# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 1 Introduction
Using the same QMAS-PAW methodology, [PERSON] et al. [140] proposed that in the NdFe\({}_{11}\)TiX compound, where \(X=\) B, C, N, O, and F, nitrogen is the most suitable dopant for permanent magnets in terms of \(\mu_{0}M_{s}\) and MAE. [PERSON] et al. [92] performed first-principles calculations (QMAS-PAW) of the magnetic properties of the NdFe\({}_{11}M\) compound, where \(M=\) Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn. They discovered that the calculated formation energy of the NdFe\({}_{11}\)Co compound is negative compared to the Nd\({}_{2}\)Fe\({}_{17}\) compound (the Th\({}_{2}\)Zn\({}_{17}\)-type structure), bcc-Fe, hcp-Co, and the CoFe compound (CsCl-type structure), indicating that Co could stabilize the ThMn\({}_{12}\) structure in bulk form. Contrary to Ti replacement, Co replacement does not diminish \(\mu_{0}M_{s}\) meaningfully. [PERSON] et al. [141] studied (QMAS-PAW) the effects of interstitial nitrogenation on the magnetic properties of the ThMn\({}_{12}\)-type compounds \(RE\)Fe\({}_{11-X}\)Ti\({}_{X}\) (\(x=0,1\)) with \(RE=\) Nd, Sm, Y. They found that the evolution in MAE by nitrogenation is self-sufficient of Ti replacement and does not seem to have much dependence on the \(RE\) element [141]. [PERSON] et al. [142] performed finite temperature ab initio (QMAS-PAW, AkaiKKR) MC calculations of \(\mu_{0}M_{s}\) and MAE to find improvements in the indirect 4/(Nd)-3\(d\)(Fe) exchange coupling to enhance the high-temperature properties of the NdFe\({}_{12}\)N-type compounds. Using AkaiKKR-CPA formalism, [PERSON] et al. [143] assessed intersite magnetic exchange couplings in the NdFe\({}_{12}\) and NdFe\({}_{12}X\) (\(X=\) B, C, N, O, and F) compounds with the ThMn\({}_{12}\) structure. They found that that MAE deteriorated rapidly with increasing temperature in the \(X=\) N system, albeit nitrogenation was dominant compared to other dopants in terms of improving the low-temperature magnetic properties. The MFA, with exchange couplings as input parameters, was used to calculate \(T_{c}\). The introduction of \(X\) (\(X=\) B, C, N, O, and F) causes substantial variations in the magnetic couplings of the NdFe\({}_{12}\) compound and has a momentous consequence in terms of \(T_{c}\). [PERSON] et al. [144] presented a first-principles study of \(RE\)Fe\({}_{12-X}\)Cr\({}_{x}\) (\(RE=\) Y, Nd, Sm) compounds with the ThMn\({}_{12}\) structure using the QMAS -PAW package to calculate the lattice parameters of the \(RE\)Fe\({}_{12-x}M_{x}\) (\(M=\) Cr, Co) system. In this study, Fe and the dopants (Co or Cr) were treated within the KKR-CPA (AkaiKKR method), and \(T_{c}\) was calculated within MFA. The calculations indicated an improvement in \(T_{c}\) over the addition of Cr, \(x\leq 0.5\) in the \(RE\)Fe\({}_{12}\)\(RE\)Fe\({}_{12-X}Cr_{x}\) compound. On the contrary, above \(x>0.5\), \(T_{c}\) diminishes as the Cr concentration increases. [PERSON] et al. [145] performed an ab initio investigation (QMAS-PAW) to study the effects of \(RE\)(\(M\)) site replacement and pressure on the structural stability of the \(RE\)Fe\({}_{12}\) compounds, where \(RE=\) La, Pr, Nd, Sm, Gd, Dy, Ho, Er, Tm, Lu, Y, or Sc, and the group-IV element \(M=\) Zr or Hf. They found that the formation energy has a firm resemblance with the atomic radius of \(RE\) metal, in particular the formation energy with respect to simple substances diminishes as the atomic radius diminishes, except for \(RE=\) Sc and \(M=\) Hf. The calculated formation energies with respect to the \(RE_{2}\)Fe\({}_{17}\) compound (in both Th\({}_{2}\)Zn\({}_{17}\) and Th\({}_{2}\)Ni\({}_{17}\)-type structures) and bcc Fe were also reported. These calculations show that the formation energy is positive, which means that one cannot make the \(RE\)Fe\({}_{12}\) phase more stable than the \(RE_{2}\)Fe\({}_{17}\) phase, and partial replacement for Fe is needed to stabilize the ThMn\({}_{12}\) structure. [PERSON] et al.