## 3 Results and Discussion
The temperature dependence of \(\rm H_{cross}\) as is shown in the inset of Figure 4 together with its fit with the power law  
\[\rm H_{cross}(T)=\rm H_{cross}(0)(1-T/T^{*})^{n} \tag{2}\]  
where \(\rm H_{cross}(0)\approx 0.55\) T is the value of \(\rm H_{cross}\) at T = 0 K, \(\rm T^{*}\approx 20.75\) K indicates when the phenomenon is undetectable, and n \(\approx 0.27\) is the exponent. The study of \(\rm H_{cross}(T)\) line can be interesting since below it the sample shows a field behavior of the pinning energy almost constant which could allow a better transport of current. In order to find the irreversibility line, the critical current density \(\rm J_{c}\) versus H curves have been shown in the main panel of Figure 5. A second magnetization peak phenomenon, similar to others observed in literature for iron-based superconductors [34; 35; 36; 37], has been detected. The second peak position \(\rm H_{sp}\), individuated by a black dashed line in the main panel of Figure 5, typically identifies the transition between the elastic and the plastic distortion of the vortex lattice in the framework of a strong pinning [38; 39; 40; 41]. The \(\rm H_{sp}\) values have been extracted at the different temperatures and plotted in the inset(a) of Figure 5. In particular, the \(\rm H_{sp}(T)\) values have been fitted with the power law  
\[\rm H_{sp}(T)=\rm H_{sp}(0)(1-T/T^{*})^{n} \tag{3}\]  
where \(\rm H_{sp}(0)\approx 1.3\) T is the value of \(\rm H_{sp}\) at T = 0 K, \(\rm T^{*}\approx 30.4\) K indicates when the phenomenon is undetectable, and n \(\approx 0.14\) is the exponent. The \(\rm H_{sp}(T)\) line is very appealing for applications since for H approaching \(\rm H_{sp}\) the \(\rm J_{c}\) is increasing with the field while for H \(>\)\(\rm H_{sp}\) it is decreasing. On the other hand, the black solid line in the main panel of Figure 5 indicates the irreversibility field \(\rm H_{irr}\) values. Specifically, \(\rm H_{irr}\) can be obtained with  
Figure 4: Field dependence of the pinning energy at 2.5 K. The data are fitted with the power law \(\rm U(H)\propto H^{-\alpha}\). Fit details are reported in the text. Inset: \(\rm H_{cross}\) versus T data are fitted with \(\rm H_{cross}=\rm H_{cross}(0)\) (\(1-T/T^{*}\))\({}^{n}\). Fit results are reported in the text. the criterion of \(J_{c}\) = 100 A/cm\({}^{2}\)[42]. In the inset(b) of Figure 5, H\({}_{irr}\) versus temperature is shown together with the fit with the equation  
\[H_{irr}(T)=H_{irr}(0)(1-T/T^{*})^{n} \tag{4}\]  
where H\({}_{irr}(0)\approx 26\) T is the value of H\({}_{irr}\) at T = 0 K, T\({}^{*}\approx 31.1\) K indicates when the phenomenon is undetectable, and n \(\approx\) 0.86 is the exponent. The H\({}_{irr}\)(T) line is very important since it individuates the vortex liquid region where no pinning forces act and high dissipations occur in the material. Naturally, this region must be avoided in the framework of power applications of superconductivity. Finally, m(T) curves have been performed in ZFC conditions at different magnetic fields (see the main panel of Figure 6) to evaluate the H\({}_{c2}\) values. Particularly, they have been estimated by determining the onset of the magnetization drop at the different fields. H\({}_{c2}\)(T) curve is shown in the inset of Figure 6 together with the fit with the power law  
Figure 1:0  
where H\({}_{c2}(0)\approx 212\) T is the value of H\({}_{c2}\) at T = 0 K, T\({}_{c}\) = 35 K is the critical temperature of the sample at H \(\approx\) 0 T [15], and n \(\approx\) 0.9 is the exponent. The H\({}_{c2}\)(T) line is important to determine the maximum appliable magnetic field to the material without its transition to the normal state. Figure 1:1 Critical current density \(J_{c}\) as a function of the field at different temperatures. The black horizontal line is the irreversibility line while the black dashed line individuates the second peak positions. Inset (**a**): Second peak values H\({}_{sp}\) versus temperature.