A phenomenological approach to study the effect of uniaxial anisotropy on the magnetization of ferromagnetic nanoparticles

We study the effect of the uniaxial anisotropy in a system of ideal, noninteracting ferromagnetic nanoparticles by means of a thermodynamical model. We show that the effect of the anisotropy can be easily assimilated in a temperature shift Ta∗, in analogy to what was proposed by Allia et al. (2001) in the case of interacting nanomagnets. The phenomenological anisotropic Ta∗ parameter can be negative, indicating an antiferromagnetic-like behavior, or positive, indicating a ferromagnetic-like character as seen in the inverse susceptibility behavior as a function of temperature. The study is done considering an easy axis distribution to take into account the anisotropy axis dispersion in real samples (texture). In the case of a volumetric uniform distribution of anisotropy axes, the net effect makes Ta∗ to vanish, and the magnetic susceptibility behaves like a conventional superparamagnetic system, whereas in the others a finite value is obtained for Ta∗. When magnetic moment distribution is considered, the effect is to enhance the Ta∗ parameter, when the dispersion of the magnetic moments becomes wider.