RESUMO
Shape anisotropy is of primary importance to understand the magnetic behavior of nanoparticles, but a rigorous analysis in polyhedral morphologies is missing. In this work, a model based on finite element techniques has been developed to calculate the shape anisotropy energy landscape for cubic, octahedral, and truncated-octahedral morphologies. In all cases, a cubic shape anisotropy is found that evolves to quasi-uniaxial anisotropy when the nanoparticle is elongated ≥2%. This model is tested on magnetosomes, â¼45 nm truncated octahedral magnetite nanoparticles forming a chain inside Magnetospirillum gryphiswaldense MSR-1 bacteria. This chain presents a slightly bent helical configuration due to a 20° tilting of the magnetic moment of each magnetosome out of chain axis. Electron cryotomography images reveal that these magnetosomes are not ideal truncated-octahedrons but present ≈7.5% extrusion of one of the {001} square faces and ≈10% extrusion of an adjacent {111} hexagonal face. Our model shows that this deformation gives rise to a quasi-uniaxial shape anisotropy, a result of the combination of a uniaxial (Ksh-u = 7 kJ m-3) and a cubic (Ksh-c = 1.5 kJ m-3) contribution, which is responsible for the 20° tilting of the magnetic moment. Finally, our results have allowed us to accurately reproduce, within the framework of the Landau-Lifshitz-Gilbert model, the experimental AC loops measured for these magnetotactic bacteria.
