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and controlled clinical trials started to be conducted. It has been discovered that cancer cells undergo apoptosis at temperatures of 42–45 °C in contrast to healthy cells that are able to withstand those temperatures (Cavaliere et al. 1967).

      Depending on the location, depth, and stage of the malignancy, three main types of hyperthermia have been developed for clinical applications: whole body, regional, and local hyperthermia. In the case of deep‐seated and propagated metastasis, whole‐body hyperthermia is used. In this case, the entire body is heated up through hot water baths, electric blankets, hot wax, thermal chambers, or infrared radiators (Chicheł et al. 2007). Heat delivering to advanced stage tumors is realized by regional hyperthermia by means of thermal perfusion or external arrays of applicators (Falk and Issels 2001). The treatment of localized superficial tumors is often carried out by local hyperthermia, in which the heat is applied using electromagnetic waves such as radio waves, microwaves, and ultrasound, generated by applicators placed at the surface or under the skin of superficial cancer. Although in local hyperthermia, there is a better control of the area exposed to heat and a better heat uniformity, canceling the drawbacks of the first two types of hyperthermia, it is mainly focused on small and superficial cancer regions. The small penetration depth of the generated heat (in the order of a few centimeters) hampers its utilization for the cure of deep cancerous regions. However, deep cancer cell therapy can be achieved by replacing the heating sources with MNPs delivered only to the cancer cells. The capability of MNPs, once internalized in cancer cells, to convert electromagnetic energy into thermal energy, upon their exposure to an external alternating magnetic field (AMF), allows to locally raise the temperature of the cancerous region up to a level at which cellular apoptosis can be initiated.

As such, the new noninvasive local hyperthermia method, called magnetic hyperthermia (MH), has become one of the most promising innovative cancer therapies (Piñeiro et al. 2015). It possesses numerous advantages over “traditional” therapies, mostly relying on the physico‐chemical properties of MNPs. First, the MNPs can be potentially injected anywhere in the body, the injection being less invasive and allowing the treatment of all kinds of tumors with limited side effects (Nedelcu 2008). Second, the MNPs can be functionalized with a recognition moiety (i.e. antibodies, proteins) in order to increase the selectivity to malignant cells, therefore, increasing the internalization of the MNPs in a specific type of cancer cells (Cherukuri et al. 2010). Nevertheless, the MNPs can be magnetically targeted toward the cancer region by using an external magnetic field gradient. Once the MNPs have been internalized into the cancer cells, they can remain inside the cells even after their multiplication, meaning that a subsequent hyperthermic treatment can be applied without large reinjection of MNPs (Jordan et al. 1999).

      It is known that at room temperature, the macroscopic magnetic materials hold a permanent magnetic dipole moment. All the individual magnetic spins originating from electrons movements are aligned along a particular direction called the easy axis. As a result, the individual magnetic spins can possess two opposite orientations (up and down). These two orientations are separated by a barrier of magnetocrystalline anisotropy energy. When the size of the magnetic materials is reduced to the nanoscale, up to several tens of nanometers, this energetic barrier can be overcome with the aid of the thermal energy. Other ways saying, the magnetic dipole moment of MNPs is not anymore fixed along the easy axis as in the case of macroscopic magnetic materials. This new magnetic property is known as superparamagnetism (SP). In this novel state, the value of the magnetization (which basically represents the sum of all individual magnetic spins) is randomly distributed by the thermal effect. Upon the application of an external AMF, all the individual magnetic spins are flipped, while the magnetization direction is reversed. The provided magnetic energy is released as heat in a phenomenon known as Neel relaxation. The delay between the application of the AMF and the magnetic spins flipping gives rise to a torque that leads to the rotation of MNPs in liquids. The rotational friction between MNPs and the liquid environment also produces heat in a process described as Brownian relaxation.

      The capacity of MNPs to generate heat under an external AMF is quantified by the specific absorption rate (SAR) or specific loss power (SLP). This parameter provides a measure of the rate at which energy is absorbed per unit mass of MNPs. The SAR values strongly depend on the magnetic properties of MNPs (saturation magnetization, coercive field, and magnetic anisotropy) which in turn are governed by the structure, size, size distribution, shape, and composition of MNPs (Périgo et al. 2015). On the other hand, the SAR values can theoretically be increased as much as necessary, by increasing the frequency (f) and the amplitude (H) of the applied AMF (Glöckl et al. 2006). From the practical point of view, this approach is limited by difficulties in designing equipment able to generate large f and high H and, more importantly, by the increased harm produced to healthy cells as a consequence of the occurrence of eddy currents in conducting media (Spirou et al. 2018). For clinical applications, several safety conditions in terms of the H × f product were proposed (Mamiya and Jeyadevan 2019). Based on real tests on patients who were exposed to AMF for a duration that exceeds one hour, according to Atkinson–Brezovich criterion, it was largely accepted that the product H × f should be limited to 5 × 10⁸ A m⁻¹ s⁻¹ (Hergt and Dutz 2007). This limit can be increased 10 times if the treatment is applied to small body regions (Hergt and Dutz 2007).

Two classes of SPIONs, magnetite (Fe₃O₄), and maghemite (Fe₂O₃) have been approved for clinical use by FDA for MRI applications. They have been both tested in vivo for clinical MH therapy (Maier‐Hauff et al. 2011; Wilczewska et al. 2012). In Europe, this form of therapy was clinically approved in the case of glioblastoma treatment. A clinical trial was also performed on prostate cancer (Maier‐Hauff et al. 2011). Since the SAR values of spherical SPIONs (having a diameter of ~10 nm) are very low, drastically decreasing when they are localized into cells or tissues as a consequence of the intracellular clustering (Hilger et al. 2005), the SPIONs were not able to deliver sufficient heat to completely destroy the tumors. As such, for a complete elimination of the tumor, the MH has been used in conjunction with other therapies (chemo‐ and/or radiotherapies). In this case, aggressive side effects have been observed.

      As a result, the scientific community involved in MH research has focused on the elaboration of biocompatible iron oxide MNPs (IOMNPs) with enhanced magnetic properties and better MH performance. They have to be capable of completely destroying the tumors at doses below their intrinsic toxicity and safety levels of AMF. In order to accomplish this goal, two major scientific strategies emerged. The first strategy consisted in increasing the size of SPIONs, by keeping them in the SP limit, thereby increasing the Ms and consequently their SAR values. The Neel relaxation, which prevails when SPIONs are confined inside cellular endosomal compartments due to the considerable reduction of Brownian relaxation, is governed by the magnetic anisotropy. In the case of MNPs with large surface to volume ratio, surface contributions to magnetic properties become significant. Hence, the magnetic anisotropy of MNPs is dominated by the surface anisotropy, which originates from the spin direction discrepancy between core and surface. As such, it is directly associated with MNPs shape. This is the reason why the second strategy focused on controlling the shape of SPIONs by using different synthesis methods.

      The influence of the mean size of SPIONs on SAR values has been the subject of many studies. For instance, Jeun et al. reported an increase of the SAR values from 45 to 322 W g_Fe⁻¹ H × f = 1.3 × 10⁹ A m⁻¹ s⁻¹) when the SPIONs diameter is increased from 4.5 to 22.5 nm (Jeun et al. 2012). Other studies reported maximum SAR values of 447 W g_Fe⁻¹ (H × f = 9.8 × 10⁹ A m⁻¹ s⁻¹) (Gonzales‐Weimuller et al. 2009), 702 W g_Fe⁻¹ (H × f = 6.3 × 10⁹ A m⁻¹ s⁻¹) (Müller et al. 2013) and 950 W g_Fe⁻¹ (H × f = 18.9 × 10⁹ A m⁻¹ s⁻¹) (Lévy et al. 2008) for SPIONs with mean diameter of 14, 15.2 and 17.7 nm, respectively, synthesized using different protocols. Finally, Fortin et al. demonstrated both experimentally and theoretically that the SAR values of SPIONs increase from 4 to 1650 W g_Fe⁻¹ (H × f = 17.5×10⁹ A m⁻¹ s⁻¹) when

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