## 4 Conclusions  
Highly crystalline Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) nanoparticles (\(0\leq x\leq 1\)), with average sizes between 7.8 nm and 11.8 nm, as was revealed by TEM measurements, have been synthesized using the hydrothermal method. Elemental analysis by EDS has confirmed the presence of Co, Fe, Mn, and O elements in all studied compounds. Raman spectroscopy was employed in analyzing the cation distribution. It was found to be more likely that Fe\({}^{3+}\) would be placed on octahedral sites while Fe\({}^{2+}\) would, in turn, be displaced to tetrahedral sites while Mn ions will enter both sites. The Mn cations always exhibit Raman signatures at lower wavenumbers than Fe cations due to the larger crystalline radius of Mn when compared to Fe. The Fe-O band at 677 cm\({}^{-1}\) is clearly present in all the samples, meaning that a population of Fe cations always occupies the tetrahedral sites. The T\({}_{26}\)(2) band, representing an overlap of octahedral Mn-O and Fe-O vibrations, exhibited a significant shift from 466 cm\({}^{-1}\) at an Mn substitution rate of 0.2 to 445 cm\({}^{-1}\) at an Mn substitution rate of 0.9. This is indicative of increasing Mn occupancy of both tetrahedral and octahedral sites, hence both Mn\({}^{2+}\) and Mn\({}^{4+}\) are present in Co\({}_{1-x}\)Mn\({}_{x}\)Fe\({}_{2}\)O\({}_{4}\) ferrites. The modifications in the intensities of the Raman modes attributed to the Fe ions located in the tetrahedral sites and octahedral sites show modifications in the inversion degree due to Mn substitution. The magnetic properties of the studied samples follow the structural changes. The saturation magnetizations, determined at 4.2 K, of our samples are much higher compared with previous reports. Doping with Mn in nanocrystalline cobalt ferrite enhanced the magnetic properties due to changes in the cation distribution among the two sublattices. The higher magnetic moments compared with previous reported data can be explained by the presence in our compounds of Mn\({}^{4+}\) ions located preferentially on tetrahedral sites while Mn\({}^{2+}\) prefer octahedral sites. It can also be explained by the high quality and crystallinity of our samples, the nanoparticles being almost monodomain. Large values of the coercive field were found at 4.2 K for all samples, and they decreased with the Mn content. On the other hand, one can see that hysteresis is almost absent in all investigated samples at room temperature.  
In the future, we intend to conduct in vitro hyperthermia experiments and to cover these nanoparticles with a BaTiO\({}_{3}\) shell in order to test the possibility of controlling the shell's electric polarization with a magnetic field for possible applications in cancer treatment.  
Conceptualization, R.T. and R.D.; investigation, A.S., R.B., R.D., R.A., L.B.-T. and F.N.; resources, A.S. and R.T.; formal analysis, A.S., R.B., R.D., R.A., L.B.-T. and F.N.; writing--original draft preparation, A.S., F.N., R.D. and R.T.; writing--review and editing R.D. and R.T.; visualization, R.D. and R.T.; supervision, R.D. and R.T.; project administration, R.T.; funding acquisition, R.T. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author due to privacy.  
The authors declare no conflicts of interest.