Abstract
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.
Highlights
As their applications strongly depend on their magnetic properties, which rely on material, size, shape, or organization of Magnetic Nanoparticles (MNP) systems, it is crucial to extract reliable results on the magnetic state and behavior of the MNPs
Collective magnetic behavior of uniaxial Co(hcp) single domain MNPs has been compared to Stoner-Wohlfarth (SW) averaged hysteresis loop (Fig. 2(a))
Hysteresis loops from micromagnetic simulations of Co(hcp) NPs were averaged with Arithmetic (A) (Fig. 2(a)) or Spheroidal (S) (Fig. 2(b)) methods in order to generate the magnetization reversal loop of their randomly-oriented and non-interacting ensemble, using from 3 (Δφ = 45○) to 19 (Δφ = 5○) calculations
Summary
Magnetic nanoparticles (MNPs) offer a wide range of magnetic behaviors, from single-domain configuration and superparamagnetic states to shape-dependent magnetic anisotropies and many other features that convert them in useful materials with plenty of applications in medicine –including hyperthermia treatment, imaging, or targeted drug delivery,4– environmental sciences –from water purification to waste treatment,6– or information technology. As their applications strongly depend on their magnetic properties, which rely on material, size, shape, or organization of MNP systems, it is crucial to extract reliable results on the magnetic state and behavior of the MNPs.Micromagnetic simulations allow the study of magnetization states in complex MNP arrangements at a high computational cost.9In addition, when studying magnetization reversal processes in anisotropic systems, as more simulations are required to proper study the effects of field directionality on magnetic properties, computational costs escalate. As 1D, 2D or 3D crystalline systems can take advantage of periodic boundary conditions to extend their simulation scope, saving huge amounts of simulation time, typically, the study of 0D materials in 3D arrangements requires an increasing number of simulations due to the higher range of potential directions and arrangements with significant effects on magnetic properties.even if large numbers of uniaxial nanoparticles can be approximated as macrospins with Stoner-Wohlfarth (SW) behavior, and be studied using probabilistic Monte-Carlo Methods, such systems require excessive simulation times and cannot resolve intrinsic magnetic processes of the particles like domain-wall scitation.org/journal/adv formation, which have been studied in literature by treating each nanoparticle individually, losing the collective behavior.. Magnetic nanoparticles (MNPs) offer a wide range of magnetic behaviors, from single-domain configuration and superparamagnetic states to shape-dependent magnetic anisotropies and many other features that convert them in useful materials with plenty of applications in medicine –including hyperthermia treatment, imaging, or targeted drug delivery,4– environmental sciences –from water purification to waste treatment,6– or information technology.7,8 As their applications strongly depend on their magnetic properties, which rely on material, size, shape, or organization of MNP systems, it is crucial to extract reliable results on the magnetic state and behavior of the MNPs. Micromagnetic simulations allow the study of magnetization states in complex MNP arrangements at a high computational cost..
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