## 3 Results and Discussion  
### Morphology and Structure of the Clusters  
The clusters of cobalt ferrite (CoFe\({}_{2}\)O\({}_{4}\)) nanoparticles herein studied were acquired by means of a solvothermal method, which, by tuning the PEG 6000 amount in the reaction medium [24; 32], allows for the production of clusters with different average size. Figure 1 includes overview images from the transmission electron microscopy (TEM) of the samples of clusters employed, as well as the three different forms of cluster analysed in terms of their size distribution (Gaussian fit): A, B and C, with average diameters of 97 \(\pm\) 23 nm, 155 \(\pm\) 34 nm and 192 \(\pm\) 38 nm, respectively.  
Figure 2 comprises the structural and magnetic characterization of the designed clusters, taking in consideration X-ray diffraction (XRD), Raman spectroscopy and vibrating sample magnetometry (VSM). The XRD analysis of the clusters from the different samples shows three similar patterns (Figure 2a), where we find distinct peaks that may be associated with a spinel structure. The observed peaks correspond to (220), (311), (400), (511) and (440) diffracted planes of this cubic structure, taking into account the CoFe\({}_{2}\)O\({}_{4}\) bulk of the normal spinel structure. The lattice parameter derived from the refining of these data via the Le Bail technique is a = 0.8380 nm (with very small variations between the three samples),  
which is compatible with that previously reported for cobalt ferrite nanoparticles [33]. The different intensity ratios between diffracted peaks, comparing the three samples, can be explained in terms of the average size of the nanoparticles of CoFe\({}_{2}\)O\({}_{4}\) forming the final clusters [20].  
A complementary analysis of the crystalline structure of the samples was performed using Raman spectroscopy, since it can provide paired information, for example, in terms of different cationic arrangements in the spinel crystalline structure [34; 35]. Given the nature of the samples, an excitation wavelength of 633 nm was employed. Figure 2b includes the Raman spectra of the three nanostructures, indicating the typical group-theory vibration modes of CoFe\({}_{2}\)O\({}_{4}\) (dotted lines), the T\({}_{2g}\) (1) (not included), E\({}_{g}\), T\({}_{2g}\) (2), T\({}_{2g}\) (3), A\({}_{1g}\) (1) and A\({}_{1g}\) (2) modes, as in Ref. [36]. The Raman bands observed for the three samples at 300 (E\({}_{g}\)), 470 (T\({}_{2g}\) (2)), 565 (T\({}_{2g}\) (3)), 621 (A\({}_{1g}\) (1)) and 680 (A\({}_{1g}\) (2)) cm\({}^{-1}\), match these vibration modes expected, and confirm the CoFe\({}_{2}\)O\({}_{4}\) as the main component of the three samples of clusters.  
For a matching confirmation, the magnetic properties of the designed samples were checked by vibrating sample magnetometry. Figure 2c includes the field-dependent magnetization at ambient temperature of the synthesized clusters A, that is, with an average diameter of 97 \(\pm\) 23 nm, and formed by very small nanoparticles. The value (76 Am\({}^{2}\)/kg) of saturation magnetization registered when applying a magnetic field up to 7 T is very close to the value of bulk cobalt ferrite (\(\sim\)80 Am\({}^{2}\)/kg) and the small difference can be argued considering the magnetic dead layer of nanoparticles, which slightly decreases the magnetic response per mass of sample. The lack of coercivity in this type of cluster stems from the superparamagnetic behaviour, given the very small size of the nanoparticles forming the clusters themselves [37].  
Figure 1: TEM images at 12,000\(\times\) magnification (scale bar, 500 nm) and particle size distribution of clusters A (red), B (black) and C (blue).