## 3 Results and Discussions  
The morphology, composition and nanostructure of the NRs and NTs were investigated by a combination of TEM and XRD analyses. In Figure 1a,b, the representative TEM images are included for both samples. Considering the NRs and NTs as hollow cylinders, we determined the corresponding average dimensions from the TEM images as summarized in Table 1: the length, inner and outer diameters and wall thickness (see Figure S1 in the Supplementary Information for the corresponding size distributions). As indicated, both samples presented a similar wall thickness but the radius and especially the length of the NTs was much higher than the NRs. Therefore, the volume of the NTs was greater than that of the NRs. In the inset to these images, we obtained a clearer depiction of the internal nanostructure of these samples. As can be seen, the NRs seemed to consist of semispherical nanograins of around 17 nm while the NTs were composed of nanorod-like units, 70 \(\pm\) 20 nm long and 7 \(\pm\) 3 nm wide, bound together as we already described in [39]. The differences in the internal nanostructure of both samples can be related to the differences in the growth process: the ratio of NaH\({}_{2}\)PO\({}_{4}\):2H\({}_{2}\)O and Na\({}_{2}\)SO\({}_{4}\) to FeCl\({}_{3}\):6H\({}_{2}\)O determined the morphology of the nanostructure. In our case, we fixed the concentration of FeCl\({}_{3}\):6H\({}_{2}\)O and Na\({}_{2}\)SO\({}_{4}\) and varied the concentration of NaH\({}_{2}\)PO\({}_{4}\):2H\({}_{2}\)O. We found that the lower concentration of NaH\({}_{2}\)PO\({}_{4}\):2H\({}_{2}\)O promoted the growth of the NTs and the higher concentration of NaH\({}_{2}\)PO\({}_{4}\):2H\({}_{2}\)O promoted the growth of the NRs. On the other hand, XRD patterns (Figure 1c) with well-defined peaks clearly revealed the crystalline nature of both samples. The position of these peaks indicated that the NRs and NTs, after the reduction process in the presence of hydrogen/argon (7% hydrogen), were mainly composed of Fe\({}_{3}\)O\({}_{4}\) although a small amount of \(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) could not be discarded. The average crystallite size of Fe\({}_{3}\)O\({}_{4}\), as calculated using the Debye-Scherrer formula, was around 17 nm for the NRs, supporting the values obtained in the TEM analysis. To evaluate how the different nanostructures of the NRs and NTs affected their magnetic response, we first carried out a magnetic characterization both as a function of the magnetic field and temperature. In Figure 2a, we present the ZFC/FC M-T curves measured at 50 Oe between 5 and 300 K. As observed, the ZFC and FC M-T curves for the NRs and NTs followed a similar trend, presenting a high irreversibility and no sign of \begin{table}
\begin{tabular}{c c c c c} \hline  & **Length (nm)** & \begin{tabular}{c} **Inner Diameter** \\ **(nm)** \\ \end{tabular} & \
\begin{tabular}{c} **Outer Diameter** \\ **(nm)** \\ \end{tabular} &
\begin{tabular}{c} **Wall Thickness** \\ **(nm)** \\ \end{tabular} \\ \hline
**NRs** & \(55\pm 5\) & \(55\pm 5\) & \(110\pm 15\) & \(55\pm 5\) \\
**NTs** & \(470\pm 45\) & \(110\pm 20\) & \(170\pm 20\) & \(55\pm 5\) \\ \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the iron oxide NRs and NTs. The length corresponds to the “height” of the hollow cylinder and the difference between the inner and outer diameters gives the wall thickness. Figure 1: TEM images of (**a**) the iron oxide NRs and (**b**) NTs. In the insets, zoom-in images of a single NR and NT are included. (**c**) XRD data of the iron oxide NRs and NTs. The lower patterns with black squares correspond with the JCPDS data for bulk Fe3O4 (JCPDS No. 19-0629). blocking in the range of temperatures studied. This indicated that, despite the relatively small volume of nanograins forming both samples, neither the NRs nor the NTs were in a superparamagnetic (SPM) state even at room temperature.