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 d
iamagnetism, 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.
The charged Fermi gas with a small Lande-factor $g$ is expected to be diamagnetic, while that with a larger $g$ could be paramagnetic. We calculate the critical value of the $g$-factor which separates the dia- and para-magnetic regions. In the weak-f
ield limit, $g_{c}$ has the same value both at high and low temperatures, $g_{c}=1/sqrt{12}$. Nevertheless, $g_{c}$ increases with the temperature reducing in finite magnetic fields. We also compare the $g_{c}$ value of Fermi gases with those of Boltzmann and Bose gases, supposing the particle has three Zeeman levels $sigma=pm1, 0$, and find that $g_{c}$ of Bose and Fermi gases is larger and smaller than that of Boltzmann gases, respectively.
It has been suggested that either diamagnetism or paramagnetism of Bose gases, due to the charge or spin degrees of freedom respectively, appears solely to be extraordinarily strong. We investigate magnetic properties of charged spin-1 Bose gases in
external magnetic field, focusing on the competition between the diamagnetism and paramagnetism, using the Lande-factor $g$ of particles to evaluate the strength of paramagnetic effect. We propose that a gas with $g<{1/sqrt{8}}$ exhibits diamagnetism at all temperatures, while a gas with $g>{1/2}$ always exhibits paramagnetism. Moreover, a gas with the Lande-factor in between shows a shift from paramagnetism to diamagnetism as the temperature decreases. The paramagnetic and diamagnetic contributions to the total magnetization density are also calculated in order to demonstrate some details of the competition.
In superconducting ferromagnets for which the Curie temperature $T_{m}$ exceeds the superconducting transition temperature $T_{c}$, it was suggested that ferromagnetic spin fluctuations could lead to superconductivity with p-wave spin triplet Cooper
pairing. Using the Stoner model of itinerant ferromagnetism, we study the feedback effect of the p-wave superconductivity on the ferromagnetism. Below $T_{c}$, the ferromagnetism is enhanced by the p-wave superconductivity. At zero temperature, the critical Stoner value for itinerant ferromagnetism is reduced by the strength of the p-wave pairing potential, and the magnetization increases correspondingly. More important, our results suggest that once Stoner ferromagnetism is established, $T_m$ is unlikely to ever be below $T_c$. For strong and weak ferromagnetism, three and two peaks in the temperature dependence of the specific heat are respectively predicted, the upper peak in the latter case corresponding to a first-order transition.
