Mean field magnetization of gapped anisotropic multiplet

Some materials have a large gap between the ground and first excited states. At temperatures smaller than the gap value, the thermodynamic properties of such materials are mainly ruled by the ground state. It is also common to find materials with magnetocrystalline anisotropy, which arises due to interatomic interactions. The present paper uses a classical approach to deal large angular momenta in such materials. Based on analytical expressions for the thermodynamics of paramagnetic gapped anisotropic multiplets, we use mean field theory to study the influence of the anisotropy upon the properties of interacting systems. We also use Landau theory to determine the influence of the anisotropy in first and second order phase transitions. It is found that the anisotropy increases the critical temperature, and enlarges the hysteresis of first order transitions. We present analytical expressions for the quantities analyzed.