## 1 Introduction  
Superparamagnetic hyperthermia (SPMHT) for alternative and noninvasive cancer therapy uses magnetic nanoparticles that have a superparamagnetic behavior in an external magnetic field [1, 2, 3, 4, 5, 6, 7]. By the effect of magnetic relaxation [2, 8, 9] in an alternating magnetic field with amplitude H and frequency f of hundreds of kHz, the magnetic nanoparticles are heated [1]. Thus, by introducing magnetic nanoparticles into the tumor by various techniques using modern nanobotechnology [10], and then heating them by magnetic relaxation following the application of the magnetic field from the outside, the temperature of approx. 43 \({}^{\circ}\)C required for the destruction of tumor cells can be obtained. So, superparamagnetic hyperthermia uses the natural thermal effect to destroy tumor cells, being a new technique, alternative to classical techniques (chemo- and radiotherapy), and also non-invasive, having low or even no toxicity [7, 10, 11, 12] compared with classical techniques that have a high degree of toxicity on the body. Today, superparamagnetic hyperthermia is considered as the method of the future in cancer therapy due to the very promising results obtained so far both in vitro, in vivoand in clinical trials [7; 10; 11; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. However, the effectiveness and efficiency of superparamagnetic hyperthermia in destroying tumor cells depends very much on the magnetic nanoparticles used for it. Most viable results have been obtained so far by using Fe\({}_{3}\)O\({}_{4}\) nanoparticles (magnetic) [13; 14; 15; 16; 17; 18; 19; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39], but also other magnetically soft ferromagnetic nanoparticles (which have low magnetic anisotropy) [40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51]. However, magnetite nanoparticles, although they seem to be the most suitable in terms of magnetic characteristics and efficiency in obtaining a high specific dissipated power, they have a major disadvantage, namely: the size of the nanoparticles which is too large, in the range of 14-17 nm, for obtaining superparamamagnetic hyperthermia in optimal conditions [1; 28; 52; 53]. This can cause problems of cellular toxicity, and to reduce it requires the use of low concentrations of nanoparticles in therapy, which will decrease the effectiveness of superparamagnetic hyperthermia. Elimination of this major drawback could be done using CoFe\({}_{2}\)O\({}_{4}\) ferrite nanoparticles, by replacing Fe\({}^{2+}\) ions in the lattice of magnetite (Fe\({}^{3+}\)[Fe\({}^{2+}\), Fe\({}^{3+}\)]O\({}_{4}\)\({}^{2-}\)[54] with Co\({}^{2+}\) ions in the ratio of 1:1 (Fe\({}^{3+}\)[Co\({}^{2+}\), Fe\({}^{3+}\)]O\({}_{4}\)\({}^{2-}\). Thus, an inverse spinel will be obtained as in the case of magnetite having the saturation magnetization (425 kA/m) close to that of the magnetite (480 kA/m), but a considerably higher magnetic anisotropy: 200 kJ/m\({}^{3}\)[55] compared to only 11 kJ/m\({}^{3}\)[54] in the case of magnetite. The slight decrease in magnetization in the case of cobalt ferrite will not significantly influence in terms of superparamagnetic hyperthermia, but the large increase in magnetic anisotropy (of ~18 times) will radically change the hyperthermic behavior, both in terms of the specific loss power as well as of the heating temperature of the nanoparticles. Thus, the high magnetic anisotropy in the case of cobalt ferrite nanoparticles leads to obtaining a maximum heating rate for very small nanoparticles, of the order of a few nm [1]. The reduced size of CoFe\({}_{2}\)O\({}_{4}\) nanoparticles will have at least two major beneficial effects in the superparamagnetic hyperthermia of tumors: (i) the reduction of cellular toxicity [12] due to reduced nanoparticle size, and (ii) the possibility of intracellular therapy by superparamagnetic hyperthermia [56]. These are two very important issues to consider in magnetic hyperthermia in addition to increasing the specific loss power, on which the effectiveness of tumor therapy greatly depends.