Transverse Transport in Two-Dimensional Relativistic Systems with Non-Trivial Spin Textures

TL;DR

This paper reveals that the transverse resistivity in magnetic systems with skyrmions includes an additional 'non-collinear' Hall effect term, which is crucial for accurately interpreting transport measurements of complex spin textures.

Contribution

It introduces and characterizes the non-collinear Hall effect, an essential correction to the traditional Hall effect expressions in systems with non-trivial spin textures.

Findings

The NHE term depends on magnetic texture, spin-orbit coupling, and crystal structure.

The NHE magnitude scales with spin-orbit interaction strength.

Including NHE improves the decoding of spin textures from transport data.

Abstract

Using multiple scattering theory, we show that the generally accepted expression of transverse resistivity in magnetic systems that host skyrmions, given by the linear superposition of the ordinary (OHE), the anomalous (AHE) and the topological Hall effect (THE), is incomplete and must be amended by an additional term, the "non-collinear" Hall effect (NHE). Its angular form is determined by the magnetic texture, the spin-orbit field of the electrons, and the underlying crystal structure, allowing to disentangle the NHE from the various other Hall contributions. Its magnitude is proportional to the spin-orbit interaction strength. The NHE is an essential term required for decoding two- and three-dimensional spin textures from transport experiments.