The Magnus Force on Skyrmions in Ferromagnets and the Quantum Hall Effect

TL;DR

This paper investigates whether skyrmions in ferromagnets and quasiparticles in the quantum Hall effect experience a Magnus force, concluding that the Magnus and Lorentz forces are equivalent descriptions of the same physical phenomenon.

Contribution

It clarifies that the Magnus force on skyrmions and the Lorentz force on quantum Hall quasiparticles are fundamentally the same, resolving a potential misconception.

Findings

Magnus and Lorentz forces are equivalent descriptions.

Skyrmions in ferromagnets experience a Magnus force.

Quantum Hall quasiparticles do not experience an additional Magnus force.

Abstract

The topological solitons, or ``skyrmions'', in a planar ferromagnet experience a Magnus force proportional to the product of their velocity and the surrounding magnetization. It has been suggested that the charged quasiparticles near filling factor $\nu=1$ in the $GaAs$ quantum Hall effect are skyrmions. If so we might expect this spin-induced Magnus force to act on the quasiparticles in addition to the Lorentz force they experience because of their charge. We show that this is not the case, and that the Magnus and Lorentz forces are merely different descriptions of the same physical effect.