Extraordinary Magnetic Hardening In Nanowire Assemblies: The Geometry And Proximity Effects

Brown's theorem on coercivity of ferromagnetic materials has predicted that the coercivity level is substantially higher than in practice for all the materials studied in experiments in the past seven decades, which is known as the Brown's paradox. In this paper, a system with a coercivity close to the one predicted by Brown's theorem is investigated. Cobalt nanowires are obtained by chemical synthesis that give rise to coercive forces significantly higher than the magnetocrystalline anisotropy field, verifying the Brown's theorem. It is found that the coercivity is strongly dependent on the nanowire diameter, the alignment of the wires in an assembly, and the packing density of the assembly. An analysis based on the current experimental results and related literature reveals a coercivity ceiling in consideration of geometrical dimensions and the effective magnetic anisotropy. Quantitative information is obtained about the proximity effect on the coercivity and the magnetization which shows the correlation between the energy product and the packing density. Furthermore, it is found that by coating the nanowires with Fe, the energy density can be enhanced. These findings provide a guideline for materials design of future high-performance permanent magnets that take advantage of shape anisotropy at the nanoscale.