Magnetic Properties of a Bose-Einstein Condensate

TL;DR

This paper investigates the magnetic properties of a spin-1 Bose-Einstein condensate of sodium atoms, revealing a phase diagram where the system exhibits ferromagnetism below the condensation temperature and shows discontinuities in magnetization derivatives.

Contribution

It constructs a phase diagram for a spin-1 Bose gas in a magnetic field, highlighting ferromagnetic behavior and magnetization discontinuities at the phase boundary.

Findings

Magnetization is proportional to condensate fraction in zero magnetic field.

System is ferromagnetic below the Bose-Einstein condensation temperature.

Discontinuities in second derivatives of magnetization occur along the phase boundary.

Abstract

Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behaviour of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation $T_{BEC}$ increases with magnetic field. In particular the system is ferromagnetic below $T_{BEC}$ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetisation with regard to temperature or magnetic field are discontinuous along the phase boundary.