Suppression of Intrinsic Hall Effect through Competing Berry Curvature in Cr$_{1+\delta}$Te$_2$

We conducted a comprehensive analysis of the magnetic and electronic transport properties of the layered chalcogenide Cr$_{1+\delta}$Te$_2$ in its single crystalline form. This material exhibits a ferromagnetic transition at a critical temperature of $T_C = 191$ K, characterized by significant thermal hysteresis in the magnetization data below this temperature. Measurements of isothermal magnetization, magnetocaloric effect, and magnetoresistance indicate that the system exhibits strong magnetocrystalline anisotropy, with the $c$-axis serving as the easy axis of magnetization. The Cr$_{1+\delta}$Te$_2$ compound shows pronounced anomalous Hall effect (AHE); however, existing experimental and theoretical data do not provide a clear understanding of the nature and origin of this phenomenon. Our experimental findings suggest that the skew scattering mechanism primarily accounts for the observed AHE. In contrast, our theoretical study reveals the presence of gapped nodal points accompanied by non-zero Berry Curvature, which are expected to contribute towards intrinsic AHE. A detailed analysis of the electronic band structure, obtained through density functional theory calculations, reveals that the Berry Curvature at different nodal points exhibit both positive and negative signs. These opposing contributions largely cancel each other out, thereby significantly diminishing the intrinsic contribution to the AHE.