In the Hall effect, a linear transverse resistivity is observed as a function of applied magnetic field and it turns into an anomalous behavior generating a finite value at zero field in ferromagnets. This anomalous value usually scales with the magnetization. Karplus and Luttinger have explained it considering spin–orbit interaction in which the matrix elements of the current operators are the essential contribution to the intrinsic anomalous Hall effect (AHE) . However, recent progress provides a deeper understanding for the intrinsic contribution of the AHE in terms of the Berry curvature wherein electrons pick up a transverse velocity even in the absence of an external magnetic field . The Berry curvature vanishes for conventional antiferromagnets which exhibit zero AHE. In contrast, the noncollinear Weyl metal Mn3Ge with a very small magnetization exhibits a very large AHE, emphasizing the role of the Berry curvature.
Very recently, many Heusler compounds have been identified as Weyl semimetals, which exhibit non-zero Berry curvatures around their Weyl points. This, in addition to the fact that Heusler compounds have high transition temperatures, make them ideal candidates to show a large intrinsic AHE at room temperature . Heusler compounds provide a flexible platform for tuning the Berry curvature based on simple electron counting rules. Our group is known worldwide for the research in Heusler compounds [4,5]. In this proposal, we suggest to measure the AHE of different series of Heusler compounds and to tune their AHE by controlling the Berry phase. The research will benefit from the strong support from the theory group.
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