Three-dimensional micromagnetic calculations for naturally shaped magnetite: Octahedra and magnetosomes

A three-dimensional micromagnetic algorithm for modelling naturally shaped particles is presented. It uses a FFT accelerated calculation of the demagnetizing energy. Exchange energy calculation directly takes into account the micromagnetic boundary condition. A rectangular grid enclosing the particle is chosen to economically fit the shape. After verifying that the new program reliably reproduces previous calculations, the program is used to determine room temperature magnetization structures and single domain to vortex transition sizes. These calculations are performed for octahedral magnetite and magnetosomes of different elongations. The least energy magnetization structures of octahedral particles are similar to the flower and vortex states found for cubic particles. The critical size d0 above which an inhomogeneous magnetization structure has lower energy than the homogeneous flower state as well as the grain-size dependence of Mrs/Ms, closely resemble cubic particles. However, meta-stable flower states persist up to much larger grain size in octahedral magnetite. This explains previous observations of large TRM/ARM peaks in hydrothermal magnetite. In realistic magnetosome geometries, the SD-PSD transition is shifted towards larger grain sizes as compared to previous estimates based on elongated rectangular grains. For substantially elongated grains, this is a result of the alignment of the particles' long edge with the crystallographic easy axis. For more equidimensional grains, the rounded ends of magnetosomes reduce spin deflection at the top and bottom edges. Thereby, the formation of nucleation centers is effectively inhibited even without additional stabilization by magnetostatic interaction within a magnetosome chain.