# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 1 Introduction
[134] performed theoretical investigations (HTS-TB-LMTO-ASA) of the 1280 compounds derived from the ThMn\({}_{12}\)-type crystal structure in order to estimate their \(\mu_{0}H_{a}\) and (\(BH\))\({}_{\rm max}\). HTS has led to several auspicious phases such as NdFe\({}_{12}X\) or NdFe\({}_{11}\)Ti\(X\) (\(X\) = B, C, N) with (\(BH\))\({}_{\rm max}\)\(\sim\)600 kJ/m\({}^{3}\) and \(\mu_{0}H_{a}\)-10 T. [PERSON] et al. [135] used the HTS-TB-LMTO-ASA methodology to study the influence of the substituted atom site preference on \(\mu_{0}M_{s}\) and \(\mu_{0}H_{a}\) of the \(RE\)Fe\({}_{11}A\)-type compound, where \(A\) = Al, Si, Ti, V, Cr, Co, Ni, and Cu. [PERSON] et al. [136] used the HTS-TB-LMTO-ASA methodology to screen the magnetic properties of over 2000 different _RE-TM-X_ compounds with 1-11 and 1-11-1\(X\) (the YNi\({}_{9}\)In\({}_{2}\)-type) structures as prospective candidates for new hard-magnetic phases. [PERSON] et al. [137] used the combined MD, Morse potentials, and modified EAM (MEAM) to investigate the probability distributions for Ti substitutions in \(RE\)\(T\)\({}_{\rm 12-x}\)Ti\({}_{x}\) (\(RE\) = Nd and Sm; \(TM\) = Fe and Co) alloys over the atom positions within the structure. The authors concluded that Ti substitution, while stabilizing the structure, also results in a considerable reduction in the spin magnetic moment due to Ti aligning _anti-parallel_ to the net internal magnetization and reducing the magnetic moment of the neighboring iron \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & \(\mu_{0}M_{s}(T)\) & \(\mu_{0}H_{a}(T)\) & \(T_{c}(K)\) & \(|BH|_{max}\Big{(}\frac{H}{m^{3}}\Big{)}\) & **References** \\ \hline Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) & 1.61 & 7.6 & 588 & 515 & [7; 8; 9; 10; 11; 12; 13; 14] \\ \hline SmFe\({}_{11}\)Ti\({}_{1}\) & 1.14–1.22 & 8.3–10.5 & 584 & 258 & [23; 34] \\ \hline (Sm\({}_{0.8}\)Zr\({}_{0.2}\))(Fe\({}_{0.75}\)Co\({}_{0.25}\))\({}_{11.5}\)Ti\({}_{0.5}\) & 1.58 & 7.4 & 880 & 495 & [69] \\ \hline (Sm\({}_{0.8}\)Y\({}_{0.2}\))(Fe\({}_{0.80}\)Co\({}_{0.20}\))\({}_{11.5}\)Ti\({}_{0.5}\) & 1.50 & 11.0 & 820 & 447 & [73; 78] \\ \hline Sm\({}_{0.94}\)(Fe\({}_{0.81}\)Co\({}_{0.19}\))\({}_{11}\)Ti\({}_{1.08}\) & 1.43 & 10.9 & 800 & 406 & [75] \\ \hline (Sm\({}_{0.77}\)Zr\({}_{0.24}\))(Fe\({}_{0.80}\)Co\({}_{0.19}\))\({}_{11.5}\)Ti\({}_{0.65}\) & 1,53 & 8.4 & 830 & 465 & [75] \\ \hline (Sm\({}_{0.92}\)Zr\({}_{0.08}\))(Fe\({}_{0.75}\)Co\({}_{0.25}\))\({}_{11.35}\)Ti\({}_{0.65}\) & 1.47 & \(>\)9.0 & 843 & 429 & [76] \\ \hline Sm(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) & 1.78 & 12.0 & 859 & 630 & [126] \\ \hline (Sm\({}_{0.74}\)Zr\({}_{0.20}\))(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) & 1.86 & 9.8 & 875 & 688 & [80; 84] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Saturation magnetization, anisotropy field, Curie temperature, and maximum energy product values of 1:12 magnets. atoms. The \(8i\) position has the best probability for substitution followed by the \(8j\) and \(8f\) positions, and this conclusion agrees with the results by [PERSON] et al. [138]. [PERSON] et al. [79] performed an ab initio study of the electronic structure of CeFe\({}_{11}\)Ti\({}_{1}\). The authors used the HE-DFT methodology, which incorporates a combined approach of atom-centered LCAO, PW-VASP, and FPLMTO. The calculations confirmed that Ti stabilizes the CeFe\({}_{11}\)Ti structure and Ce\({}^{+3}\) causes the large MAE. [PERSON] et al. [139] performed ab initio (Wein2k, FP-LDA + U, VASP) calculations of \(\mu_{0}M_{s}\) and \(\mu_{0}H_{a}\) of the SmFe\({}_{12}\) compound dopped by B, C, and N, indicating a possible way to improve these properties through interstitial doping of the SmFe\({}_{12}\) compound by \(2p\) electron elements. [PERSON] et al. and [PERSON] et al. [11; 138] (QMAS-PAW) found that Ti substitution in the NdFe\({}_{12}\) compound diminishes \(\mu_{0}M_{s}\) substantially, whereas it scarcely alters MAE. They also showed that interstitial nitrogenation substantially raises \(\mu_{0}M_{s}\) and the uniaxial MAE of the NdFe\({}_{11}\)Ti compound.