## 3 Results and Discussions
In this respect, we compared the obtained M-H loops with those measured for the 15 nm nanospheres [56] and 65 \(\times\) 6 nm nanorods [35], which had a size similar to the nanograins of the NRs and NTs, respectively (see Figure S2 in the Supplementary Information). As depicted, the M-H loops for the nanospheres and nanorods presented a nearly null coercive field (<20 Oe) and a normalized remanence (<0.05), thereby showcasing the importance of the interactions when these nanospheres and nanorods formed part of the multigranular NRs and NTs, respectively. Curiously, in both cases, the \(\rm{M_{S}}\) value of the NRs and NTs was lower than that of nanospheres and nanorods. This would support the presence of a higher magnetic disorder in these multigrain nanostructures in comparison with their nanograins, as mentioned before. In order to get an estimation of the effective anisotropy in these samples, we carried out radio frequency (RF) transverse susceptibility (TS) measurements. The TS method is a precise tool for investigating the anisotropic magnetic properties of different magnetic systems including MNPs [57; 58]. TS spectra typically display peaks at the anisotropy  
Figure 3: Transverse susceptibility (TS) measurements for the iron oxide NRs and NTs: (**a**) TS bipolar curves measured at 300 K, (**b**) temperature dependence of anisotropy field, \(\rm{H_{K}}\), (the expected Verwey temperature is indicated by \(\rm{T_{V}}\)), (**c**) peak height difference (\(\rm{\eta}\)) and (**d**) maximum change in TS (\(\rm{\Delta_{XT}}/\rm{\chi_{T}}\))\({}_{max}\) vs. temperature curves as obtained from the peaks in the TS bipolar curves. fields (H\({}_{\text{K}}\)) and switching fields (H\({}_{\text{S}}\)) as the DC field is swept from a positive to a negative saturation. The bipolar TS curves taken at 300 K for the NRs and NTs are depicted in Figure 3a. In both cases, two peaks could be observed indicating that the switching peaks were merged with the anisotropic peak. This resulted in a slight difference in the positive and negative H\({}_{\text{K}}\) values together with a difference in the peak height. The estimated H\({}_{\text{K}}\) values are represented as a function of the temperature in Figure 3b. The H\({}_{\text{K}}\) values at room temperature were 450 and 510 Oe for the NRs and NTs, respectively. These values were appreciably higher than those obtained for the coercive field. An increase in H\({}_{\text{K}}\) has been previously related to an increase in the strength of dipolar interactions [57]. Therefore, in our case, these results would suggest the presence of stronger intraparticle interactions for the NTs in comparison with the NRs. As shown in Figure 3b, with a decreasing temperature, these values remained more or less constant but they rapidly increased below the Verwey transition (\(\sim\)110 K), reaching 690 and 595 Oe below 30 K for the NTs and NRs, respectively. Therefore, even if the ZFC/FC M-T measurements of the Verwey transition were not evident, the TS measurements clearly revealed its presence. Finally, we must remark that below 30 K, the H\({}_{\text{K}}\) value remained constant, probably due to the system entering into a frozen collective magnetic state [57; 59]. In addition, another parameter that could be analyzed from the TS curves was the peak height difference, n\({}_{\text{t}}\). It has been previously shown that the n\({}_{\text{t}}\)ends to increase with an increasing interaction strength [57]. In this respect, in Figure 3c, we plotted the n(T) curves for both the NRs and NTs. In the whole range of temperatures analyzed, the peak height difference (n) was lower for the NRs than for the NTs, supporting once again the presence of stronger intraparticle interactions for the NTs. The thermal evolution of nfollowed a trend similar to that of H\({}_{\text{K}}\) vs. T. The maxima in the n(T) curves marked the Verwey transition (\(\sim\)110 K).