Spin waves in a Bose Ferromagnet

TL;DR

This paper investigates spin waves in a Bose ferromagnet, revealing that the ferromagnetic transition occurs above Bose-Einstein condensation and that coupled spin waves form a single mode with a quadratic spectrum influenced by both phases.

Contribution

It introduces a two-fluid Ginzburg-Landau model for Bose ferromagnets, showing coupled spin waves and a temperature-dependent spin-wave stiffness coefficient.

Findings

Ferromagnetic transition occurs above Bose-Einstein condensation.

Coupled spin waves produce a single mixed mode.

Spin-wave stiffness coefficient shows a sharp bend at BEC temperature.

Abstract

It is shown that the ferromagnetic transition takes place always above Bose-Einstein condensation in ferromagnetically coupled spinor Bose gases. We describe the Bose ferromagnet within Ginzburg-Landau theory by a "two-fluid" model below Bose-Einstein condensation. Both the Bose condensate and the normal phase are spontaneously magnetized. As a main result we show that spin waves in the two fluids are coupled together so as to produce only one mixed spin-wave mode in the coexisting state. The long wavelength spectrum is quadratic in the wave vector ${\bf k}$, consistent with usual ferromagnetism theory, and the spin-wave stiffness coefficient $c_s$ includes contributions from both the two phases, implying the "two-fluid" feature of the system. $c_s$ can show a sharp bend at the Bose-Einstein condensation temperature.