Bicritical and tricritical phenomena in uniaxial ferromagnets

The phase diagrams of a spin-1 uniaxial ferromagnetic model with both exchange anisotropy and single-ion anisotropy ($D$) are studied in the mean-field approximation. In the absence of an external magnetic field a bicritical point (BCP) is found in the ($D,T$) plane for the transverse ($K$) to parallel ($J$) coupling ratio $\frac{K}{J}>0.462\mathrm{}$. As the exchange anisotropy is decreased the BCP moves towards the temperature axis. In the limit of the isotropic exchange the BCP is located on the $T$ axis. In the presence of a field along the parallel (transverse) direction two symmetric lines of tricritical points (TCP) are generated in the ($D$, $H_z\left(H_{\perp }\right)$, $T$) space. These lines meet at the BCP. For a significantly wide range of $\frac{D}{J}$ and $\frac{K}{J}$ values TCP prevails in the ($H_z \left(H_{\perp }\right)$, $T$) plane. Application of a transverse (parallel) field generates the wing coexistence surfaces. The whole thermodynamic space is experimentally accessible. Outside the above ranges, one may still have a TCP in the ($H_{\perp }$, $T$) plane, but not in the ($H_z$,$T$) phase diagram. Some special features of the ($H_z$,$T$) phase diagram are also discussed.