Impact of lattice distortions on magnetocrystalline anisotropy and magnetization in (Nd1−xPrx)2Fe14B alloys

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.