Analytical Maximum Energy Product (BH)max Model for Rare-Earth-Free Magnets: Core-Shell Nanostructure

Abstract

This article presents an analytical model for the maximum energy product [(BH)(max)] in core-shell structured magnetic exchange-coupled nanomagnets. The model was validated by comparing its results to the (BH)(max) from core-shell magnets reported in the literature. This approach can serve as a universal model for designing core-shell magnets that achieve the desired (BH)(max). The (BH)(max) was determined under two distinct nucleation field (HN) conditions: H-N <= M-r/2 and H-N >= M-r/2, where M-r is the remanent magnetization. In addition, two different values of magnetic hysteresis loop squareness (SQ = M-r/M-S) were used: 1.0 and 0.7. The soft magnetic shell&apos;s remanent magnetic flux density (B-r) ranged from 0.7 to 2.2 T, while the core diameter (D-h) varied between 50 and 250 nm in this (BH)(max) model. The low-temperature phase (LTP) MnBi-core/soft-shell nanomagnet can achieve a (BH)(max) of 40 MGOe at a Br of 1.6 T, with a shell thickness (delta(S)) of 40 nm, a Dh of 250 nm, and a volume fraction of the hard-core (f(h)) of 0.43. The (BH)(max) of the hexaferrite (SrFe12O19)/soft-shell (1.9 T) nanomagnet can be improved from 5.8 (single hexaferrite phase) to 20 MGOe. This approach achieves the desired (BH)(max) of the rare-earth(RE)-free permanent magnet, thereby tackling issues related to RE mineral security and unstable supply chains.