Impact of Lattice Distortions on Magnetocrystalline Anisotropy and Magnetization in (Nd$_{1-x}$Pr$_x$)$_2$Fe$_{14}$B Alloys

TL;DR

This work addresses how lattice distortions at interfaces alter the magnetocrystalline anisotropy and magnetization in $({ m Nd}_{1-x}{ m Pr}_{x})_2{ m Fe}_{14}{ m B}$. It combines experimental structure determination ( synchrotron XRD and Cs-STEM) with first-principles FPKKR+CPA calculations to quantify $K_{ m u}$ and $J_{ m s}$ under controlled distortions and Pr content. The key findings show that compressive strain along [110] up to about $25\%$ can drive $K_{ m u}$ negative,Pr-rich alloys exhibit greater sensitivity to distortion, and Pr substitution raises bulk $K_{ m u}$ but may reduce interfacial coercivity; these results supply strain-aware parameters for micromagnetic simulations. The study bridges ab initio predictions with device-scale considerations, informing strategies to engineer coercivity via interface design and Pr-doping in Nd-Fe-B magnets.

Abstract

Nd$_{2}$Fe$_{14}$B -- a widely used permanent magnet -- has magnetocrystalline anisotropy constants that differ between the bulk and interface regions. This study explores the effects of lattice distortion on the magnetocrystalline anisotropy ($K_{\rm u}$) and magnetization of (Nd$_{1-x}$Pr$_x$)$_2$Fe$_{14}$B. Nd$_2$Fe$_{14}$B alloys were fabricated; scanning transmission electron microscopy revealed a compressive strain of up to 25% near grain boundaries. Using the full-potential Korringa--Kohn--Rostoker method, we calculated the strain dependence of $K_{\rm u}$, showing that although $K_{\rm u}$ is 4.2 MJ/m$^3$ under strain-free conditions at 0 K, it becomes negative in regions with 25% compressive strain. Additionally, Pr$_{2}$Fe$_{14}$B exhibits a larger $K_{\rm u}$ than Pr$_{2}$Fe$_{14}$B under undistorted conditions, whereas Pr-rich alloys exhibit a more pronounced reduction in $K_{\rm u}$ under strain. These findings highlight the critical influence of lattice distortions on magnetic properties. The calculated strain-dependent magnetic anisotropy parameters provide valuable inputs for future micromagnetic simulations, aiding the design of advanced magnetic materials.

Figures (8)

• Figure 1: Rietveld refinement results of (a) $\rm Nd_2Fe_{14}B$ and (b) $\rm Pr_2Fe_{14}B$, showing the observed XRD data (Obs), fitted pattern (Calc), fitted background, and residual. The $2\theta$ range of 57$\degree$ to 91$\degree$ was not measured, to shorten the data-acquisition time.
• Figure 2: Demagnetization curves of the hot-deformed magnet and the Nd-Cu diffusion-processed magnet.
• Figure 3: Cs-STEM images of Nd-Cu diffusion-processed magnets. (a) Bright-field STEM image showing the in-plane $c$-axis. (b) Drift-corrected Cs-STEM image along the $ab$-axis (along the [110] direction). (c) Unit-cell images of the surface and (d) internal regions.
• Figure 4: Strain analysis of Nd-Cu diffusion-processed magnets. (a) Brightness profile along the white arrow in Fig. \ref{['fig:stem']}. The minima correspond to the centers of the Nd $4f$ and $4g$ sites. (b) Quantification of interfacial strain based on the differences in distances between adjacent peaks. $h$ represents the value of the smoothing parameter in kernel density estimation. A larger $h$ indicates more smoothing.
• Figure 5: The $\delta a$ dependence of $K_{\rm u}$ and $J_{\rm s}$ for $\rm Nd_2Fe_{14}B$, where the lattice constant $c$ is fixed ($\delta c = 0$). The inset shows the $\delta a$ dependence of the total magnetic moment, with the unit of $\mu_{\rm B}$ per formula unit.