3.1.2. From Ferromagnetic and Ferrimagnetic to Superparamagnetic Behavior

3.1.2. From Ferromagnetic and Ferrimagnetic to Superparamagnetic Behavior As the size of the particles composing a ferromagnet or ferrimagnet decreases, the amount of energy required to create domain walls in this material increases. Below a critical diameter, the coercivity of the material tends to zero due to the anisotropy energy reduction [51]. When the ferromagnetic or ferrimagnetic particle diameter is small enough (of the order of 100 nm or smaller [57,60,61]), and while the thermal energy overcomes the anisotropy energy, the assembly of individual spin magnetic moments behaves as a single As the size of the particles composing a ferromagnet or ferrimagnet decreases, the amount of energy required to create domain walls in this material increases. Below a critical diameter, the coercivity of the material tends to zero due to the anisotropy energy reduction [51]. When the ferromagnetic or ferrimagnetic particle diameter is small enough (of the order of 100 nm or smaller [57,60,61]), and while the thermal energy overcomes the anisotropy energy, the assembly of individual spin magnetic moments behaves as a single super-spin [62] and the particle exhibits a single magnetic domain structure [52,57]. Although the existence of single-domain ferromagnets was predicted in the 1930s [63], important theoretical advances notably by Néel [64], and new measurement methods were required before applications based on this particular magnetism type emerged [65].

super-spin [62] and the particle exhibits a single magnetic domain structure [52,57]. Although the existence of single-domain ferromagnets was predicted in the 1930s [63], important theoretical advances notably by Néel [64], and new measurement methods were required before applications based on this particular magnetism type emerged [65]. In the absence of an external magnetic field, the single-domain magnetization direction is determined by the magnetocrystalline anisotropy of single-domain nanoparticles, which represents the easy (preferred), intermediate, and hard magnetization directions [51]. In the case when the net magnetization of single-domain particles flips randomly very fast under the influence of thermal fluctuations, the magnetization is nulled [52]. When a magnetic field is applied to them, as shown in Figure 1B, the super-spins of indi-In the absence of an external magnetic field, the single-domain magnetization direction is determined by the magnetocrystalline anisotropy of single-domain nanoparticles, which represents the easy (preferred), intermediate, and hard magnetization directions [51]. In the case when the net magnetization of single-domain particles flips randomly very fast under the influence of thermal fluctuations, the magnetization is nulled [52]. When a magnetic field is applied to them, as shown in Figure 1B, the super-spins of individual particles align in the direction of the magnetic field, and the net magnetization increases rapidly and saturates: a behavior shared with paramagnetism. However, unlike paramagnets, materials of this type have a very high magnetic susceptibility due to the ferromagnetic or ferrimagnetic nature of the super-spin. This remarkable behavior is referred to as superparamagnetism [66]. It must be noted that not all single-domain particles are concerned with superparamagnetism [48].

vidual particles align in the direction of the magnetic field, and the net magnetization increases rapidly and saturates: a behavior shared with paramagnetism. However, unlike paramagnets, materials of this type have a very high magnetic susceptibility due to the Superparamagnetic materials exhibit remarkable biophysical properties that have been exploited in the medical field since the late 1970s for diagnostic and therapeutic applications [67–72]. Firstly, their interaction with the protons of water molecules allows them to be used as a contrast agent in MRI. Secondly, when excited by an alternative magnetic field (AMF) at the appropriate frequency and amplitude, they release thermic energy, which led to the development of MHT, suitable for cancer treatment. More generally, they lose their magnetism when the external magnetic field is removed [73]. In addition to their physical properties, the biocompatibility of iron-based particles explains their increasing use in medicine. Indeed, the human body is able to handle, store and eliminate iron, which is used in several physiological processes such as oxygen transport, DNA synthesis, energy production, and metabolism [66].

The biomedical potential of superparamagnetic materials led to the emergence of a new class of biocompatible superparamagnetic agents referred to as SPIONs, or ultra-small SPIONs when their size is up to 50 nm, monocrystalline iron oxide (MION) between 10 nm and 30 nm [74], or sometimes SPIO (for superparamagnetic iron oxide particles) for particles having a diameter greater than 50 nm [75]. For simplification purposes, the appellation of SPION will be used hereafter to designate all magnetic nanometric particles.

Each SPION consists of a core containing water-insoluble magnetite or maghemite crystals made of thousands of paramagnetic Fe ions [75,76] encapsulated in a biodegradable coating, which strongly influences the magnetic properties of the agent. In addition to preventing the aggregation of SPIONs, which increases the risk of vascular embolism, the coating is used to target specific tissues and thus direct its biodistribution. Particles are suspended in a biocompatible fluid before being administered to a subject. The amount of iron ions contained in a single nanoparticle explains the high contrast capabilities of SPION-based agents [61].
