Magnetic susceptibility curves of a nanoparticle assembly, I: Theoretical model and analytical expressions for a single magnetic anisotropy energy

We study a model system made of non-interacting monodomain ferromagnetic nanoparticles, considered as macrospins, with a randomly oriented uniaxial magnetic anisotropy. We derive a simple differential equation governing the magnetic moment evolution in an experimental magnetic susceptibility measurement, at low field and as a function of temperature, following the well-known Zero-Field Cooled/Field Cooled (ZFC/FC) protocol. Exact and approximate analytical solutions are obtained, together for the ZFC curve and the FC curve. The notion of blocking temperature is discussed and the influence of various parameters on the curves is investigated. A crossover temperature is defined and a comparison is made between our progressive crossover model (PCM) and the crude “two states” or abrupt transition model (ATM), where the particles are assumed to be either fully blocked or purely superparamagnetic. We consider here the case of a single magnetic anisotropy energy (MAE), which is a prerequisite before considering the more realistic and experimentally relevant case of an assembly of particles with a MAE distribution (cf. part II that follows).

Research Highlights► Adifferential equation for ZFC/FC curves of a particle assembly is established. ►Exact and approximate analytical solutions are obtained. ►A comparison is made with the abrupt blocked/superparamagnetic transition model. ►The notion of blocking temperature is discussed. ►The influence of various parameters on the susceptibility curves is investigated.