## 4 Conclusions  
In summary, we showed that intraparticle magnetic interactions can play a crucial role in the heating efficiency of multigranular nanostructures. When the nanograins bind together to form this kind of nanostructure, the strength of the intraparticle interactions increases with the increasing volume. As we have seen in the case of NRs and NTs, this gives rise to an increase in the effective anisotropy of the nanostructures in comparison with the isolated nanograins, which tends to make them become magnetically blocked at the range of temperatures relevant for magnetic hyperthermia. These blocked magnetic nanostructures present high anisotropy fields at room temperature (450 Oe for NRs and 510 Oe for NTs), which deter their heating efficiency. This was precisely observed in the AC hyperthermia measurements carried out. In the range of fields analyzed (0-400 Oe), both NRs and NTs gave rise to minor loop hysteresis losses and therefore lower SAR values (110 W/g for NRs and 80 W/g for NTs) especially when compared with the isolated nanograins, which reached SAR values up to three times higher. These results indicate that in the range of field amplitudes and frequencies currently relevant for clinical hyperthermia, multigranular nanostructures with a lower volume and therefore weaker intraparticle interactions are preferred as heating mediators. Therefore, in our case, multigranular NRs, despite their lower effective anisotropy and saturation magnetization, present a better heating efficiency compared with the NTs. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/nano11061380/s1](https://www.mdpi.com/article/10.3390/nano11061380/s1)]([https://www.mdpi.com/article/10.3390/nano11061380/s1](https://www.mdpi.com/article/10.3390/nano11061380/s1)), Figure S1: The size distribution histograms for (a-c) NRs and (d-f) NTs, Figure S2: TEM images and size distributions of 15 nm nanospheres (a,b) and 65\(\times\)6 nm nanorods (d-f). In addition, the M-H loops measured at 300 K for the nanospheres (c) and the nanorods (g) are also included. The insets are a zoom-in of the low field region of these M-H loops., Figure S3: Peak height difference (n) curves calculated from positive and negative saturation magnetization (\(M_{\text{sat}}\)) for NRs and NTs., Figure S4: (a) AC loops and (b) SAR vs H curves for NTs, NRs, and 15 nm nanospheres and 65 \(\times\) 6 nm nanorods, similar to the constituent nanograins. **Author Contributions:** Conceptualization, R.D. and J.A.M. ; methodology, R.D., V.K., Z.N., I.R., E.G. and J.A.G. ; validation, R.D. and J.A.M. ; formal analysis, R.D. and J.A.M. ; investigation, R.D. ; resources, E.G., J.A.G., M.-H.P. and H.S. ; data curation, R.D. and J.A.M. ; writing--original draft preparation, R.D. and J.A.M. ; writing--review and editing, V.K., Z.N., I.R., E.G., J.A.G., M.-H.P. and H.S. ; supervision, R.D., M.-H.P. and H.S. ; project administration, M.-H.P. and H.S. ; funding acquisition, R.D., J.A.M., M.-H.P. and H.S. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED), grant number 103.02-2019.314. The Spanish Government is acknowledged for the \"Nanotechnology in translational hyperthermia (HIPERNANO)\" research network (RED2018-102626-T) and for funding under the project number MAT2017-83631-C3. Research at USF was supported by US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering, Award No. DE-FG02-07 ER46438. Basque Government is also acknowledged for funding under the project number IT-1005-16 and for the postdoctoral fellowship POS_2020\(1\)0028. **Data Availability Statement:** Not applicable. **Acknowledgments:** This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 103.02-2019.314.