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MA: Fachverband Magnetismus

MA 40: Skyrmions III (joint session MA/TT)

MA 40.1: Vortrag

Mittwoch, 18. März 2020, 15:00–15:15, POT 6

Noncommutative geometry and the anomalous Hall effect in chiral spin textures — •Fabian R. Lux¹, Frank Freimuth¹, Stefan Blügel¹, and Yuriy Mokrousov^1,2 — ¹Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany — ²Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany

We demonstrate that the anomalous Hall effect (AHE) in chiral magnetic textures can naturally be described in the language of Alain Connes’ noncommutative geometry which provides it with a deep geometrical interpretation. For periodic magnetic structures, the formalism reduces to the well-known Kubo-Bastin equations, but its applicability extends to all aperiodic cases in general. Under the assumption of a slowly varying texture, we derive the first order correction to the conventional AHE which is linear in the gradients of the magnetization texture [1]. This chiral Hall effect is neither proportional to the net magnetization nor to the emergent magnetic field that is responsible for the topological Hall effect and thus introduces an interesting twist in the interpretation of experimental data.

We acknowledge funding from Deutsche Forschungsgemeinschaft (DFG) through SPP 2137 “Skyrmionics".

[1] F. R. Lux et al., arXiv:1910.06147 (2019)