## Magnetic Properties of the Y(Co-Fe-Ni)\({}_{5}\) Alloys  
Table 3 presents the results of the FREMTO calculations of the site-projected spin, \(m^{(s)}\), and orbital, \(m^{(o)}\), moments of the YCo\({}_{5}\) compound. According to [37], Y and Co spins should align in an antiparallel fashion (AF) that is predicted in the present self-consistent calculations. The calculated total moment, \(m^{(tot)}\) = 7.82 \(\upmu_{\text{B}}\)/f.u., is slightly smaller than the experimentally reported value of 8.30 \(\upmu_{\text{B}}\)/f.u. [29]. The calculated spin moments are 1.55 \(\upmu_{\text{B}}\) and 1.47 \(\upmu_{\text{B}}\) for 2c and 3g sites, correspondingly, which are larger than the recorded experimental values of 1.44 \(\upmu_{\text{B}}\) and 1.31 \(\upmu_{\text{B}}\)[16; 28]. The calculated orbital moments are 0.14 \(\upmu_{\text{B}}\) and 0.11 \(\upmu_{\text{B}}\) for 2c and 3g sites, correspondingly, which are smaller than recorded experimental data of 0.26 \(\upmu_{\text{B}}\) and 0.24 \(\upmu_{\text{B}}\)[16]. It is important to mention that the present FREMTO calculations reflect the experimental (spin flip-neuron scattering) observation; for the YCo\({}_{5}\) compound, the orbital moment of Co1(2c) atoms is bigger than the orbital moment of Co2(3g) atoms [16; 19; 23; 25], which was confirmed by the previous calculations [37; 56; 71]. The large MAE of the YCo\({}_{5}\) compound comes from a big orbital allowance from Co\({}_{1}\)(2c) sites, which are located in the same plane as Y\({}_{1}\)(1a) sites [19; 23; 25]. Appropriately, Co\({}_{1}\)(2c) atoms have a big positive MAE allowance, while Co\({}_{2}\)(3g) atoms have a small negative MAE allowance. In line with ref. [71], the axial (positive) MAE of the YCo\({}_{5}\) magnet can be achieved only if orbital moments on the Co\({}_{1}\)(2c) atoms are bigger than the orbital moments of the Co\({}_{2}\)(3g) atoms. The same outcome was reached in a past study [3; 4]; in the SmCo\({}_{5}\) magnet, the orbital moment on Co\({}_{1}\)(2c) atom is bigger than on Co\({}_{2}\)(3g) atom. Calculations [3] anticipated MAE of the SmCo\({}_{5}\) magnet would be \(K_{\text{I}}\) = 19.63 MJ/m\({}^{3}\), which is actually close to the experimental data \(K_{\text{I}}\) = 17.2 MJ/m\({}^{3}\)[3]. A mean-field treatment for the Curie temperature, \(T_{c}\), can be formulated as [133; 134]:  
\[T_{c}=\ \frac{2}{3}\times\frac{E_{tot}^{DLM}-E_{tot}^{AF}}{k_{B}}\]  
where \(\left(E_{tot}^{DLM}-E_{tot}^{AF}\right)\) is the difference among the ground state total energies of the DLM and the AF state, and \(k_{B}\) is the Boltzmann constant. Principally, an assessment of the Curie temperature can be achieved from the total energy difference between the ferromagnetic (or antiferromagnetic) and the paramagnetic states. However, in line with [133], the difference between the total energies can be substituted by the difference between the effective single-particle (one atomic specie) energies, which are directly associated with AF and DLM states (the so-called mean-field treatment). In the present work, \(E_{tot}^{DLM}\) and \(E_{tot}^{AF}\) are calculated at the equilibrium volumes for DLM and AF states, correspondingly. According to the present EMTO-DLM and EMTO-AF calculations, \(T_{c}\) = 891.8 K for the YCo\({}_{5}\) magnet, which is in good accord with the experimental data \(T_{c}\) = 920 K [28], which is essentially bigger than that of the commonly used Nd\({}_{2}\)Fe\({}_{14}\)B magnet (\(T_{c}\) = 588 K [7]). The similar EMTO calculations reveal \(T_{c}\) = 1149.3 K for the YFe\({}_{5}\) compound, although, as was mentioned in the Introduction, this compound does not exist in the Y-Fe phase diagram. However, as was also mentioned in the Introduction, there is an experimentally observed [42] tendency of the Curie temperature to increase with Fe doping of the