Thermodynamics of three-dimensional magnetic nanoparticles

A three-dimensional system of non-interacting nanoparticles with uniaxial anisotropies is studied. Equilibrium thermodynamical properties are derived by evaluating the partition function. When external field is applied perpendicular to the anisotropy axis, the system exhibits a second-order phase transition with order parameter being the magnetization parallel to the field. Contrary to a superparamagnetic particle, the magnetization shows a maximum at finite temperature. Moreover, it is found that the magnetic susceptibility considerably deviates from Curie law. This can be misinterpreted as a ferromagnetic or antiferromagnetic coupling among magnetic particles, depending on the angle between the anisotropy axes and the external magnetic field.