Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films

TL;DR

This paper derives a nonlinear hydrodynamic model for ferromagnetic thin films that reveals the breaking of Galilean invariance and predicts fluid-like magnetic behaviors including Mach cones and instabilities.

Contribution

It introduces an exact dispersive hydrodynamic formulation of the Landau-Lifshitz equation that accounts for full nonlinearity and exchange dispersion, highlighting Galilean invariance breaking.

Findings

Hydrodynamic equations break Galilean invariance in ferromagnetic thin films.

Identification of uniform hydrodynamic states with fluid-like magnetic behaviors.

Prediction of Mach cone formation and modulational instability in the system.

Abstract

Microwave magnetodynamics in ferromagnets are often studied in the small-amplitude or weakly nonlinear regime corresponding to modulations of a well-defined magnetic state. However, strongly nonlinear regimes, where the aforementioned approximations are not applicable, have become experimentally accessible. By re-interpreting the governing Landau-Lifshitz equation of motion, we derive an exact set of equations of dispersive hydrodynamic form that are amenable to analytical study even when full nonlinearity and exchange dispersion are included. The resulting equations are shown to, in general, break Galilean invariance. A magnetic Mach number is obtained as a function of static and moving reference frames. The simplest class of solutions are termed uniform hydrodynamic states (UHSs), which exhibit fluid-like behavior including laminar flow at subsonic speeds and the formation of a Mach cone and wave-fronts at supersonic speeds. A regime of modulational instability is also possible, where the UHS is violently unstable. The hydrodynamic interpr