## 1 Introduction  
Three principal material parameters define the intrinsic properties of hard magnetic materials: (i) spontaneous (saturation) magnetization, \(M\)s, (ii) Curie temperature, \(T_{c}\), and (iii) magnetocrystalline anisotropy energy (MAE), characterized by its first-order anisotropy coefficient, \(K_{1}\)[1]. These three parameters all need to be large for an economically effective permanent magnet, i.e., \(T_{c}\)\(\sim\)2 550 K, \(M_{s}\)\(\sim\)2 1 MA/m, \(K_{1}\)\(\sim\)2 4 MJ/m\({}^{3}\). By incorporating transition-metal (TM) with rare-earth-metal (RE) atoms in numerous intermetallic compounds [1; 2], one produces a material with these fascinating magnetic properties. In our previous papers [3; 4], we suggested a new economically effective permanent magnet, SmFe\({}_{3}\)CoNi, that was developed from the well-known SmCo\({}_{5}\) blueprint. More contemporary neodymium magnets of the Nd-Fe-B type are superior to the SmCo\({}_{5}\) magnet because of their greater maximum energy product emerging from their iron-rich stoichiometry. Our proposed SmFe\({}_{3}\)CoNi magnet, however, eliminated most of the detriment of the SmCo\({}_{5}\) magnet while maintaining its superior high-temperature effectiveness over neodymium magnets. According to ref. [5], the price of Sm and Co is moderately high, which makes reducing the price of the SmCo\({}_{5}\) magnet a dominant objective. The authors [5] claim that the rare-earth (RE) Y (225 RMB/kg) is cheaper than Sm (450 RMB/kg), and by limited substitution of Sm with Y atoms, a high performance (Sm\({}_{1\times}\)Y\({}_{x}\)) Co\({}_{5}\) magnet can be prepared. The YCo\({}_{5}\) compound (the CaCu\({}_{5}\)-type structure) is isostructural with SmCo\({}_{5}\). The YCo\({}_{5}\) magnet exhibits significant MAE of \(K_{1}\) -6.5 MJ/m\({}^{3}\) (3.41 meV/f.u.) [6], which is excessive compared to that of the Nd\({}_{2}\)Fe\({}_{14}\)B (Neomax) magnets (\(K_{1}\) -4.9 MJ/m\({}^{3}\), [7]). It furthermore has a Curie temperature (\(T_{c}\) \(\sim\)987 K, [6]) almost twice that of the Neomax (\(T_{c}\) \(\sim\)588 K, [7]). However, Nd\({}_{2}\)Fe\({}_{14}\)B presently prevails the worlds wholesale for permanent magnets (\(-\)62%) [8; 9] because it has the biggest energy production sustained by its record energy product (\(BH\))\({}_{max}\)\(\sim\)512 kJ/m\({}^{3}\)[7], more than twice that of the YCo\({}_{5}\) magnets, (\(BH\))\({}_{max}\) = 224 kJ/m\({}^{3}\)[10; 11]. The YCo\({}_{5}\) magnet is probably the most studied magnet with the CaCu\({}_{5}\)-type structure. It has been explored both experimentally and theoretically in the past due to its unique qualification as a \"gap\" permanent magnetic material [5; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 77; 80]. Actually, almost all experimental papers on the YCo\({}_{5}\) magnet have been dedicated to studying MAE of the undoped magnet as well as doped with Sm, Nd, Ge, Fe, Cu, and Ni [5; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 54; 56; 57; 58; 59; 60; 62; 66; 67; 68; 69; 70; 72; 73; 77; 80]. MAE, the Curie temperature, and the energy product, which are 5.7 MJ/m\({}^{3}\), 921 K, and 224 kJ/m\({}^{3}\), correspondingly, were first reported in refs. [10; 11; 12]. Slightly higher values, \(K_{1}\) -6.4 MJ/m\({}^{3}\) and \(T_{c}\) -987 K, were reported in ref. [15]. According to [PERSON] and [PERSON] [28], the Curie temperature is \(T_{c}\) -920 K. [PERSON] [17] studied the temperature dependence of MAE of the YCo\({}_{5}\) magnet. Later, similar measurements were performed by [PERSON] et al. [54]. Refs.