# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 1 Introduction
[146] used BO to optimize the composition of the \(R\)EFe\({}_{12}\)-type compound; specifically, the composition of \((RE_{1-\alpha_{s}}Z_{\alpha})(\text{Fe}_{1-\beta}\text{Co}_{\beta})_{12-Y}\text{ Ti}_{\gamma}\) (\(RE\)= Nd, Sm, Y; \(Z\) = Zr, Dy) was improved in terms of the formation energetics, \(\mu_{0}M_{s}\), \(\mu_{0}M_{a}\) and \(T_{c}\). This scheme is based on the ab initio calculations (QMAS-PAW) and implementation of the KKR-CPA (AkaiKKR-CPA) technique to treat the compositional disorder. The authors identified 10 ThMn\({}_{12}\)-type systems with the highest value of \(\mu_{0}M_{s}\), although only Nd(Fe\({}_{0.7}\)Co\({}_{0.3}\))\({}_{12}\) with \(\mu_{0}M_{s}\) = 1.89 T and \(T_{c}\) = 1143 K and (Sm\({}_{0.7}\)Zr\({}_{0.3}\))(Fe\({}_{0.9}\)Co\({}_{0.1}\))\({}_{12}\) with \(\mu_{0}M_{s}\) = 1.77 T and \(T_{c}\) = 1002 K have the negative formation energy with respect to the unary system. The highest \(T_{c}\) = 1310 K was projected for the Sm(Fe\({}_{0.2}\)Co\({}_{0.8}\)) alloy, which has a negative formation energy in respect to the unary system and a significant \(\mu_{0}M_{s}\) = 1.47 T.  
[PERSON] et al. [85], both experimentally and theoretically, studied how the particle size and alloy composition influence the thermal stability of the ThMn\({}_{12}\)-type phase. A definite stabilizing effect is accomplished by replacing Fe with elements such as Ti, V, or Ga. However, aligning to ab initio calculations (QMAS-PAW), the SmFe\({}_{11}M\) compound, where \(M\) = Ti and V, shows lower energy in respect to the combination of \(\alpha\)-Fe and SmFe\({}_{2}\) (resistance to decomposition), with preferable occupation of \(8i\) sites for \(M\). The SmFe\({}_{11}\)Ga compound (\(M\) = Ga) also exhibits lower energy with respect to the combination of \(\alpha\)-Fe and SmFe\({}_{2}\) with preferential occupation of \(8j\) sites for Ga, but is not as stabilized as for M = Ti and V. However, the Ga dopant shows a smaller reduction in \(\mu_{0}M_{s}\) in comparison with Ti or V dopants. Therefore, Ga is the most successful stabilizing element when \(\mu_{0}M_{s}\) is considered. [PERSON] et al. [147] used combined ab initio (AkaiKKR-CPA) methodology and experimental data from neutron diffraction to inspect the optimal chemical composition of the SmFe\({}_{12}\) compound doped by Zr, Ti, and Co. They found that in the Zr-substituted SmFe\({}_{12}\) magnet, Zr occupies both Sm(\(2a\)) and Fe(\(8i\)) roughly equally in terms of energetics. While using Ti as the stabilizing element cannot be avoided, it was found that the lower bound is around 0.5 Ti atoms, which is close to what has been attained experimentally [65; 68; 69; 75]. The Zr dopant also improves the structural stability and \(\mu_{0}M_{s}\) of the SmFe\({}_{12}\) magnet, which is in perfect agreement with the experimental data [80]. [PERSON] et al. [148] performed an ab initio study (LCAO-CRYSTAL and PW-CASP) on the effects of doping the CeFe\({}_{11}\)Ti compound with Co and Ni. The authors of [149] showed that the addition of Co (Ni) slightly improves (diminishes) \(\mu_{0}M_{s}\) and \(\mu_{0}H_{a}\). In our previous papers [149; 150; 151], we suggested increasing \(\mu_{0}M_{s}\) and \((BH)_{\text{max}}\) in the well-known SmCo\({}_{5}\) and YCo\({}_{5}\) magnets by substituting Co with Fe and using Ni as a thermodynamic stabilizer. In most studies, the \(R\)EFe\({}_{12}\) (ThMn\({}_{12}\)-type structure) magnets have been stabilized in the form \(RE\)(Fe,Co)\({}_{11}M_{1}\), where \(M_{1}\) = Ti, V, Al, Si, Ga, Cr, Mn, Mo, Nb, Ta, W, Re, H, and N. A handful of papers have been published where the \(R\)EFe\({}_{12}\) magnet dopped with Ni was studied. [PERSON] et al. [91] studied the crystallographic and magnetic properties of the replaced Y(Fe\({}_{1-x}M_{x}\))\({}_{11}\)Ti\({}_{1}\) alloys, where \(M\) = Co, Ni, and Si. The thermomagnetic analysis indicated that \(\mu_{0}M_{s}\) has a maximum at \(x\) = 0.07 for the Y(Fe\({}_{1-x}\)Ni\({}_{x}\))\({}_{11}\)Ti\({}_{1}\) alloys. \(T_{c}\) increases when Fe is substituted by Ni.