## 1 Introduction
An increase in density was found due to the decrease of the porosity while saturation magnetization decreased with increasing Mn\({}^{3+}\) concentration. The authors assume that Mn\({}^{3+}\) ions are located on the octahedral sites of the ferrite sub-lattice. [PERSON] et al. have shown the important role of metal cations distribution in the metal ferrites [34]. According to them, in case of metal cations segregation and the appearance of continuous cross-linking, the diffusion of the cations will be necessary until the correct stoichiometry is achieved. Higher temperatures are necessary for diffusion, and finally larger nanocrystals and broader size distribution will be obtained. [PERSON] et al. studied the effect of Mn substitution on the Co site on the magnetic properties of cobalt ferrite [35]. According to [PERSON] et al., the Co\({}^{2+}\), Fe\({}^{3+}\), and Mn\({}^{2+}\) ions are randomly distributed over the A- and B-sites, as revealed by Mossbauer spectroscopy. The cation site occupancies and the strength of the exchange interactions were reported to be responsible for modifications in magnetization and transition temperature, while the coercivity diminishing with Mn content was explained by the anisotropic nature of Co ions. [PERSON] et al. reported the cation distribution in Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\)[36]. As an example, in a sample with x\(-\)0.1, it was found that Co ions occupy 4%, Mn ions 8%, and Fe ions 88% of tetrahedral sites while the remaining ions are located in octahedral sites, confirming the results obtained by [PERSON] et al. [37]. As the Mn content increases, a redistribution of cation within the octahedral site was observed. [PERSON] et al. have shown that the Co\({}^{2+}\) ion occupies both the tetrahedral and octahedral sites; this is in contradiction with [PERSON] et al., who reported that the Co\({}^{2+}\) ion prefers the octahedral sites [38]. [PERSON] and [PERSON] reported that in Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) nano-particles produced via a microwave assisted combustion method, the energy gap decreases with addition of Mn\({}^{2+}\) ions. All samples exhibit weak ferromagnetic behavior, with saturation magnetization increasing with Mn\({}^{2+}\) ions content and decreasing in coercivity, associated with low anisotropy of MnFe\({}_{2}\)O\({}_{4}\)[39]. [PERSON] et al. studied the Mn\({}^{2+}\) substitution's impact on Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) nanoparticles, with \(x=0.0-0.5\), synthesized via hydrothermal method. They have shown that the crystallite size increases from 8 to 14 nm with Mn content having a narrow size distribution (spherical morphology). Magnetic measurements have shown that the saturation magnetization has a maximum value of 70.86 emu/g for the compound with \(x=0.3\)[40]. Previously we have studied the structural and magnetic properties of CoFe\({}_{2}\)O\({}_{4}\), NiFe\({}_{2}\)O\({}_{4}\), MnFe\({}_{2}\)O\({}_{4}\), and Co\({}_{1-x}\)Zn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) nanoparticles and CoFe\({}_{2}\)O\({}_{4}\) @SiO\({}_{2}\) @Au nanocomposites designed for magnetoplasmonic applications [15; 41; 42; 43; 44]. We have found that the saturation magnetization for the nickel and cobalt ferrites have values close to the bulk ones, while for manganese ferrites, these were 60% of the bulk value. The smaller magnetization of manganese ferrite was explained by the existence of cation vacancies [41]. We have shown that for low Zn content (\(x<0.4\)), in Co\({}_{1-x}\)Zn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\), the Zn ions preferentially substitute the Co\({}^{2+}\) ions in the tetrahedral sites. High values of the magnetization were found, increasing with the Zn content for \(x<0.5\), and were attributed to the substitution of Co ions in the tetrahedral sites. At higher Zn concentration, the total magnetization of the Co\({}_{1-x}\)Zn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) nanoparticles decreases due to the replacement of the Co ions with Zn in the octahedral sites [42].