Topological Hall effect induced by classical large-spin background: $su(2)$ path-integral approach

TL;DR

This paper uses an $su(2)$ path-integral approach to show that lattice electrons coupled to a classical large-spin background can exhibit a topological Hall effect even without scalar spin chirality.

Contribution

It introduces a novel $su(2)$ path-integral method to analyze the topological Hall effect induced by classical large-spin textures.

Findings

Electrons can exhibit topological Hall effect without scalar spin chirality.

The $su(2)$ path-integral approach effectively captures the influence of classical spin backgrounds.

Large-spin limit simplifies the quantum spin background to a classical texture.

Abstract

The $su(2)$ coherent-state path-integral technique is employed to study lattice electrons strongly coupled to a quantum spin background. In the large-spin limit it is replaced with its classical counterpart that breaks the time-reversal symmetry. The fermions propagating through a classical large-spin texture may then exhibit the topological Hall effect which arises even for a zero scalar spin chirality of the underlying spin background.