## Magnetic Properties of the Y(Co-Fe-Ni)\({}_{5}\) Alloys
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Component:** & **Y\({}_{1}\)(1a)** & **Co\({}_{1}\)(2c)** & **Co\({}_{2}\)(3g)** \\ \hline \(m^{(s)}\) (\(\mu_{B}\)) & \(+0.31\) & \(-1.55\) & \(-1.47\) \\ \hline \(m^{(o)}\)(\(\mu_{B}\)) & \(-0.01\) & \(-0.14\) & \(-0.11\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Site-projected spin, \(m^{(s)}\), and orbital, \(m^{(o)}\), magnetic moments for the YCo\({}_{5}\) compound: FREMTO calculations. \(m^{(tot)}\) = 7.82 \(\upmu_{\text{B}}\)/f.u. YCo\({}_{5}\) magnet, i.e., from \(T_{c}\) = 930 K (the YCo\({}_{5}\) compound) to \(T_{c}\) = 1020 K (the Y(Co\({}_{0.8}\)Fe\({}_{0.2}\))\({}_{5}\) compound). Our calculations qualitatively reflect this tendency. Figure 4 shows the Curie temperature calculated within the EMTO-CPA technique of the pseudo-binary YFe\({}_{3}\)(Ni\({}_{1-x}\)Co\({}_{x}\))\({}_{2}\) alloys where Fe atoms occupy all 3g-type sites and the occupation of the 2c-type sites continuously changes from pure Ni (the YFe\({}_{3}\)Ni\({}_{2}\) compound) to pure Co (the YFe\({}_{3}\)Co\({}_{2}\) compound). The dotted line corresponds to the calculated Curie temperature of the YCo\({}_{5}\) magnet, \(T_{c}\) = 891.8 K. The calculated Curie temperature is equal to 572.6 K and 1097.7 K for the YFe\({}_{3}\)Ni\({}_{2}\) and YFe\({}_{3}\)Co\({}_{2}\) magnets, correspondingly. Although the calculated Curie temperature of the YFe\({}_{3}\)Ni\({}_{2}\) compound lies about 320 K below of the Curie temperature of the YCo\({}_{5}\) magnet, this deficiency can be removed by substituting 70 at.% of Ni by Co. The Curie temperature of the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet is equal to 899.9 K.  
According to the present calculations, the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet shows an enormous total moment of \(m^{(tot)}\) -9.79 \(\mu_{\rm B}\), essentially due to the iron atoms that each contribute with 2.45 \(\mu_{\rm B}\). The total moment of the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet is thus essentially bigger than that of the traditional YCo\({}_{5}\) magnet that has a calculated total moment of \(m^{(tot)}\) -7.82 \(\mu_{\rm B}\). The experimental values of saturation magnetization (\(M_{s}\)) and the maximum energy product (\((BH)_{max}\)) for the YCo\({}_{5}\) magnet are 0.85 MA/m and 224 kJ/m\({}^{3}\), correspondingly [6; 10; 11]. Because saturation magnetization and magnetic moment are approximately proportional, \(M_{s}\) \(\sim\)\(m^{(tot)}\), and the maximum energy product is approximately proportional to the square of the saturation magnetization, \((BH)_{max}\) -(\(M_{s}\))\({}^{2}\)[135], one can evaluate that saturation magnetization for the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet is proportional to:  
\[M_{s}(YFe_{3}(Ni_{0.3}Co_{0.7})_{2}) \sim \frac{m^{(tot)}(YFe_{3}(Ni_{0.3}Co_{0.7})_{2})}{m^{(tot)}(YCo_{5 })}\times M_{s}(YCo_{5}) \approx \frac{9.79}{7.82}\times 0.85\frac{MA}{m}\approx 1.064\frac{MA}{m}\]  
and the maximum energy product for the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet should be approximately:  
\[(BH)max(YFe_{3}(Ni_{0.3}Co_{0.7})_{2}) \sim \left(\frac{M_{s}(YFe_{3}(Ni_{0.3}Co_{0.7})_{2})}{M_{s}(YCo_{5 })}\right)^{2}\times(BH)_{max}(YCo_{5})\approx 1.252^{2}\times 224\frac{ kJ}{m^{3}}=351\frac{ kJ}{m^{3}},\]  
Figure 4: The Curie temperature of the pseudo-binary YFe\({}_{3}\)(Ni\({}_{1-x}\)Co\({}_{x}\))\({}_{2}\) alloys. The dotted line corresponds to the calculated Curie temperature of the YCo\({}_{5}\) magnet. which is \(\sim\)69% of the record maximum energy product of the Nd\({}_{2}\)Fe\({}_{14}\)B magnet, \((BH)_{max}\) = 512 kJ/m\({}^{3}\)[7]. Particularly, the YFe\({}_{3}\)(Ni\({}_{0.3}\)Co\({}_{0.7}\))\({}_{2}\) magnet, which has a Curie temperature similar to the YCo\({}_{5}\) magnet, is a substantially steadier magnet than the YCo\({}_{5}\) magnet (its maximum energy product should be \(\sim\)57% larger).