Shape-optimized ferromagnetic particles with maximum theoretical microwave susceptibility

This paper uses a shape-dependent form of Snoek´s relation to show that the geometry of soft ferromagnetic objects can be chosen to maximize their linear susceptibilities at microwave frequencies. Composites made with such objects can fill a critical void in the frequency range (1 to 20 GHz) where thin films or spherical objects do not yield the maximum susceptibility allowed by Snoek´s relation. The relatively small intrinsic anisotropies of soft ferromagnetic materials necessitate the use of shape anisotropy to maximize the susceptibility. Our results can be used to determine the optimum shape and the maximum theoretical susceptibility achievable at a given microwave frequency. The results show that a susceptibility enhancement by a factor of 10-100 can be obtained in the 1-20 GHz frequency range (0.3-7 GHz for low loss applications) by using oblate spheroids with aspect ratios between 10 and 1000. Keeping the thickness below the skin depth will require lateral dimensions ~1-1000 μm. Fabrication and measurements of such objects are discussed in a companion paper