The mechanisms underlying the enhancement of magnetic anisotropies (MAs) of Sm ions, owing to valence electrons at the Sm site and the screened nuclear charges of ligands, are clarified using a detailed analysis of crystal fields (CF). In order to investigate the finite-temperature magnetic properties, we developed an effective spin model for $\mathrm{Sm}{\mathrm{Fe}}_{12}X$ ($X$=H, B, C, and N) and $\mathrm{Sm}{\mathrm{Fe}}_{11}M$ ($M$=Ti, V, and Co), where the magnetic moments, CF parameters, and exchange fields were determined by first-principle calculations. Using this model, the MA constants and magnetization curves at finite temperatures were investigated using a recently introduced analytical method [Yoshioka, Tsuchiura, and Novák, Phys. Rev. B 102, 184410 (2020)]. In $\mathrm{Sm}{\mathrm{Fe}}_{12}X$, the doped light elements $X$ are assumed to be at the $2b$ site, and in $\mathrm{Sm}{\mathrm{Fe}}_{11}M$, the substitution site of Fe is systematically investigated for all inequivalent $8f, 8i$, and $8j$ sites. We found that the first-order MA constant $K_1$ is increased by a factor of about two when hydrogen is doped to the $2b$ site and when Fe is replaced by Ti or V at the $8j$ site, owing to the attraction of the prolate $4f$ electron cloud to the screened positive charges of the surrounding ligand ions. We found that when Fe is replaced by Co, the MA increases at all temperatures regardless of the substitution site. The substituted Co attracts electrons, which reduces the electron density in the region from the Sm site to the empty $2b$ site. This causes the $4f$ electron cloud at the Sm site to be fixed along the $c$-axis direction, which improves the MA. The calculated temperature dependence of $K_1\left(T\right)$ and $K_2\left(T\right)$ in $\mathrm{Sm}{\mathrm{Fe}}_{11}\mathrm{Co}$ qualitatively reproduces the experimental results in the case of $\mathrm{Sm}{\left({\mathrm{Co}}_x{\mathrm{Fe}}_{1-x}\right)}_{12}$ for $x=0.1$ and 0.07. The first-order magnetization process is observed at low temperatures in $\mathrm{Sm}{\mathrm{Fe}}_{12}$ itself and in many variations of $\mathrm{Sm}{\mathrm{Fe}}_{12}$-based compounds prepared using element doping and substitution. This is mainly due to the competition between the conditions $K_1>0$ and $K_2<0$, and that of $K_1<-6K_2$ owing to the ${\mathrm{ThMn}}_{12}$ structure having a vacancy at the $2b$ site.

• Received 1 August 2021
• Revised 18 November 2021
• Accepted 21 December 2021

DOI:https://doi.org/10.1103/PhysRevB.105.014402