# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 1 Introduction
Because \(\kappa\) should be larger than one for a compound to be regarded as a permanent magnet material [18], the Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{12}\) alloys have a prospective use as the main phase of the high-performance permanent magnet material if the ThMn\({}_{12}\)-type phase can be bulk-stabilized. Table 1 summarizes the intrinsic properties of some ThMn\({}_{12}\)-type structure magnets together with properties for Neomax (Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\)). Note that the Sm(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) and (Sm\({}_{0.74}\)Zr\({}_{0.26}\))(Fe\({}_{0.8}\)Co\({}_{0.2}\))\({}_{12}\) magnets are epitaxially grown thin films and are unstable in bulk. Multiple theoretical approaches have investigated \(RE\)(Fe,Co)\({}_{11}TM_{1}\) magnets. These include augmented spherical waves within the local spin density-functional (ASW-LSDF), molecular dynamics (MD) and Monte Carlo (MC), embedded atom method (EAM), full-potential linearized muffin orbital (FPLMTO), tight-binding linear-muffin orbital atomic sphere approximation (TB-LMTO-ASA) in conjunction with computational high-throughput screening (HTS), hybrid-exchange density functional theory (HE-DFT), linear combination of atomic orbitals (LCAO), pseudopotential Vienna ab initio (VASP) package, full-potential linearized augmented plane wave (FLAPW) within WIEN2K package, Hubbard I method (LDA + U), Quantum Materials Simulator and projected augmented-wave (QMAS-PAW), Korringa-Kohn-Rostoker coherent-potential approximation (AkaiKKR-CPA), mean field approximation (MFA), and Bayesian optimization (BO) approaches [11; 132; 133; 134; 135; 136; 137; 138; 139; 140; 141; 142; 143; 144; 145; 146; 147; 148]. [PERSON] [125] performed ASW-LSDF calculations for the YFe\({}_{12}\) and YFe\({}_{8}\)_TM\({}_{4}\)_ (_TM_ = Ti, V, Cr, Mn, Mo, and W) compounds with the ThMn\({}_{12}\)-type structure, in which the _TM_ atoms occupy the (8\(i\)) sites. These calculations showed that the YFe\({}_{12}\) compound is thermodynamically unstable. The calculated reduction in saturation magnetization of the YFe\({}_{12-x}\)M\({}_{x}\) (\(1\leq x\leq 3\)) compounds after substituting Fe(8\(i\)) atoms by an \(M\) atom is in a good accordance with the experimental data [125]. [PERSON] et al. [132] used classical MD to show that each _TM_ = (Cr, V, Mo, and Ti) substantially reduces the cohesive energy of the Sm(Fe,_TM_)\({12}\) compound and stabilizes the ThMn\({}_{12}\)-type structure. The sequence of site preference occupation is 8\(i>8j>8f\), with the 8\(i\) occupation resulting in extreme energy reduction. [PERSON] and [PERSON] [133] used the FPLMTO method to study the intrinsic properties of the \(RE\)(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)TiZ alloys, where \(RE\) = Y and Ce, interstitially dopped by \(Z\) = H, C, and N. The calculated \(\mu_{0}M_{s}\), \(\mu_{0}H_{a}\), and \(T_{c}\) values of the YFe\({}_{11}\)Ti\({}_{1}\), YCo\({}_{11}\)Ti\({}_{1}\), CeFe\({}_{11}\)Ti\({}_{1}\), and CeCo\({}_{11}\)Ti\({}_{1}\) compounds agree with the experimental data, although the Ti atom should have a strong preference to occupy the 8\(i\) sites, as observed by [PERSON] et al. [33]. The site inclination of Co atoms in the Y(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{1}\) compound with \(x<0.4\) is: 8\(j>8f\) \(>8i\) concurs with the neutron scattering experiments by [PERSON] et al. [131]. According to [PERSON] and [PERSON] [133], the maximum magnetization of the Y(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{1}\) and Ce(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{1}\) alloys occurs at \(x\) = 0.2, while in experiments it takes place at \(x\) = 0.3 [54] and \(x\) = 0.1-0.15 [15] for the Y(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{1}\) and Ce(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{1}\) alloys, respectively. In addition, the calculated \(T_{c}\) of the RECo\({}_{11}\)Ti\({}_{1}\) compound is significantly higher than the calculated \(T_{c}\) of the \(RE\)Fe\({}_{11}\)Ti\({}_{1}\) compound [133], which agrees well with the experimental data [64]. [PERSON] et al.