# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 1 Introduction
[65] utilized Zrto develop a (Nd,Zr)(Fe,Co)\({}_{11.5}\)Ti\({}_{0.5}\)N magnet. In order to diminish the lattice mismatch in interatomic distances quoted above, the part of the \(RE\) element in the \(2a\) sites can be substituted with the smaller Zr atoms (the atomic radius of Zr is \(\sim\)12% less than that of Nd). Thus, a combined alloying with both Zr and TM (for example, Ti) could make possible to achieve stability with the ThMn\({}_{12}\)-type magnet with less than one TM (for example Ti) atom per formula unit. [PERSON] et al. [69] mentioned that the hard magnetic characteristics of strip-cast (Sm\({}_{0.8}\)Zr\({}_{0.2}\))(Fe\({}_{0.75}\)Co\({}_{0.25}\))\({}_{11.5}\)Ti\({}_{0.5}\) alloy are \(\mu_{0}M_{s}\) = 1.58 T, \(\mu_{0}H_{a}\) = 7.41 T at low temperature (\(T\) = 20 \({}^{\circ}\)C), which are similar to those of the Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) magnet (\(\mu_{0}M_{S}\) = 1.61 T, \(\mu_{0}H_{a}\) = 7.6 T). However, the Curie temperature (\(T_{c}\) = 880 K) significantly outperforms the Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) magnet (\(T_{c}\) = 584 K). [PERSON] et al. [73; 78] synthesized via arc melting (and annealed) the (Sm\({}_{0.8}\)Y\({}_{0.2}\))(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{11.5}\)Ti\({}_{0.5}\) magnet with \(\mu_{0}M_{S}\) = 1.50 T, \(\mu_{0}H_{a}\) = 11 T at room temperature and \(T_{c}\) = 820 K. Both the \(\mu_{0}H_{a}\) and \(T_{c}\) significantly outperform those of the Nd\({}_{2}\)Fe\({}_{14}\)B magnet. [PERSON] et al. 2016 [123] discovered that Zr replacement stabilizes the (Nd\({}_{1-\alpha}\)Zr\({}_{\alpha}\))(Fe\({}_{0.75}\)Co\({}_{0.25}\))\({}_{11.25}\)Ti\({}_{0.75}\)Ni\({}_{1.2-1.4}\) (\(\alpha\) = 0-0.3) magnets and displays a higher \(\mu_{0}M_{S}\) = 1.62 T at \(\alpha\) = 0.1 than the Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) magnet. According to [PERSON] et al. [75], for the Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{11}\) alloys, the largest \(\mu_{0}M_{s}\) = 1.43 T and \(\mu_{0}H_{a}\) = 10.9 T at room temperature are accomplished for the Sm\({}_{0.94}\)(Fe\({}_{0.81}\)Co\({}_{0.19}\))\({}_{11}\)Ti\({}_{11.08}\) magnet (\(x\) = 0.19), with a corresponding Curie temperature of 800 K. The \(\mu_{0}M_{s}\) could be improved by decreasing the Ti replacement for Fe from Ti\({}_{1}\) to Ti\({}_{0.5}\) and with partial replacement of Sm by Zr. According to [PERSON] et al. [75], for the (Sm\({}_{0.77}\)Zr\({}_{0.24}\))(Fe\({}_{0.80}\)Co\({}_{0.19}\))\({}_{11.5}\)Ti\({}_{0.65}\) magnet, \(\mu_{0}M_{s}\) = 1.53 T and \(\mu_{0}H_{a}\) = 8.4 T, with \(T_{c}\) = 830 K.  
The \(RE\)Fe\({}_{12}\) compounds are unstable as bulk materials, although they have been seen in thin films [11; 13; 75; 80; 82; 93; 124; 126; 127; 128; 129; 130; 131]. [PERSON] et al. [126] synthesized epitaxial Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{12}\) films (\(x\) = 0, 0.1 and 0.2) (without stabilizing elements) on W- and V-buffered single-crystalline MgO substrates. The intrinsic hard magnetic properties of the Sm(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) thin films are higher than those of Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) at room temperature (\(\mu_{0}M_{s}\) = 1.78 T, \(\mu_{0}H_{a}\) = 12 T, \((BH)_{max}\) = 630 kJ/m\({}^{3}\)), while the Curie temperature is also improved (\(T_{C}\) = 859 K). Additionally, [PERSON] et al. [80; 84] reported that \(\mu_{0}M_{s}\) increases via partial replacement of Sm in Sm(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) with Zr. For the (Sm\({}_{0.74}\)Zr\({}_{0.26}\))(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) magnet, \(\mu_{0}M_{s}\) = 1.86 T, \(\mu_{0}H_{a}\) = 9.8 T, and \(T_{c}\) = 675 K [80; 84]. [PERSON] et al. [129] evaluated the magnetic hardness factor, \(\kappa\) = \((K_{1}/\mu_{0}M_{s})^{2}\)/\({}^{1/2}\) of the Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{12}\) magnets at 300 K and found that \(\kappa\) is equal to 1.38, 1.28, and 1.24 for \(x\) = 0.0, 0.07, and 0.2, respectively.