## 3 Results and Discussion
### The Specific Loss Power in the Linear Approximation
#### 3.3.1 Maximum Specific Loss Power
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**H (kA/m)** & **f\({}_{1}\) (kHz)** & **D\({}_{0}\) (nm)** & **\(\Delta\)T\({}_{\rm hm}\) (\({}^{\circ}\)C)** & **\(\Delta\)t\({}_{\rm m}\) (s)** & **\(\Delta\)T\({}_{\rm ho}\) (\({}^{\circ}\)C)** & **\(\Delta\)t\({}_{\rm o}\) (s)** \\ \hline
5 & 1000 & 5.88 & 41.99 & 212.07 & 18 & 44.19 \\
15 & 334 & 6.25 & 33.06 & 46.57 & 18 & 12.80 \\
30 & 167 & 6.46 & 28.81 & 18.15 & 18 & 6.14 \\
45 & 111 & 6.58 & 27.28 & 11.15 & 18 & 4.08 \\
60 & 83 & 6.67 & 26.72 & 8.08 & 18 & 3.07 \\ \hline \hline \end{tabular}  
* \(\Delta\)T\({}_{\rm ho}\) = 43–25 \({}^{\circ}\)C; ** (\(\pm\)0.01).  
\end{table} 
Table 5: The values of the optimal heating times (\(\Delta\)t\({}_{\rm o}\)) of the CoFe\({}_{2}\)O\({}_{4}\) nanoparticles under the optimal parameters given in Table 3, for the volume fraction of 0.017. The table also shows the values of the maximum variation of the heating temperature (\(\Delta\)T\({}_{\rm hm}\)) of the nanoparticles and their corresponding durations (\(\Delta\)t\({}_{\rm m}\)) under the given conditions. Considering all the above results obtained for both \(\epsilon\) of 0.017 and 0.15 we can say that for all other values of \(\epsilon\) in the range 0.017-0.15 the optimal heating of the nanoparticles at temperatures of 43 \({}^{\circ}\)C will be possible. The optimal heating times (\(\Delta\)t\({}_{\rm o}\)) will be found between the two limits given in Tables 4 and 5, for each value of the magnetic field. For example, in the case of the applied magnetic field of 5 kA/m the optimal heating times of the nanoparticles in order to reach the effective temperature of 43 \({}^{\circ}\)C will be in the range of 5.01-44.19 s, depending on the value of the volume fraction (\(\epsilon\)). Figure 10: The time variation of heating temperature (\(\Delta\)T\({}_{\rm h}\)) of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles in optimal conditions given in Table 3 for volume fraction of 0.017 and two values of magnetic field: (**a**) 5 kA/m and (**b**) 60 kA/m. Also, according to the data in Tables 4 and 5, it results that the optimal heating times of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles are quite short in all cases, being fulfilled the condition of magnetic hyperthermia not to affect healthy cells. In conclusion, according to the results obtained, we can say that in all cases considered for the optimally established range (Table 3, values marked in green) an efficient heating of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles will be obtained, and, therefore, these can be successfully used in superparamagnetic hyperthermia. Even if the maximum specific loss power (P\({}_{\text{sM}}\)) within the admissible biological limit in the case of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles is significantly lower (Table 3) than in the case of magnetite nanoparticles [28,53], still CoFe\({}_{2}\)O\({}_{4}\) nanoparticles can be used successfully in superparamagnetic hyperthermia, because under the optimal conditions established by us the nanoparticles can be heated to the optimum temperature of 43 \({}^{\circ}\)C necessary in magnetic hyperthermia for the effective destruction of tumor cells. Thus, the issue of efficient heating of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles under conditions of low specific loss power (point (iv) of Section 3.2) has also been clarified.