# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 5 Discussion and Conclusions  
The present calculations show that the SmNi\({}_{4}\)(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{8}\) alloys could be stable; fabricated in bulk form within the whole compositional range; and have significant \(\mu_{0}M_{\rm s}\) values of 1.38-1.57 T, 1.39-1.53 T, and 1.36-1.42 T (depending on the model); \(T_{c}\) values of 853 K, 928 K, and 995 K; \(\mu_{0}H_{\rm a}\) values of 6.09 T, 8.02 T, and 10.54 T; and \(\kappa\) values of 1.40, 1.62, and 1.88 for \(x=0.0\), 0.1, and 0.2, respectively. As mentioned in the Introduction, the economic requirement for a permanent magnet is fulfilled if \(\mu_{0}M_{\rm s}\) -\(\geq\) 1.25 T, \(T_{c}\) -\(\geq\) 550 K, \(\mu_{0}H_{\rm a}\) -\(\geq\) 3.75 T, and \(x>1\)[1; 2; 17], which means the SmNi\({}_{4}\)(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{8}\) magnets could be suitable for industrial applications. The most promising SmNi\({}_{4}\)(Fe\({}_{0.9}\)Co\({}_{0.1}\))\({}_{8}\) magnet outperforms most of the intrinsic properties of the widely used Neomax magnets (\(T_{c}\) = 588 K and \(\mu_{0}H_{\rm  
In accordance with our previous calculations [149,150], substituting most of Co with Fe in the SmCo\({}_{5}\) magnet (the CaCu\({}_{5}\)-type structure) and using Ni as a thermodynamic stabilizer engenders the formation of the SmFe\({}_{3}\)CoNi magnet, which has exceptional magnetic properties, such as a high \(T_{\rm c}\) = 1103 K, powerful magnetic anisotropy (\(K_{\rm 1}\) = 9.2 MJ/m\({}^{3}\), about twice that of the Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) magnet at \(K_{\rm 1}\) = 4.9 MJ/m\({}^{3}\)), and \(\mid BH\mid_{\rm max}\) = 362 kJ/m\({}^{3}\), which is about 70% of \(\mid BH\mid_{max}\)-515 kJ/m\({}^{3}\) (Neomax). Ni has also been used as the stabilizing element in the YCo\({}_{5}\) magnet (the CaCu\({}_{5}\)-type structure) in order to provide the maximum amount of Fe to favor high magnetization of the YFe\({}_{3}\)CoNi magnet \(\mid BH\mid_{max}\)-309 kJ/m\({}^{3}\)[151]. When considering why Ni acts as a stabilizer, it is important to realize that the favored structure depends rather sensitively on the number of \(d\) electrons in the compound, i.e., the filling (occupation) of electrons in the \(d\)-band. Figure 9 shows the calculated formation energies (EMTO) of the SmFe\({}_{12}\), SmCo\({}_{12}\), and SmNi\({}_{12}\) compounds in respect to the unary systems \(\alpha\)-Sm, \(\alpha\)-Fe, \(\alpha\)-Co, and \(\alpha\)-Ni as a function of the number of \(3d\) electrons per TM atom. Increasing the \(3d\) electron count (more Ni) greatly stabilizes the Sm\(TM_{12}\) compound. An obvious consequence of this behavior is that one should be able to recover the crystal stability of a Sm(Fe,Co)\({}_{12}\) compound by doping it with \(3d\) electrons from nickel. From Figure 9, one can conclude that an Sm(Fe\({}_{1-x-y}\)Co\({}_{2}\)Ni\({}_{y}\))\({}_{12}\) alloy with at least 7.76 \(3d\) electrons per \(TM\) atom is stable. This result is consistent with the previously discovered stabilization of the hexagonal Sm\(TM_{5}\) (the CaCu\({}_{5}\)-type structure) compound [149]. According to [PERSON] et al. [149], the efforts to enhance the magnetism of the stable SmCo\({}_{5}\) magnets through the substitution of some amount of Co for Fe were limited because the SmFe\({}_{5}\) compound does not exist in the CaCu\({}_{5}\)-type structure. To compensate for the reduction in \(d\) electrons due to the Fe/Co substitution (Fe has about one \(3d\) electron less than Co), we simply added nickel, which has about one more \(3d\) electron than cobalt, so that the structural stability was ensured. Nickel acts as a thermodynamic stabilizer in the Sm-Fe-Co-Ni alloys, and in present case, adding a certain amount of Ni helps to stabilize the SmNi\({}_{4}\)(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{8}\) magnets in the ThMn\({}_{12}\)-type structure. Our calculations revealed that the SmNi\({}_{4}\)Co\({}_{8}\) magnet exhibits a significant axial MAE with \(K_{\rm 1}\) = 9.41 MJ/m\({}^{3}\).