Regensburg 2025 – scientific programme

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MA: Fachverband Magnetismus

MA 23: Focus Session: Magneto-Transport and Magneto-Optics of Higher Orders in Magnetization I

MA 23.4: Talk

Wednesday, March 19, 2025, 10:45–11:00, H20

Multipolar anisotropy in anomalous Hall effect from spin-group symmetry breaking — •Zheng Liu — University of Science and Technology of China, Hefei, China

Traditional view of the anomalous Hall effect (AHE) in ferromagnets is that it arises from the magnetization perpendicular to the measurement plane and that there is a linear dependence on the latter. However, this view is squarely challenged by a number of experiments recently, urging for a thorough theoretical investigation on the fundamental level. We find that for strong magnets, it is more appropriate and fruitful to regard the AHE as a spin-group symmetry breaking phenomenon where the critical parameter is the spin-orbit interaction strength, which involves a much smaller energy scale. Born out of our framework is a rich multi-polar relationship between the anomalous Hall conductivity and the magnetization direction, with each pole being expanded progressively in powers of the spin-orbit coupling strength. For the leading order contribution, i.e., the dipole, its isotropic part corresponds to the traditional view, and its anisotropic part can lead to the in-plane AHE where the magnetization lies within the measurement plane. Beyond the dipolar one, the octupolar structure offers the leading order source of nonlinearity and hence introduces unique anisotropy where the dipolar structure cannot. The dipolar and octupolar structure offers a unified explanation for the in-plane AHE recently observed in various ferromagnets. Our theory lays the ground for decoding the coupling between various transport and optical phenomena and the magnetic orders.

Keywords: Anomalous Hall effect; Nonlinear magneto-transport; Spin group; Spin-orbit coupling