Design of superparamagnetic nanoparticle-materials for high-frequency inductor cores

The progress in the semiconductor industry has resulted in great demand for high-frequency magnetic materials applicable in microfabricated inductor cores. Nanocomposite materials, containing magnetic nanoparticles in a non-conducting matrix, may provide a solution for materials with high susceptibility or permeability and low power loss in the MHz regime, where traditional ferrites fail in performance. Here, we present a design guide for usage of magnetic nanoparticles in such materials. We use statistical mechanics methods to derive the magnetic susceptibility of nanoparticles in case of uniaxial or cubic anisotropy, as function of particle size and applied field direction, and investigate shape and interaction effects on the susceptibility. Using the derived susceptibilities, with inductor-core applications in mind, we show that close-to-spherical particles of materials with high saturation magnetization and low magnetic anisotropy, such as FeNi$_3$, are optimal. Additionally, the particle size shall be optimized to be as large as possible while maintaining superparamagnetic behaviour at the relevant frequency. Based on this, we predict that high particle susceptibilities of $>$700 (/$>$1500) are possible for randomly oriented (/uniaxially aligned) 20$\pm$1 nm diameter FeNi$_3$ particles, together with high-frequency stability, shown by low out-of-phase component at 2 MHz. This implies that materials containing nanoparticles have the potential to be tuned to outperform state-of-the-art ferrite inductor-core materials at MHz-frequencies.