## 3 Results and Discussions
Although we could not discard that a few of these nanograins were above the blocking temperature (supposing a wide size distribution), the high blocking temperature could be more likely related to an enhancement of the effective anisotropy of the NRs and NTs in comparison with the isolated nanograins. There are several factors that can increase the effective anisotropy including surface disorder, shape effects and, of course, magnetic interactions. Similar ZFC/FC M-T curves have been reported in the literature for interacting iron oxide based MNPs [44; 45]. In this respect, it was also remarkable that the Verwey transition (the expected position of the Verwey temperature is indicated in the Figure by T\({}_{\rm V}\)) [46; 47; 48], which is related to the crystal structure of Fe\({}_{3}\)O\({}_{4}\) and typically appears as a sudden drop in the magnetization around 110-120 K, was not well-defined in these ZFC/FC M-T curves. A similar smearing of the Verwey transition in other magnetite based MNPs has been associated with the effect of non-stoichiometry, surface disorder and dipolar interactions [49; 50; 51; 48]. We further studied the magnetic responses of the NRs and NTs by measuring the magnetization as a function of the field, the so-called M-H loops, at 300 K (Figure 3b). In this case, we observed several clear differences between the NRs and NTs. The saturation magnetization (M\({}_{\rm S}\)) value for the NTs was around 70 emu/g while for the NRs it was lower, around 55 emu/g. Both M\({}_{\rm S}\) values were smaller than the theoretical value expected for bulk magnetite (-92 emu/g). There could have been a presence of \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) in these samples, which would reduce their M\({}_{\rm S}\) value but as both NRs and NTs were reduced under the same conditions during the synthesis procedure, this would not explain the \(>25\%\) difference in the M\({}_{\rm S}\) of both samples. Therefore, this decrease in M\({}_{\rm S}\) was probably associated with size effects and a surface disorder, suggesting that these effects were more significant in the case of NRs. Figure 2: Magnetization measurements for the iron oxide NRs and NTs: (**a**) the ZFC/FC M-T curves measured at 50 Oe (the expected Verwey temperature is indicated by T\({}_{\rm V}\)); (**b**) the M-H loops measured at 300 K with a zoom into the low field region (inset). If we focused on the low field region of the magnetic hysteresis (M-H) loops, as depicted in the inset to Figure 2b, we observed that both NRs and NTs presented a clear hysteresis, supporting the absence of an SPM state at room temperature. Despite the relatively small volume of the magnetic nanograins composing both samples, the absence of SPM behavior indicated that the magnetic interactions played an important role. The obtained values for the coercive field and normalized remanence were \(\rm{H_{C}}=140\) Oe and \(\rm{M_{r}}/\rm{M_{S}}=0.17\) for the NRs while for the NTs, \(\rm{H_{C}}=270\) Oe and \(\rm{M_{r}}/\rm{M_{S}}=0.22\). The lower coercivity for the NRs in comparison with the NTs pointed towards a lower effective anisotropy for the former. In addition, the fact that the normalized remanence in both cases was much lower than the expected value for magnetically blocked and randomly aligned MNPs (\(\rm{M_{r}}/\rm{M_{S}}\sim 0.5\), according to the Stoner-Wohlfarth model [52]) confirmed the important role of the magnetic interactions in our samples. Concerning this, different studies have revealed that in aggregated nanoparticles, by increasing the size of the aggregate, the effect of the intraparticle interactions becomes increasingly relevant [25; 53; 54; 55]. Therefore, as both NRs and NTs were formed by nanograins of a similar volume (-2600 nm\({}^{3}\)) but the total volume of the NTs was nearly 15 times greater than that of the NRs, the intraparticle interactions were going to be more relevant for the NTs than for the NRs. This has an important effect in their heating efficiency as we will see later.