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Superparamagnetism (SPM) is an attractive material property often appearingin nanoscaled single domain (SD) configurations. However, not all SD particlesare superparamagnetic, which depends on a few parameters including materialtype, temperature, measurement time and magneto crystalline anisotropy. Thenon-linear magnetisation response of magnetic particles can be interpreted byclassical Langevin approach but its applicability is limited to pure SD-SPMbehaviour. The classical Langevin equation lacks parameters to account forpossible remanence and coercivity in SD regime, resultantly, the SD-nonSPMpossibility is left untreated. To solve this issue, we propose a new model byincluding SD coercivity parameters in classical Langevin equations. The newmodel 1) combines steady or time varying magnetisation dynamics and temperatureor particle size dependent coercivity and 2) helps to calculate coercivitycompensated magnetisations and susceptibilities directly. The model covers fullspectrum of SD diameters and defines the switching between superparamagneticand non-superparamagnetic states more precisely.

Coercivity weighted Langevin magnetisation; A new approach to interpret  superparamagnetic and nonsuperparamagnetic behaviour in single domain  magnetic nanoparticles