Differentiating superparamagnetic and non-superparamagnetic behaviour in single domain magnetic nanoparticles by coercivity weighted Langevin magnetisation

Superparamagnetism (SPM) is an attractive material property often appearing in nanoscaled single domain (SD) configurations. However, not all SD particles are superparamagnetic, which depends on a few parameters including material type, temperature, measurement time and magneto crystalline anisotropy. The non-linear magnetisation response of magnetic particles can be interpreted by classical Langevin approach but its applicability is limited to pure SD-SPM behaviour. The classical Langevin equation lacks parameters to account for possible remanence and coercivity in SD regime, resultantly, the SD-nonSPM possibility is left untreated. To solve this issue, we propose a new model by including SD coercivity parameters in classical Langevin equations. The new model 1) combines steady or time varying magnetisation dynamics and temperature or particle size dependent coercivity and 2) helps to calculate coercivity compensated magnetisations and susceptibilities directly. The model covers full spectrum of SD diameters and defines the switching between superparamagnetic and non-superparamagnetic states more precisely.