Introduction of thermal activation in forward modeling of hysteresis loops for single-domain magnetic particles and implications for the interpretation of the Day diagram

Synthetic hysteresis loops were generated by numerically solving the classical Stoner- Wohlfarth model and a thermally activated Stoner-Wohlfarth model for a set of randomly oriented magnetic grains. Although computationally intensive this method allows forward modeling of hysteresis loops of single-domain (SD) and viscous grains. In the classic Stoner-Wohlfarth model the shape of the modeled loops can be modified by changing the distribution of the anisotropy energy but all the loops will all have similar hysteresis parameters Msr/Ms and Hcr/Hc corresponding to that of a theoretical assemblage of SD particles. The thermally activated Stoner-Wohlfarth model, which allows the magnetic moment of each grain to switch between two energy minima according to Boltzmann statistics, extends the SD model toward superparamagnetic (SP) grains and introduces a volume dependency. Numerical simulation using the thermally activated model shows that the shapes of SD loops are modified by the effect of the thermal energy if the particles are sufficiently small. The major effect of the thermal disturbance is observed in highly viscous particles (smaller than approximately 0.03 mm in diameter, for magnetite) where it strongly reduces the coercivity and to a lesser extent the remanent magnetization. The effect on the hysteresis parameters is a large increase in Hcr/Hc and a decrease in Msr/Ms, by factors that vary with anisotropy distribution, grain volume and measurement time. For certain grain sizes, these result in hysteresis parameters that are similar to those attributed to pseudosingle-domain (PSD) grains.