Conserved momenta of ferromagnetic solitons through the prism of differential geometry

Abstract

The relation between symmetries and conservation laws for solitons in a ferromagnet is complicated by the presence of gyroscopic (precessional) forces, whose description in the Lagrangian framework involves a background gauge field. This makes canonical momenta gauge-dependent and requires a careful application of Noether's theorem. We show that Cartan's theory of differential forms is a natural language for this task. We use it to derive conserved momenta of the Belavin--Polyakov skyrmion, whose symmetries include translation, global spin rotation, and dilation.

Submission to SciPost

References in corpus (5)

• Spin Transfer Torques
• Dynamics of domain walls in magnetic nanostrips
• Magnon-skyrmion scattering in chiral magnets
• Dynamics of a vortex domain wall in a magnetic nanostrip: an application of the collective coordinate approach
• Field momentum and gyroscopic dynamics of classical systems with topological defects

Cited by in corpus (6)

• Skyrmion Helicity: Quantization and Quantum Tunneling Effects
• Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
• Anomalous Continuous Translations
• Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
• Gyroscopic tensor of a magnetic soliton
• Topological dipoles of quantum skyrmions