The Magnetic Susceptibility of Non-Interacting Nanoparticles

We have calculated the low-field magnetic susceptibility $\chi$ of a system consisting of non-interacting mono-dispersed nanoparticles using a classical statistical approach. The model makes use of the assumption that the axes of symmetry of all nanoparticles are aligned and oriented at a certain angle $\psi$ with respect to the external magnetic field. An analytical expression for the temperature dependence of the susceptibility $\chi(T)$ above the blocking temperature is obtained. The derived expression is a generalization of the Curie law for the case of anisotropic magnetic particles. We show that the normalized susceptibility is a universal function of the ratio of the temperature over the anisotropy constant for each angle $\psi$. In the case that the easy-axis is perpendicular to the magnetic field the susceptibility has a maximum. The temperature of the maximum allows one to determine the anisotropy energy.