## 3 Results
### Magnetic Properties  
#### 3.3.1 Magnetization Measurements  
Magnetization vs. magnetic field intensity curves measured for all the three samples at 300 and 2.5 K are shown in Figure 4a,b and Figure 5. The results of these magnetic measurements are summarized in Table 4. The magnetization curves measured for the three types of NPs at RT do not exhibit any residual magnetization (remanence) when the intensity of the applied magnetic field is zero (Figure 4a). When the magnetization curves are normalized to their respective maximum values (saturation or close to saturation magnetization, M\({}_{\text{s}}\)) the M vs. H curve of sample C tends to the saturation magnetization in a different way compared to the those of the other samples (Figure 4b). This is probably due to the different sizes of the in situ NPs with respect to ex situ and bare NPs. The curves measured at low temperature show a hysteresis loop with a remanence (Figure 5 and Table 4). These results demonstrate that the three types of NPs have a superparamagnetic behaviour. The saturation magnetization of bare NPs is within the range of values reported in the literature for magnetite NPs with a size around 10 nm but less than that of bulk magnetite (92 emu/g). This reduction in M\({}_{\text{s}}\) for magnetite and other iron oxides in the form of NPs could be due to the \"magnetically dead layer\" at the surface of the NPs [36]. However, the less ordered crystal structure of the NPs prepared by co-precipitation compared to those obtained by high temperature synthetic routes could be responsible for the lower M\({}_{\text{s}}\)[37]. The lower M\({}_{\text{s}}\) may be due also to the formation of a layer of maghemite at the surface of the NPs since bulk maghemite has a M\({}_{\text{s}}\) lower (74 emu/g) than magnetite. Bare and ex situ coated NPs have comparable M\({}_{\text{s}}\) and the smaller value of the latter could be tentatively attributed to a reduction in the magnetic moment at the surface of the NPs due to the bonding of citrate ions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & **M\({}_{\text{s}}\) (emu/g) at 300 K** & **M\({}_{\text{s}}\) (emu/g) at 2.5 K** & **M\({}_{\text{r}}\)/M\({}_{\text{s}}\)** & **H\({}_{\text{c}}\) (Oe)** \\ \hline A (bare NPs) & 66 & 74 & 0.31 & 423 \\ B (Fe\({}_{3}\)O\({}_{4}\) NPs cit. ex situ) & 58 & 68 & 0.29 & 342 \\ C (Fe\({}_{3}\)O\({}_{4}\) NPs cit. in situ) & 40 & 51 & 0.23 & 511 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Saturation magnetization M\({}_{\text{s}}\) measured at 300 K and 2.5 K, ratio of the residual (M\({}_{\text{r}}\)) and M\({}_{\text{s}}\) at 2.5 K, coercitive field (Oe) at 2.5 K for the three samples. The M\({}_{\rm s}\) for the in situ NPs is much smaller than for the other two kinds of sample and this is consistent with the smaller size of the NPs as determined by XRD. The M\({}_{\rm r}\)/M\({}_{\rm s}\) for the three samples is ca. 0.3, well below the value (0.5) expected for non-interacting, single domain, uniaxial superparamagnetic NPs. This is an indication of magnetic interactions among the NPs in the aggregates [38]. The coercive fields, comparable to the values reported for magnetite NPs of similar size at temperature around 2-5 K [39], do not show a clear dependence on the particle size. The superparamagnetic behaviour of the NPs is confirmed by the FC/ZFC measurements (Figure 6). Figure 4: Magnetization (emu/g) vs. magnetic field intensity (Oe) curves of samples A, B and C measured at RT. The inset in the low right part of the figure shows that the NPs do not have a remanence at 300 K (**a**); Curves of the magnetization vs. magnetic field intensity normalized to their respective maxima of samples A, B and C measured at RT (**b**). Figure 5: Magnetization vs. magnetic field intensity curves of samples A, B and C measured at 2.5 K. In the inset an enlarged region around the zero of the magnetic field intensity is shown.