3.1.1. Magnetic Behavior of Ferromagnetic and Ferrimagnetic Materials

Ferrimagnetism and ferromagnetism are the magnetism types of interest for medical or industrial applications, thanks to the strong magnetic response they provide. Ferromagnetic and ferrimagnetic materials show a similar temperature dependence of magnetization and the ability, under particular conditions, to exhibit a non-zero net magnetization at zero magnetic fields [48].

The ferromagnetic materials (e.g., Fe, Ni, or Co) are characterized by strong (negative) exchange interactions which are opposed to the thermal agitation effect [51]. As a consequence, the atomic magnetic moments undergo a parallel self-alignment inducing a spontaneous magnetization even in the absence of an external magnetic field. Ferrimagnets are characterized by an anti-alignment of atomic magnetic moments of non-equal magnitudes. Iron oxides such as magnetite (Fe3O4) and ferrites are examples of ferrimagnetic materials [48,52]. The spontaneous magnetization of these materials remains true below the Curie temperature (Tc) for ferromagnets and below the Néel temperature for

ferrimagnets [51,53,54]. Above these critical temperatures, the thermal energy overcomes the exchange interactions and the material is then a paramagnet [48]. *Pharmaceutics* **2022**, *14*, x FOR PEER REVIEW 7 of 39 *Pharmaceutics* **2022**, *14*, x FOR PEER REVIEW 7 of 39 *Pharmaceutics* **2022**, *14*, x FOR PEER REVIEW 7 of 39 *Pharmaceutics* **2022**, *14*, x FOR PEER REVIEW 7 of 39



Ferrimagnetism and ferromagnetism are the magnetism types of interest for medical or industrial applications, thanks to the strong magnetic response they provide. Ferromagnetic and ferrimagnetic materials show a similar temperature dependence of magnetization and the ability, under particular conditions, to exhibit a non-zero net magnetization at zero magnetic fields [48]. The ferromagnetic materials (e.g.**,** Fe, Ni, or Co) are characterized by strong (negative) exchange interactions which are opposed to the thermal agitation effect [51]. As a consequence, the atomic magnetic moments undergo a parallel self-alignment inducing a spontaneous magnetization even in the absence of an external magnetic field. Ferrimagnets are characterized by an anti-alignment of atomic magnetic moments of non-equal Ferrimagnetism and ferromagnetism are the magnetism types of interest for medical or industrial applications, thanks to the strong magnetic response they provide. Ferromagnetic and ferrimagnetic materials show a similar temperature dependence of magnetization and the ability, under particular conditions, to exhibit a non-zero net magnetization at zero magnetic fields [48]. The ferromagnetic materials (e.g.**,** Fe, Ni, or Co) are characterized by strong (negative) exchange interactions which are opposed to the thermal agitation effect [51]. As a consequence, the atomic magnetic moments undergo a parallel self-alignment inducing a spontaneous magnetization even in the absence of an external magnetic field. Ferrimag-3.1.1. Magnetic Behavior of Ferromagnetic and Ferrimagnetic Materials Ferrimagnetism and ferromagnetism are the magnetism types of interest for medical or industrial applications, thanks to the strong magnetic response they provide. Ferromagnetic and ferrimagnetic materials show a similar temperature dependence of magnetization and the ability, under particular conditions, to exhibit a non-zero net magnetization at zero magnetic fields [48]. The ferromagnetic materials (e.g.**,** Fe, Ni, or Co) are characterized by strong (negative) exchange interactions which are opposed to the thermal agitation effect [51]. As a consequence, the atomic magnetic moments undergo a parallel self-alignment inducing a spontaneous magnetization even in the absence of an external magnetic field. Ferrimag-3.1.1. Magnetic Behavior of Ferromagnetic and Ferrimagnetic Materials Ferrimagnetism and ferromagnetism are the magnetism types of interest for medical or industrial applications, thanks to the strong magnetic response they provide. Ferromagnetic and ferrimagnetic materials show a similar temperature dependence of magnetization and the ability, under particular conditions, to exhibit a non-zero net magnetization at zero magnetic fields [48]. The ferromagnetic materials (e.g.**,** Fe, Ni, or Co) are characterized by strong (negative) exchange interactions which are opposed to the thermal agitation effect [51]. As a consequence, the atomic magnetic moments undergo a parallel self-alignment inducing a spontaneous magnetization even in the absence of an external magnetic field. Ferrimag-The understanding and observation of the microscopic magnetic structure of ferromagnetic materials began in the middle of the 20th century [50,55,56]. Ferromagnetic materials are organized in small regions within which the magnetic moments are aligned in parallel, whereas the net magnetization of all regions is null in the absence of an external magnetic field. These regions, called magnetic domains, are separated by micrometric magnetic walls in which the orientation disrupts by 90◦ or 180◦ [51]. In the absence of a magnetic field, every domain can have a specific orientation [57,58]. The domain formation relies on a combination of exchange interactions and other contributions such as magnetostatic energy (the energy inherent to time-independent magnetic fields) allowing minimization of its total magnetic energy [50,51,55].

3.1.1. Magnetic Behavior of Ferromagnetic and Ferrimagnetic Materials

3.1.1. Magnetic Behavior of Ferromagnetic and Ferrimagnetic Materials

magnitudes. Iron oxides such as magnetite (Fe3O4) and ferrites are examples of ferrimagnetic materials [48,52]. The spontaneous magnetization of these materials remains true below the Curie temperature (Tc) for ferromagnets and below the Néel temperature for ferrimagnets [51,53,54]. Above these critical temperatures, the thermal energy overcomes the exchange interactions and the material is then a paramagnet [48]. The understanding and observation of the microscopic magnetic structure of ferromagnetic materials began in the middle of the 20th century [50,55,56]. Ferromagnetic materials are organized in small regions within which the magnetic moments are aligned in parallel, whereas the net magnetization of all regions is null in the absence of an external magnetic field. These regions, called magnetic domains, are separated by micrometric magnetic walls in which the orientation disrupts by 90° or 180° [51]. In the absence of a magnetic field, every domain can have a specific orientation [57,58]. The domain formation relies on a combination of exchange interactions and other contributions such as nets are characterized by an anti-alignment of atomic magnetic moments of non-equal magnitudes. Iron oxides such as magnetite (Fe3O4) and ferrites are examples of ferrimagnetic materials [48,52]. The spontaneous magnetization of these materials remains true below the Curie temperature (Tc) for ferromagnets and below the Néel temperature for ferrimagnets [51,53,54]. Above these critical temperatures, the thermal energy overcomes the exchange interactions and the material is then a paramagnet [48]. The understanding and observation of the microscopic magnetic structure of ferromagnetic materials began in the middle of the 20th century [50,55,56]. Ferromagnetic materials are organized in small regions within which the magnetic moments are aligned in parallel, whereas the net magnetization of all regions is null in the absence of an external magnetic field. These regions, called magnetic domains, are separated by micrometric magnetic walls in which the orientation disrupts by 90° or 180° [51]. In the absence of a magnetic field, every domain can have a specific orientation [57,58]. The domain fornets are characterized by an anti-alignment of atomic magnetic moments of non-equal magnitudes. Iron oxides such as magnetite (Fe3O4) and ferrites are examples of ferrimagnetic materials [48,52]. The spontaneous magnetization of these materials remains true below the Curie temperature (Tc) for ferromagnets and below the Néel temperature for ferrimagnets [51,53,54]. Above these critical temperatures, the thermal energy overcomes the exchange interactions and the material is then a paramagnet [48]. The understanding and observation of the microscopic magnetic structure of ferromagnetic materials began in the middle of the 20th century [50,55,56]. Ferromagnetic materials are organized in small regions within which the magnetic moments are aligned in parallel, whereas the net magnetization of all regions is null in the absence of an external magnetic field. These regions, called magnetic domains, are separated by micrometric magnetic walls in which the orientation disrupts by 90° or 180° [51]. In the absence of a magnetic field, every domain can have a specific orientation [57,58]. The domain fornets are characterized by an anti-alignment of atomic magnetic moments of non-equal magnitudes. Iron oxides such as magnetite (Fe3O4) and ferrites are examples of ferrimagnetic materials [48,52]. The spontaneous magnetization of these materials remains true below the Curie temperature (Tc) for ferromagnets and below the Néel temperature for ferrimagnets [51,53,54]. Above these critical temperatures, the thermal energy overcomes the exchange interactions and the material is then a paramagnet [48]. The understanding and observation of the microscopic magnetic structure of ferromagnetic materials began in the middle of the 20th century [50,55,56]. Ferromagnetic materials are organized in small regions within which the magnetic moments are aligned in parallel, whereas the net magnetization of all regions is null in the absence of an external magnetic field. These regions, called magnetic domains, are separated by micrometric magnetic walls in which the orientation disrupts by 90° or 180° [51]. In the absence of a magnetic field, every domain can have a specific orientation [57,58]. The domain for-The external magnetic field progressively forces the domains to align in the direction of the field. As a consequence, the domains with a direction close to the applied magnetic field grow to the detriment of others, until all domains finally align in this direction [51]. At this stage, saturation magnetization is achieved [54]. Ferromagnets and ferrimagnets exhibit a non-linear relation between the applied magnetic field intensity H and the resulting magnetization M. M depends on the history of the applied magnetic field [59], or in other words, the magnetization curve of a material does not follow the same path when applying and removing the external magnetic field. Plotting M versus H leads to a hysteresis loop, reproducible in consecutive H cycles [58]. A part of the magnetic moment alignment remains after the magnetic field is removed. This is expressed by the remanence value M<sup>R</sup> [48,54] located at the intersection of the hysteresis curve with the ordinate axis in Figure 1. To nullify magnetization, a reverse magnetic field must be applied, reported by the coercivity coefficient [52].

magnetostatic energy (the energy inherent to time-independent magnetic fields) allowing

mation relies on a combination of exchange interactions and other contributions such as magnetostatic energy (the energy inherent to time-independent magnetic fields) allowing

mation relies on a combination of exchange interactions and other contributions such as magnetostatic energy (the energy inherent to time-independent magnetic fields) allowing

mation relies on a combination of exchange interactions and other contributions such as magnetostatic energy (the energy inherent to time-independent magnetic fields) allowing

The external magnetic field progressively forces the domains to align in the direction of the field. As a consequence, the domains with a direction close to the applied magnetic field grow to the detriment of others, until all domains finally align in this direction [51].

The external magnetic field progressively forces the domains to align in the direction of the field. As a consequence, the domains with a direction close to the applied magnetic field grow to the detriment of others, until all domains finally align in this direction [51].

The external magnetic field progressively forces the domains to align in the direction of the field. As a consequence, the domains with a direction close to the applied magnetic field grow to the detriment of others, until all domains finally align in this direction [51].

The external magnetic field progressively forces the domains to align in the direction of the field. As a consequence, the domains with a direction close to the applied magnetic field grow to the detriment of others, until all domains finally align in this direction [51].

minimization of its total magnetic energy [50,51,55].

minimization of its total magnetic energy [50,51,55].

minimization of its total magnetic energy [50,51,55].

minimization of its total magnetic energy [50,51,55].

by the coercivity coefficient [52].

by the absence of coercivity and hysteresis.

exhibit a non-linear relation between the applied magnetic field intensity H and the resulting magnetization M. M depends on the history of the applied magnetic field [59], or in other words, the magnetization curve of a material does not follow the same path when applying and removing the external magnetic field. Plotting M versus H leads to a hysteresis loop, reproducible in consecutive H cycles [58]. A part of the magnetic moment alignment remains after the magnetic field is removed. This is expressed by the remanence value MR [48,54] located at the intersection of the hysteresis curve with the ordinate axis

**Figure 1.** (**A**) Schematic illustration of the typical hysteresis curve of a ferromagnetic material. Starting at field H = 0, M increases towards the saturation magnetization MS (dotted line) and then decreases following a non-reversible path. MR represents the remanent magnetization obtained when H reaches zero. HC represents the coercivity, i.e., the field to apply to nullify the magnetization. The open loop area represents the hysteresis energy losses in the material during the reversal process (heat production). (**B**) Typical magnetization curve of a superparamagnetic material, characterized **Figure 1.** (**A**) Schematic illustration of the typical hysteresis curve of a ferromagnetic material. Starting at field H = 0, M increases towards the saturation magnetization M<sup>S</sup> (dotted line) and then decreases following a non-reversible path. M<sup>R</sup> represents the remanent magnetization obtained when H reaches zero. H<sup>C</sup> represents the coercivity, i.e., the field to apply to nullify the magnetization. The open loop area represents the hysteresis energy losses in the material during the reversal process (heat production). (**B**) Typical magnetization curve of a superparamagnetic material, characterized by the absence of coercivity and hysteresis.
