Investigation of the Nonlinear Dependence of Anomalous Hall Conductivity on Magnetization in Weak Itinerant Ferromagnet Surasree Sadhukhan, Igor I. Mazin

The ordinary Hall effect exists irrespective of the presence of spin-orbit coupling (SOC), whereas the anomalous Hall effect (AHE), according to the Karplus–Luttinger (KL) theory, requires both SOC and broken time-reversal symmetry. Early interpretations suggested that the AHE was proportional to the exchange splitting; however, it was later recognized that the intrinsic contribution originates from the Berry curvature near band crossings, which is, in general, independent of magnetization or exchange splitting. A common misconception is that the AHE scales linearly with magnetization, an assumption valid only for multi-domain ferromagnets, where both the anomalous Hall conductivity (AHC) and magnetization are independently proportional to the domain population imbalance, or for cases of very small exchange splittings (< SOC). Nevertheless, many experimental studies continue to assume a linear dependence of AHC on magnetization even in single-domain materials.

To test this assumption in a conceptually simple case, we performed density functional theory (DFT) calculations for ZrZn2, an itinerant ferromagnet with weak collinear magnetization, and found that the AHC does not scale proportionally with magnetization even for the case of soft magnetic moments where magnetization is varied not through non-collinear canting but

simply through varying magnetization amplitude.