Enhancement of the anomalous Hall effect by tilt of the Zeeman field in the topologically nontrivial MXenes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msup><mml:mi>

In this paper, the anomalous Hall effect of topologically nontrivial MXenes, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi>M</a:mi><a:mn>2</a:mn></a:msub><a:msup><a:mi>M</a:mi><a:mo>′</a:mo></a:msup><a:msub><a:mi mathvariant="normal">C</a:mi><a:mn>2</a:mn></a:msub><a:msub><a:mi mathvariant="normal">O</a:mi><a:mn>2</a:mn></a:msub></a:mrow></a:math>, and the electronic structure in the presence of the magnetic proximity effect are theoretically investigated. The theoretical analysis is performed in two different ways: an effective model and a multi-orbital tight-binding model generated from the first-principles band structure. These two theoretical methods provide a similar profile of Berry curvature for electronic states near the bulk band gap, and they show an unconventional rise of hollowed-out peak in the profile with the tilt of the proximity magnetic potential. The anomalous Hall conductivity is also calculated as a function of the charge density and the tilt angle of the proximity magnetic order. Then, an unconventional enhancement of anomalous Hall conductivity by the tilt of magnetic order is theoretically predicted as a result of the variation of Berry curvature.