry curvature in the K and ${\mathrm{K}}^{\prime }$ valleys, together with the finite anomalous Hall conductivity in the vicinity of the band edges, provides evidence for the anomalous Hall effect in the valley in this material. Furthermore, the valley splitting can be effectively tuned by the magnetization direction and biaxial strain, while the valley polarization can be reversed through manipulation of the magnetization direction. This study provides a new material platform and theoretical basis for the design and development of magnetically controlled valleytronic devices in double-transition-metal MXenes.

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• Anomalous Hall effect
• Valley degrees of freedom
• MXenes
• Density functional calculations