Magnetic properties of charged spin-1 Bose gases with ferromagnetic   coupling
  Magnetic properties of a charged spin-1 Bose gas with ferromagnetic interactions is investigated within mean-field theory. It is shown that a competition between paramagnetism, diamagnetism and ferromagnetism exists in this system. It is shown that diamagnetism, being concerned with spontaneous magnetization, cannot exceed ferromagnetism in very weak magnetic field. The critical value of reduced ferromagnetic coupling of paramagnetic phase to ferromagnetic phase transition $\bar I_{c}$ increases with increasing temperature. The Lande-factor $g$ is introduced to describe the strength of paramagnetic effect which comes from the spin degree of freedom. The magnetization density $\bar M$ increases monotonically with $g$ for fixed reduced ferromagnetic coupling $\bar I$ as $\bar I>\bar I_{c}$. In a weak magnetic field, ferromagnetism makes immense contribution to the magnetization density. While at a high magnetic field, the diamagnetism inclines to saturate. Evidence for condensation can be seen in the magnetization density at weak magnetic field. 
Jihong Qin, Xiaoling Jian, Qiang Gu
cond-mat.stat-mech cond-mat.quant-gas cond-mat.supr-con