6533b832fe1ef96bd129a351

RESEARCH PRODUCT

The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach

subject

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We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-interpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.