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

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.

7 pages, 2 figures

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• Resonant optical topological Hall conductivity from skyrmions
• Berry Curvature and Topological Hall Effect in Magnetic Nanoparticles
• A spin model for intrinsic antiferromagnetic skyrmions on a triangular lattice
• Monoaxial Dzyaloshinskii-Moriya interaction-induced topological Hall effect in a new chiral-lattice magnet GdPt${}_2$B
• Chern insulating state with double-$Q$ ordering wave vectors at the Brillouin zone boundary
• Interaction effects in graphene in a weak magnetic field