Anisotropic exchange in Nd–Fe–B permanent magnets

Figures & data

Figure 1. ASM simulated temperature-dependent domain wall configurations displayed by the distribution of atomistic magnetic moments (easy axis tilted from z-axis with a angle ${\theta }_0$): (a) Bloch-like wall and (b) Néel-like wall. (c) The distribution of macroscopic magnetization component ($M_z$) along x axis in (a) and z axis in (b). (d) Domain wall width ${\delta }_w$ at different temperatures.

Figure 2. Exchange stiffness (A_e) of Nd₂Fe₁₄B calculated by ASM simulation: A_e as a function of (a) temperature T and (b) normalized magnetization $m=M_{\mathrm{s}}\left(T\right)/M_{\mathrm{s}}(T=0)$. The fitting lines in (b) $\propto m^{1.2}$.

Figure 3. Interface exchange coupling strength ($J_{\mathrm{i}\mathrm{n}\mathrm{t}}$) in Nd₂Fe₁₄B/GB evaluated by first-principles calculation. Unrelaxed and relaxed structure of Nd₂Fe₁₄B/Fe_xNd_1–x system with interface located at (a) (001) plane and (b) (100) plane. (c) $J_{\mathrm{i}\mathrm{n}\mathrm{t}}$ and (d) magnetization of Fe_xNd_1–x ($M_{\mathrm{F}\mathrm{e}\mathrm{N}\mathrm{d}}$) as a function of Fe content x for both (001) and (100) interfaces. The experimental data in (d) are taken from the literature [48–50].

Figure 4. Dependency of coercivity on anisotropic exchange. Effect of anisotropic exchange stiffness of Nd₂Fe₁₄B (A_e) in single grain with GB at (a) a surface and (b) c surface (with the same $A_{\mathrm{i}\mathrm{n}\mathrm{t}}=5$ pJ/m). (c) Effect of A_e, GB composition anisotropy, and anisotropic exchange coupling between two regions ($A_{\mathrm{i}\mathrm{n}\mathrm{t}}$) in multigrain Nd–Fe–B. A_e and $A_{\mathrm{i}\mathrm{n}\mathrm{t}}$: pJ/m. $M_{\mathrm{G}\mathrm{B}}$: MA/m. Grain size: 100 nm. GB thickness: 4 nm. The external field is applied along negative z axis.