Fig. 1: Comparison of the extrinsic contributions to coercivity in RE₂Fe₁₄B magnets.

Ratio k = H_c/H_A as a function of H_A. The black, blue, and red circles represent Nd-Fe-B^13,14,15,16, Nd_0.75Pr_0.25-Fe-B^17,18,19,20, and Pr-Fe-B^21,22 magnets, respectively, developed using industrially available processes, while the black and blue 3D spheres represent the grain boundary diffusion-processed Nd-Fe-B hot-deformed magnets^23,24,25 and grain size-modified Nd_0.75Pr_0.25-Fe-B magnets^26,27, respectively. The purple circle for the (Nd, Dy)-Fe-B sintered magnet was adopted from ref. ³⁸, and a 9 wt% Dy-containing magnet was developed in this work. The H_A for Nd-Fe-B and Pr-Fe-B compounds were adopted from ref. ³⁷, while H_A for Nd_0.75Pr_0.25-Fe-B and (Nd, Dy)-Fe-B sintered magnets were calculated based on Vegard’s Law; these were confirmed by the experimental measurements shown in the Supplementary Information.