# Thermodynamics and Magnetism of SmFe\({}_{12}\) Compound Doped with Co and Ni: An Ab Initio Study
## 1 Introduction
The composition range \(x\) for stabilizing the \(RE\)Fe\({}_{12-x}M_{x}\) phase differs depending on \(M\)[125]. So far, Ti is known to be the favorite stabilizing element for \(RE\)Fe\({}_{12-x}M_{x}\) alloys with \(x\sim\) 1 [49]. The samarium-based compound SmFe\({}_{11}\)Ti\({}_{1}\) has the following magnetic properties: \(\mu_{0}H_{a}\) = 8.3-10.5 T, \(T_{c}\) = 584 K, and \(\mu_{0}M_{s}\) = 1.14-1.22 T [23; 34], and is smaller than that of Nd\({}_{2}\)Fe\({}_{14}\)B\({}_{1}\) (\(\mu_{0}M_{s}\) = 1.61 T) [4; 12; 23; 34]. The iron-rich \(RE\)Fe\({}_{12}\) compounds with the ThMn\({}_{12}\)-type structure earned attention for prospective permanent magnet utilization with regard to maximizing \(\mu_{0}M_{s}\) while minimizing Ti inclusion [20; 31; 35; 38; 46; 47; 52; 65; 68; 69; 71; 72; 73; 78; 84; 87; 89; 91; 108; 111; 113; 115; 122; 126; 127; 128; 129]. Commonly, large transition metals, such as \(TM\) = Ti, V, Cr, Nb, Mn, Mo, W, and Re, preferentially fill the 8\(i\) sites to stabilize the SmFe\({}_{11}TM\) structure [14; 49; 76]. Al, Si, and Ga also stabilize the structure by filling the 8\(f\) sites [49; 59; 76]. According to [PERSON] et al. [71], stabilization of \(RE\)(Fe,Ti)\({}_{12}\) structures, when the Ti atoms substitute part of the smaller Fe in the 8\(i\) sites, can be considered as a reduction in the local mismatches in interatomic distances limiting the orbital hybridization. The average Fe-Fe interatomic distances for Fe (8\(i\)), Fe (8\(j\)), and Fe (8\(f\)) sites are 0.271, 0.259, and 0.251 nm, respectively, where the interatomic distance on the 8\(i\) site is longer than the Fe-Fe interatomic distance in the bcc structure (\(r_{Fe}\) = 0.126 nm, \(2r_{Fe}\) = 0.252 nm) [71]. The replacement of some Fe atoms with atoms such as Ti (\(r_{\Pi}\) = 0.147 nm) stabilizes the structure while diminishing the magnetization of Ti-free compounds [49]. Therefore, it is essential to keep the concentration of stabilizers as low as possible. The prejudiced occupancy of Fe and Ti atoms at the 8\(i\) site was also evident from a neutron diffraction experiment for the YFe\({}_{11}\)Ti\({}_{1}\) compound [33]. According to [PERSON] et al. [75], the amount of magnetization of SmFe\({}_{11}M_{1}\) can be increased using two methods. The first method to improve the magnetization is Co replacement on the Fe site. Magnetic and structural properties of Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{11}\)Ti\({}_{1}\), Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{10}\)Ti\({}_{2}\), and Sm(Fe\({}_{1-x}\)Co\({}_{x}\))\({}_{10}\)Si\({}_{2}\) alloys have been explored by [PERSON] et al. [31] and [PERSON] et al. [35]. It was found that the easy magnetization direction (EMD) in these alloys occurs to change from axial, SmFe\({}_{11}\)Ti\({}_{1}\), SmFe\({}_{10}\)Si\({}_{2}\), SmFe\({}_{10.8}\)Ti\({}_{12}\), to conical, and finally to planar with elevated Co content. The planar MAE of the SmCo\({}_{11}\)Ti\({}_{1}\) compound was also discovered by [PERSON] et al. [42] and [PERSON] et al. [55]. A diagram representing the change in EMD with temperature for each \(RE\)Fe\({}_{11}\)Ti\({}_{1}\) compound (\(RE\) = Y, Pr, Nd, Sm, Gd, Th, Dy, Ho, Er, and Tm) was presented by [PERSON] et al. [50]. [PERSON] et al. [52] presented the substitution effects of Fe by Co on magnetic properties of \(RE\)(\(TM\),Ti)\({}_{12}\) (\(RE\) = Y, Sm; \(TM\) = Fe, Co) single crystals. They showed that \(RE\)Fe\({}_{1-x}\)Co\({}_{x}\)Ti\({}_{1}\) alloys have axial EMD for \(x\sim\) 0.5 \(\mu_{0}M_{s}\) with a maximum at \(x\approx\) 0.3 [52]. Co has a strong influence on the MAE of the Sm-sublattice; the first anisotropy constant, \(K_{1}\), displays a maximum at \(x\approx\) 0.1 and drastically decreases at \(x\) > 0.1. Finally, the Curie temperature grows monotonically with an increase in Co content [31; 35; 52]. The second method to improve the magnetization is to diminish the Ti content at 8\(i\) sites. Phase stability can be reached by Zr or Y replacement for Sm, which decreases the resident substructure encompassing the Fe (8\(i\)) sites. [PERSON] et al.