Long wavelength spin dynamics of ferromagnetic condensates

TL;DR

This paper develops a hydrodynamic framework for long wavelength spin dynamics in ferromagnetic Bose condensates, extending the Landau-Lifshitz equation to include superfluid velocity effects and analyzing stability and instabilities.

Contribution

It introduces a modified Landau-Lifshitz equation incorporating superfluid advection for arbitrary spin condensates, providing clearer physical insight than the Gross-Pitaevskii approach.

Findings

Derived equations of motion for ferromagnetic condensates.

Analyzed stability of magnetic structures and identified dipolar force signatures.

Discussed experimental observations of spin wave instabilities.

Abstract

We obtain the equations of motion for a ferromagnetic Bose condensate of arbitrary spin in the long wavelength limit. We find that the magnetization of the condensate is described by a non-trivial modification of the Landau-Lifshitz equation, in which the magnetization is advected by the superfluid velocity. This hydrodynamic description, valid when the condensate wavefunction varies on scales much longer than either the density or spin healing lengths, is physically more transparent than the corresponding time-dependent Gross-Pitaevskii equation. We discuss the conservation laws of the theory and its application to the analysis of the stability of magnetic helices and Larmor precession. Precessional instabilities in particular provide a novel physical signature of dipolar forces. Finally, we discuss the anisotropic spin wave instability observed in the recent experiment of Vengalattore et. al. (Phys. Rev. Lett. 100, 170403, (2008)).