## 3 Results and Discussion
Figure 3.1 Typical Raman spectra and deconvoluted main bands of Mn substituted ferrites at rates of 0.2 (**a**) and 0.9 (**b**), plots of intensity ratio of 600 and 677 cm\({}^{-1}\) modes (**c**), and the wavenumber position of the T\({}_{2g}\)(**2**) band (**d**) across the samples. with low Mn content, the saturation is attended in fields up to 4 T; in the sample with \(x=1\), the saturation is not attended in 12 T.  
The saturation magnetization \(M_{\mathrm{s}}\) at 4.2 K of Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) nanoparticles determined using the approach to saturation law are presented in Figure 3.2 The obtained values are much higher when compared with previous reports [20; 36; 40; 50]. [PERSON] et.al. have reported that doping with Ni and Mn in nanocrystalline cobalt ferrite could enhance the magnetic properties due to changings in the cation distribution between the two sublattices [51]. The calculated total magnetic moment using our approach of cation distribution closely matches the experimental observed values (see Table 1). The theoretical magnetic moments per formula unit were roughly calculated bearing in mind that Raman measurements have shown the presence of Co\({}^{2+}\), Fe\({}^{2+}\), Fe\({}^{3+}\), Mn\({}^{4+}\), and Mn\({}^{2+}\). The considered magnetic moments per ions are: 3 \(\upmu_{\mathrm{B}}\) for Co\({}^{2+}\), 4 \(\upmu_{\mathrm{B}}\) for Fe\({}^{2+}\), 5 \(\upmu_{\mathrm{B}}\) for Fe\({}^{3+}\), 3 \(\upmu_{\mathrm{B}}\) for Mn\({}^{4+}\), and 5 \(\upmu_{\mathrm{B}}\) for Mn\({}^{2+}\). The magnetic moments of the ions located on octahedral and tetrahedral sites are oriented antiparallel. The higher magnetic moments compared with previous reported data can be explained by the presence, in our compounds, of Mn\({}^{4+}\) ions located preferentially \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{\(x\)} & \multicolumn{2}{c}{**Cation Distribution**} & \multirow{2}{*}{\(M_{\mathrm{S}}\) (\(\upmu_{\mathrm{B}}\))} & \multirow{2}{*}{\(M_{\mathrm{S}}\) (\(\upmu_{\mathrm{B}}\))} & \multirow{2}{*}{\(M_{\mathrm{S}}\) (\(\upmu_{\mathrm{B}}\))} \\  & **Tetrahedral Site** & **Octahedral Sites** & & **experimental T = 4.2 k** & **experimental T = 300 k** \\ \hline
0 & (Co\({}_{0,08}\)Fe\({}_{0,92}\)) & (Co\({}_{0,92}\)Fe\({}_{1,08}\)) & 3.32 & 3.38 & 3.20 \\ \hline
0.1 & (Co\({}_{0,4}\)Mn\({}_{0,1}\)Fe\({}_{0,5}\)) & (Co\({}_{0,5}\)Fe\({}_{1,5}\)) & 5.20 & 5.16 & 4.05 \\ \hline
0.2 & (Co\({}_{0,2}\)Mn\({}_{0,2}\)Fe\({}_{0,6}\)) & (Co\({}_{0,6}\)Fe\({}_{1,4}\)) & 5.00 & 4.86 & 3.75 \\ \hline
0.3 & (Co\({}_{0,1}\)Mn\({}_{0,3}\)Fe\({}_{0,6}\)) & (Co\({}_{0,6}\)Fe\({}_{1,4}\)) & 5.20 & 5.12 & 3.30 \\ \hline
0.4 & (Co\({}_{0,3}\)Mn\({}_{0,3}\)Fe\({}_{0,4}\)) & (Co\({}_{0,3}\)Mn\({}_{0,1}\)Fe\({}_{1,6}\)) & 5.80 & 5.81 & 4.05 \\ \hline
0.5 & (Mn\({}_{0,4}\)Fe\({}_{0,6}\)) & (Co\({}_{0,5}\)Mn\({}_{0,1}\)Fe\({}_{1,4}\)) & 4.00 & 3.71 & 2.60 \\ \hline
0.6 & (Mn\({}_{0,15}\)Fe\({}_{0,85}\)) & (Co\({}_{0,4}\)Mn\({}_{0,45}\)Fe\({}_{1,15}\)) & 4.80 & 4.78 & 3.45 \\ \hline
0.7 & (Co\({}_{0,3}\)Mn\({}_{0,6}\)Fe\({}_{0,1}\)) & (Mn\({}_{0,1}\)Fe\({}_{1,9}\)) & 5.80 & 5.86 & 4.10 \\ \hline
0.8 & (Co\({}_{0,2}\)Mn\({}_{0,7}\)Fe\({}_{0,1}\)) & Mn\({}_{0,1}\)Fe\({}_{1,9}\)) & 5.60 & 5.48 & 3.75 \\ \hline
0.9 & (Co\({}_{0,1}\)Mn\({}_{0,6}\)Fe\({}_{0,3}\)) & (Mn\({}_{0,3}\)Fe\({}_{1,7}\)) & 5.80 & 5.55 & 3.80 \\ \hline
1.0 & (Mn\({}_{0,33}\)Fe\({}_{0,67}\)) & (Mn\({}_{0,67}\)Fe\({}_{1,33}\)) & 6.33 & 6.78 & 4.60 \\ \hline \end{tabular}
\end{table} 
Table 1: Site occupancies of cations for Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) samples, calculated and experimental saturation magnetization moments measured at 4.2 K and 300 K, respectively. on tetrahedral sites. It has been previously reported that Mn\({}^{2+}\) ions have the tendency to occupy octahedral sites [36]. Our high values can be explained by the high quality and crystallinity of our samples, the nanoparticles being almost monodomain, and by changes in the cation distribution between the two sublattices.