## 1 Introduction  
Functional magnetic nanostructures are of high significance not only for research professionals working in the disciplines of data storage [1], catalysis [2, 3], environmental remediation [4], and basic science [5, 6, 7, 8] but also for those working in biomedicine [9, 10, 11, 12, 13]. Recently, alternating current (AC) hyperthermia therapy using magnetic nanoparticles, especially spinal ferrites (MFe\({}_{2}\)O\({}_{4}\), \(M\) = Mn, Ni, Co, Fe), has become a promising supplementary technique to conventional cancer treatments, radiotherapy and chemotherapy, which have severe side effects [14, 15, 16, 17]. In the treatment involving magnetic hyperthermia, an external AC magnetic field is applied for heating the magnetic nanoparticles in a cancerous area in order to destroy or deactivate the cancerous cells and cause no harm to the healthy ones, resulting in minimum collateral damage. This technique has already shown promising results in cancer therapy; however, the low heating efficiency of the traditionally used spherical iron oxides, particularly magnetite (Fe\({}_{3}\)O\({}_{4}\)) and maghemite (\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)) nanoparticles, obstructs their wide application [18, 19]. Serious concern has been raised about the number of nanoparticles required for each magnetic hyperthermia treatment because of their low heating efficiency. Recent research has suggested that a significant number of nanoparticles tends to be cumulated in kidneys, liver, spleen, and other parts of the body after hyperthermia treatment [20]. Therefore, there is an increase in demand for highly efficient magnetic nanoparticles so that a minimal dose of nanoparticles can be used to achieve the therapeutic temperature range (40-44 \({}^{\circ}\)C) to kill or deactivate the cancerous cells without damaging the healthy ones [21; 22; 23; 24; 25; 26]. The heating efficiency of the nanoparticles defined in terms of the specific absorption rate (SAR) value is dependent on the saturation magnetization (\(M_{\text{S}}\)), effective magnetic anisotropy, shape, size and amount of the nanoparticles [27; 28; 29; 30; 31]. Smaller nanoparticles, in the sub-10 nm range, have been proven to have a longer circulation time in blood because they can escape the immune system. Moreover, smaller nanoparticles are stable against agglomeration and precipitation, thus avoiding the risk of blood vessel occlusion [32]. However, there is a strong decrease in \(M_{\text{S}}\), well below the \(M_{\text{S}}\) of bulk phase, upon reduction in the size [33]. Both Monte Carlo simulation and experimental results on Fe\({}_{3}\)O\({}_{4}\) nanocubes showed a SAR improvement relative to conventional spherical nanoparticles, due to the enhanced surface anisotropy as a result of the chain-like particle formation [34]. This was further verified by our group, where we have demonstrated a significant enhancement in the SAR value of Fe\({}_{3}\)O\({}_{4}\) nanorods compared to other shapes due to enhanced effective magnetic anisotropy [35; 36]. Unfortunately, only nearly spherical iron oxide nanoparticles are currently approved for biomedical applications [37; 38; 39]. Therefore, a robust strategy is needed to improve the heating efficiency of sub-10 nm iron oxide particles. It has been demonstrated that the heating efficiency of Fe\({}_{3}\)O\({}_{4}\) nanocubes (20 \(\pm\) 2 nm) can be improved with a small replacement of Fe\({}^{+2}\) with Co\({}^{+2}\) ions in B-sites, as a result of the increased magnetocrystalline anisotropy in Fe\({}_{3-x}\)Co\({}_{x}\)O\({}_{4}\) nanoparticles [40]. Even though there is a great potential of Co substituted Fe\({}_{3-x}\)Co\({}_{x}\)O\({}_{4}\) nanoparticles in improving heating efficiency, the systematical study of sub-10 nm Fe\({}_{3-x}\)Co\({}_{x}\)O\({}_{4}\) (x = 0-1) nanoparticles [32; 41] has attracted much less research effort. This restrains the possibility of using Fe\({}_{3-x}\)Co\({}_{x}\)O\({}_{4}\) (x = 0-1) nanoparticles for magnetic hyperthermia treatment.