Theoretical limits for energy density of aligned ferromagnetic nanoparticles in a nonmagnetic matrix for rare-earth-free permanent magnets

Developing permanent magnets with fewer critical elements requires understanding hysteresis effects and coercivity through visualizing magnetization reversal. Here, we numerically investigate the effect of the geometry of nanoscale ferromagnetic inclusions in a paramagnetic/nonmagnetic matrix to understand the key factors that maximize the magnetic energy product of such nanocomposite systems. Specifically, we have considered a matrix of “3 μm × 3 μm × 40 nm” dimension, which is a sufficiently large volume, two-dimensional representation considering that the ferromagnetic inclusions' thickness is less than 3.33% of the lateral dimensions simulated. Using this approach, which minimizes edge effects to approximate bulk-like magnetic behavior while remaining computationally tractable for simulation, we systematically studied the effect of the thickness of ferromagnetic strips, separation between the ferromagnetic strips due to the nonmagnetic matrix material, different saturation magnetization values, and the length of these ferromagnetic strips on magnetic coercivity and remanence by simulating the hysteresis loop plots for each geometry. Furthermore, we study the underlying micromagnetic mechanism for magnetic reversal to understand the factors that could help attain the maximum magnetic energy densities for ferromagnetic nanocomposite systems in a paramagnetic/nonmagnetic material matrix. In this study, we have used material parameters of an exemplary Alnico alloy system, a rare-earth-free, thermally stable nanocomposite, which could potentially replace high-strength NdFeB magnets in applications that do not require large energy products. However, we project the energy density (BH)max of materials with higher saturation magnetization to have an ideal theoretical limit of (BH)max ∼94 kJ/m3 (∼12 MGOe), which is ∼(35%–40%) of the energy density of Rare-Earth Free Magnets. This energy density could be higher if exchange bias from antiferromagnets, defects, and pinning is included and could stimulate further experimental work on the fabrication and large-scale manufacturing of RE-free PMs with different nanocomposite systems.