## 3 Results and Discussion
### Magnetic Properties
The largest values occur at 2 K with 77 emu/g in the sample S1, 80 emu/g in the sample S2, and a value of 84 emu/g in the sample S3; (c) shell thickness-dependent saturation magnetization values remain nearly the same with an increase in temperature from 2 to 100 K; (d) a noticeable decrease in the shell thickness-dependent saturation magnetization values appeared above 100 K. At 200 K saturation magnetization values are 73 emu/g, 77 emu/g and 80 emu/g in samples S1, S2 and S3, respectively. This reflects only a decrease of less than 5% of the initial values; (e) a pronounced decrease in the shell thickness-dependent saturation magnetization values occurred at 300 K with minimum values of 66, 69 and 72 emu/g in samples S1, S2 and S3, respectively. This reflects only a decrease of nearly 14% of the initial values. Thus, in the ZFC state, the maximum value of saturation magnetization obtained is 84 emu/g in the sample with the thickest shell (sample S3); (f) after field-cooling at 0.5 T, the magnitudes of saturation magnetization at 2 K changed only slightly in samples S1 and S3 (where the saturation magnetization increased from 77 to 80 emu/g in sample S1 and decreased slightly from 84 to 80 emu/g in sample S3); (g) after field-cooling at 0.5 T, the saturation magnetization at 2 K in sample S2 displays a drastic increase where it reaches 120 emu/g. This indicates an increase of exactly 50% of its value in the ZFC state and a nearly 50% increase of its bulk value. This reflects the significant role of field-cooling at 0.5 T in enhancing the  
Figure 5: The saturation magnetization versus field-cooling value at several temperatures (from 2 to 300 K) for each sample (**a**) S1, (**b**) S2, and (**c**) S3. saturation magnetization in sample S2. This could be attributed to the enhancement of the alignment of both the core/shell interface and the surface spins; (h) after field-cooling at 0.5 T, the magnitudes of saturation magnetization at temperatures up to 100 K remained almost equal to those at 2 K in all samples. However, a noticeable decrease of the saturation magnetization values occurs at 200 and 300 K in all samples. For example, in S2 the saturation magnetization decreased to 115 emu/g at 200 K and to 105 emu/g at 300 K, which is much larger than the maximum value obtained in the ZFC state (80 emu/g at 2 K). Interestingly, in sample S2, all the saturation magnetization values in the FC state are nearly 50% larger than the values in the ZFC state at similar temperatures. This clearly reflects the significant role of field-cooling at 0.5 T in enhancing the saturation magnetization in sample S2 even at room temperature; (i) larger field-cooling values displayed similar effect as that of the 0.5 T field-cooling value. This reflects the ineffective role of field-cooling above 0.5 T in enhancing the saturation magnetization in all samples; (j) thus, the 0.5 T can be considered as a critical field-cooling value in samples S2 where a drastic increase in saturation magnetization occurred; (k) this also shows that the shell thickness of 3 nm is a critical thickness in this core/shell nanoparticle system where a very large enhancement in saturation magnetization occurred at the field-cooling value of 0.5 T at all temperatures with a value of 120 emu/g at temperatures up to 100 K and with only slight decrease at temperatures above 100 K.  
The temperature dependence of the saturation magnetization, \(M_{\rm S}\) in bulk ferromagnetic or ferrimagnetic materials at low temperatures is governed by the [PERSON]'s law [39; 40; 41; 42]. \[M(T)=M_{0}\bigg{[}1-\bigg{(}\frac{T}{T_{o}}\bigg{)}^{\alpha_{B}}\bigg{]}\dots \tag{1}\]  
where, \(M_{0}\) is the saturation magnetization at 0 K, \(T_{0}\) is the temperature at which the \(M_{\rm S}\) becomes zero (ferromagnetic transition temperature, \(T_{\rm C}\)). The exponent \(\alpha_{B}\) is known as the [PERSON]'s exponent (\(\alpha_{B}\)) and the value of \(\alpha_{B}\) is 3/2 for bulk materials.