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The movement of the macroscopic magnetic moment in ferromagnetic systems can be described by the Landau-Lifshitz (LL) or Landau-Lifshitz-Gilbert (LLG) equation. These equations are strictly valid only at absolute zero temperature. To include temperature effects a stochastic version of the LL or LLG equation for a spin density of one per unit cell can be used instead. To apply the stochastic LL to micromagnetic simulations, where the spin density per unit cell is generally higher, a conversion regarding simulation cell size and temperature has to be established. Based on energetic considerations, a conversion for ferromagnetic bulk and thin film systems is proposed. The conversion is tested in micromagnetic simulations which are performed with the Object Oriented Micromagnetic Framework (OOMMF). The Curie temperatures of bulk Nickel, Cobalt and Iron systems as well as Nickel thin-film systems with thicknesses between 6.3 mono layer (ML) and 31ML are determined from micromagnetic simulations. The results show a good agreement with experimentally determined Curie temperatures of bulk and thin film systems when temperature scaling is performed according to the presented model.
To simulate the movement of the macroscopic magnetic moment in ferromagnetic systems under the influence of elevated temperatures, the stochastic version of the Landau-Lifshitz (LL) or the Landau-Lifshitz-Gilbert equation with a spin density of one per unit cell has to be used.
To apply the stochastic LL to micromagnetic simulations, where the spin density per unit cell is generally higher, a conversion has to be performed. OOMMF sample files MIF) are provided which can be used to determine the Curie temperature for the classical bulk magnets, iron, nickel and cobalt.
The movement of the macroscopic magnetic moment in ferromagnetic systems can be described by the Landau-Lifshitz (LL) or Landau-Lifshitz-Gilbert (LLG) equation. These equations are strictly valid only at absolute zero temperature. To include temperature effects a stochastic version of the LL or LLG equation for a spin density of one per unit cell can be used instead. To apply the stochastic LL to micromagnetic simulations, where the spin density per unit cell is generally higher, a conversion regarding simulation cell size and temperature has to be established. Based on energetic considerations, a conversion for ferromagnetic bulk and thin film systems is proposed. The conversion is tested in micromagnetic simulations which are performed with the Object Oriented Micromagnetic Framework (OOMMF). The Curie temperatures of bulk Nickel, Cobalt and Iron systems as well as Nickel thin-film systems with thicknesses between 6.3 mono layer (ML) and 31ML are determined from micromagnetic simulations. The results show a good agreement with experimentally determined Curie temperatures of bulk and thin film systems when temperature scaling is performed according to the presented model.
Clustering of magnetic nanoparticles can drastically change their collective magnetic properties, which in turn may influence their performance in technological or biomedical applications. Here, we investigate a commercial colloidal dispersion (FeraSpinTMR), which contains dense clusters of iron oxide cores (mean size around 9 nm according to neutron diffraction) with varying cluster size (about 18–56 nm according to small angle x-ray diffraction), and its individual size fractions (FeraSpinTMXS, S, M, L, XL, XXL). The magnetic properties of the colloids were characterized by isothermal magnetization, as well as frequency-dependent optomagnetic and AC susceptibility measurements. From these measurements we derive the underlying moment and Relaxation frequency distributions, respectively. Analysis of the distributions shows that the clustering of the initially superparamagnetic cores leads to remanent magnetic moments within the large clusters. At frequencies below 105 rad s−1, the relaxation of the clusters is dominated by Brownian (rotation) relaxation. At higher frequencies, where Brownian relaxation is inhibited due to viscous friction, the clusters still show an appreciable magnetic relaxation due to internal moment relaxation within the clusters. As a result of the internal moment relaxation, the colloids with the large clusters (FSL, XL, XXL) excel in magnetic hyperthermia experiments.