Improved Averaging Of Hysteresis Loops From Micromagnetic Simulations Of Non-Interacting Uniaxial Nanoparticles

Micromagnetic simulations allow us to understand the magnetization reversal of magnetic systems, but the computational cost scales up with the size and, in the case of bulk-scale systems, it becomes an impossible task to face unless certain assumptions are made (e.g. uniform and fully saturated magnetization or simplified anisotropy). However, those simplifications do not work for more complex systems with domain walls, shape anisotropy or exchange-bias. Macroscopic ensembles of non-interacting Magnetic Nanoparticles (MNP) can be modelled as an average of a set of isolated single-domain nanoparticles where magnetocrystalline anisotropies force the particle moments in a wide range of directions. To reduce computational time in such systems, we propose an optimized method of hysteresis loop averaging that takes advantage of high rotational symmetry of spherical particles and proves convenient for energy landscapes such as that in magnetocrystalline uniaxial systems. This improved method reduces the number of simulations required to generate macroscopic-like non-interacting and randomly oriented ensembles of magnetic nanoparticles (i.e. a dilute powder), as compared to the usual mean arithmetic averaging of hysteresis loops. To verify the good agreement of the averaging method we have compared our results with the well-known Stoner-Wohlfarth hysteresis loop, thus matching magnetic properties such as coercivity, remanence and energetic product with a relatively low count of simulations.