## 1 Introduction
[20; 22] represent the first review papers dedicated to the experimental study of the YCo\({}_{5}\) magnet, although [PERSON] [20] claimed that the total magnetic moment of YCo\({}_{5}\) is equal to \(m^{(tot)}\) = 7.52 \(\mu_{\rm B}\)/f.u. Higher values of the total magnetic moment for YCo\({}_{5}\), \(m^{(tot)}\) = 8.33 \(\mu_{\rm B}\)/f.u., and MAE, \(K_{1}\) -7.38 MJ/m\({}^{3}\), were also reported [29]. In regard to the SmCo\({}_{5}\) magnet, the MAE is dominated by the 3D electron contribution from Co, although the localized Sm 4f electrons are believed to influence MAE somewhat [3]. For YCo\({}_{5}\), on the other hand, magnetic anisotropy is entirely due to the Co 3d electrons because Y has no electrons occupying 4f states [16; 18; 19; 23; 24; 25; 28]. According to Refs. [16; 18; 23; 25; 28; 70], the spin-polarized neutron scattering, inelastic spin flip-neuron scattering, nuclear magnetic resonance (NMR), neutron diffraction (ND), and x-ray magnetic circular dichroism (XMCD) measurements of YCo\({}_{5}\) revealed a very large orbital contribution to the total magnetic moment from Co\({}_{1}\)(2c) sites, indicating that the large axial MAE of the YCo\({}_{5}\) magnet arises from the Co\({}_{1}\)(2c) sites. The orbital moment on the Co\({}_{2}\)(3g) sites is smaller than the orbital moment on the Co\({}_{1}\)(2c) sites and contributes to the planar MAE of the YCo\({}_{5}\) magnet [23; 25]. Several experimental studies of doping the RECo\({}_{5}\) compound with Fe or Ni [14; 31] suggest that iron atoms prefer to occupy 3g sites because they are slightly larger than cobalt atoms and are more easily accommodated in these positions. On the other hand, there are vigorous manifestations that nickel atoms conversely occupy 2c sites. According to ref. [31], the compositional dependency of the lattice constant and the interatomic distances can be satisfactory justified by nickel atoms occupying 2c rather than 3g sites in the RECo\({}_{5}\) compound. Copper atoms choose to occupy 3g sites because the atomic volume of copper is bigger than that of cobalt atoms and even bigger than that of iron atoms [31]. From a price standpoint, it is profitable to replace Co atoms with Fe because of the abundance of Fe in the Earth's crust compared to Co (by a factor of -2000) making a Fe-containing magnet economically more attractive. Furthermore, Fe is a ferromagnetic metal with a very substantial magnetization at room temperature (1.76 MA/m [7]). The YCo\({}_{5}\) magnet doped with iron has been the subject of numerous experimental papers [13; 18; 20; 34; 35; 41; 42; 52; 73; 78; 80]. Replacing all cobalt with iron to enhance magnetization in the YFe\({}_{5}\) compound produces a thermodynamically unstable phase, which is not experimentally observed within the equilibrium Y-Fe phase diagram. Contrarily, the Y(Co\({}_{1\text{-}x}\)Fe\({}_{\text{x}}\))\({}_{5}\) compounds (CaCu\({}_{5}\)-type) have been observed, with \(x\) ranging from 0.2 to 0.4 [42; 52]. Moreover, the Curie temperature of the Y(Co\({}_{1\text{-}x}\)Fe\({}_{\text{x}}\))\({}_{5}\) alloys has been found to increase from \(\sim\)930 K to \(\sim\)1020 K when varying across increasing \(x\) from 0.0 to 0.2 [42], contrary to the Y\({}_{2}\)(Co\({}_{1\text{-}x}\)Fe\({}_{\text{x}}\))\({}_{17}\) alloys that display a monotonic reduction in the Curie temperature with rising Fe amount. The orbital moment is also bigger in cobalt compared to iron, and a decrease of the MAE is thus expected for \(x>0\). The lattice constant and magnetization also enhance with \(x\) from 0 to 0.4 [52] in the Y(Co\({}_{1\text{-}x}\)Fe\({}_{\text{x}}\))\({}_{5}\) alloys. In addition to iron and nickel, copper has also been used to dope the YCo\({}_{5}\) magnet [20; 28; 31; 33; 50; 52; 53]. In contrast to the Y(Co\({}_{1\text{-}x}\)Fe\({}_{\text{x}}\))\({}_{5}\) system, Y(Co\({}_{1\text{-}x}\)Ni\({}_{\text{x}}\))\({}_{5}\) and Y(Co\({}_{1\text{-}x}\)Cu\({}_{\text{x}}\))\({}_{5}\) compounds are stable across the entire composition domain (i.e., \(x\) = 0-1).