Spin-Flux Skyrmions: Anomalous Electron Dynamics and Spin-Hall Currents

TL;DR

This paper introduces a new type of skyrmion called spin-flux skyrmion, which has a different topological structure leading to unique emergent magnetic fields and Hall effects, explaining experimental anomalies.

Contribution

The work defines spin-flux skyrmions with a distinct topological phase and derives their emergent fields, revealing new contributions to Hall conductivity not seen in conventional skyrmions.

Findings

Spin-flux skyrmions have an additional monopolar $\sigma_x$ component.

They produce a finite average emergent magnetic field at finite density.

This leads to a nontrivial Hall conductivity term explaining experimental anomalies.

Abstract

We introduce a topologically distinct skyrmion, termed a spin-flux skyrmion, which shares the same real-space magnetization profile as a conventional skyrmion but differs fundamentally in its underlying topological structure. This distinction originates from the path traced by its rotation matrices within the doubly connected SO(3) group manifold, leading to a nontrivial spinor phase of $e^{i\pi}$ upon encircling the texture. Using an explicit SU(2) gauge field formalism, we derive the emergent magnetic field components generated by both conventional and spin-flux skyrmions. While conventional skyrmions exhibit a dominant $\sigma_z$ component with weak dipolar $\sigma_x, \sigma_y$ contributions, spin-flux skyrmions possess an additional monopolar $\sigma_x$ component that yields a finite average emergent field for a finite density of skyrmions. This nontrivial component introduces a nontrivial term in the Hall conductivity, enabling a direct explanation of experimental Hall resistivity anomalies that cannot be accounted for by conventional skyrmions alone. Moreover, we show that this additional term couples to the in-plane spin polarization of conduction electrons, providing a further tunable handle to control the transverse Hall response.