Uncovering the Magnetization Multipolar Anisotropy of the Anomalous Hall Effect in Conventional Ferromagnets

Abstract The anomalous Hall effect (AHE) in ferromagnets is conventionally described by a dipolar relation between the anomalous Hall conductivity and the magnetization, which enforces their parallel alignment and thus forbids a Hall signal when the magnetization lies within the Hall plane. Here, by systematically measuring the AHE under in-plane magnetization in Fe and Ni, we uncover a multipolar anisotropy of the AHE that produces a finite in-plane anomalous Hall response in Fe(103) and Ni(111), while it vanishes in Fe(001) as dictated by crystal symmetry. The angular dependence of the in-plane AHE in Fe(103) and Ni(111) further deviates from the familiar sinusoidal form expected from dipolar behavior, revealing symmetry-allowed higher-order multipolar contributions. First-principles calculations quantitatively reproduce the experimentally extracted dipolar and octupolar coefficients for Fe, demonstrating that intrinsic Berry curvature carries a sizable multipolar anisotropy in conventional cubic ferromagnets.