Shape-dependent microwave permeability of Fe3O4 nanoparticles: a combined experimental and theoretical study

Shape anisotropy is crucial for the microwave permeability of magnetic nanoparticles. In this work, we conduct a systematic study on the shape-dependent microwave permeability of magnetic nanoparticles. Three kinds of Fe3O4 nanoparticles with different geometric shapes (rod, disc, and octahedron) are fabricated by chemical methods and their permeability is investigated through both theoretical calculation and experiment. The results suggest that the rod could exhibit the highest resonance frequency (fr), while the lowest resonance frequency could be found in the octahedron. An opposite trend is observed in the initial permeability (μ0). In order to confirm the experimental permeability, we establish an improved LL-G model, which could take both the shape anisotropy and magnetic domain structure into account by introducing a local effective anisotropy field (Heff). The good agreement between the calculated and experimental permeability proves that the model can reproduce shape-dependent microwave permeability of magnetic nanoparticles. More importantly, no fitting process is involved in this model, enabling us to predict the permeability of magnetic nanostructures independent of experiment results.