Equation of Motion for a Spin Vortex and Geometric Force

TL;DR

This paper derives the equation of motion for a spin vortex in a 2D Heisenberg ferromagnet, revealing a geometric force similar to the Magnus force, which influences quantum vortex dynamics and interactions.

Contribution

It introduces a Hamiltonian framework for spin vortices incorporating a geometric force, advancing understanding of vortex quantum dynamics in anisotropic ferromagnets.

Findings

Identification of a geometric force analogous to the Magnus force.

Implications for vortex bound states and pinning interactions.

Enhanced understanding of vortex quantum behavior.

Abstract

The Hamiltonian equation of motion is studied for a vortex occuring in 2-dimensional Heisenberg ferromagnet of anisotropic type by starting with the effective action for the spin field formulated by the Bloch (or spin) coherent state. The resultant equation shows the existence of a geometric force that is analogous to the so-called Magnus force in superfluid. This specific force plays a significant role for a quantum dynamics for a single vortex, e.g, the determination of the bound state of the vortex trapped by a pinning force arising from the interaction of the vortex with an impurity.