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In the ferromagnetic crystal, the atoms with spin magnetic moment (the orbital magnetic moment being frozen by the presence of the crystalline electric field) are located at small distances between them, thus, generating the exchange interaction that aligns the spin magnetic moments over large spatial atomic distances, which can reach up to tens of microns (μm) (magnetic domains) (Caizer 2004a). In the antiferromagnetic crystal, the equal atomic magnetic moments are aligned to 180°, thus existing as a compensation for these, so that in the absence of the external magnetic field, the magnetization is nonexistent while in the presence of a magnetic field that is very low. On the other hand, in the case of ferrimagnetics, where, in the absence of the external magnetic field, there is a noncompensation of the magnetic moments aligned to 180 as a result of the exchange interaction (more precisely a superexchange), and there will be a significantly higher magnetization in the presence of the external magnetic field, but of a lower value compared to ferromagnetics.

A classification of the diamagnetic, paramagnetic, and ferromagnetic materials, depending on the amplitude of the magnetic susceptibility (χ) (the intrinsic parameter of magnetic materials) is given below (Caizer 2013), and Table 1.1 shows the specific value ranges to magnetic susceptibility for different types of magnetic materials/substances (LIO – linear, isotropic, and homogeneous), without there being a strict delimitation between them.

Table 1.1 Magnetic susceptibility values for different bulk magnetic materials.

Type of magnetic material	Diamagnetic	Paramagnetic	Ferromagnetic
χ	−(10−4 – 10−6) (χ < 0)	10−3 – 10−5 (χ > 0)	102 – 105 (χ ≫ 0)

When the size of the magnetic material, ferro‐ or ferrimagnetic, is reduced to the range of nm – tens of nm, it was found that the magnetic properties specific to the bulk change radically, regardless of the type of magnetic ordering (Caizer 2016). Thus, in the category of magnetic materials with magnetic ordering of ferromagnetic or ferrimagnetic type, a special category appears called superparamagnetic materials. This name was introduced by Bean (Bean and Livingston 1959) in order to distinguish this material from the bulk basic magnetic ones: paramagnetic and ferromagnetic/ferrimagnetic. This is because the material itself is ordered magnetically, ferro‐ or ferrimagnetic, but behaves in the external magnetic field like a paramagnetic material. This name was introduced considering that, at the microstructural level, we do not have individual atoms with magnetic moment isolated from each other, as in the case of paramagnetics, but a magnetic structure (magnetic domain) that contains a very large number of atoms with magnetic moments (even more greater than 10⁵) coupled to each other (with magnetic ordering) as a result of the exchange or superexchange interaction. Superparamagnetic behavior is characteristic of magnetic materials with small sizes in the nanometers range, depending on the nature of the material.

In biomedical applications, the most used materials are those with magnetic ordering of ferrimagnetic or even ferromagnetic type because they present an intense magnetism and fast response to an external magnetic field. However, the most used in applications and much studied today in research for various applications are materials based on iron oxides (ferrimagnetic) (Smit and Wijin 1961) with the magnetite (Fe₃O₄) typical representative (Figure 1.2). Magnetite is an inverse spinel (Fe²⁺ Fe₂³⁺O₄²⁻) with a cubic structure in which the magnetic cations of Fe²⁺ and Fe³⁺ are found in two magnetic subllatices A (tetrahedral) and B (octahedral) having opposite magnetizations: Fe³⁺ [Fe²⁺ Fe³⁺] O₄², where the right parenthesis represents the ions from the sublatice B and Fe³⁺, from outside, the parenthesis represents the ions from the sublatice A. However, recent experiments (Garcia and Subias 2004) have shown a difference in the electric charge of Fe(B) ions, where Fe^2.5+ is present, as shown in Figure 1.2 (Parkinson et al. 2012).

Figure 1.2 Fe₃O₄ bulk unit cell (inverse spinel structure).

      Source: Parkinson et al. (2012). CC BY 3.0.

      The basic magnetic aspects of bulk magnetic material, ferromagnetic, or ferrimagnetic, and how they change in the case of nanomaterial, will be presented below considering the magnetic particles/nanoparticles for biomedical applications.

      1.1.2 The Atomic Magnetic Moment, Magnetization, and Magnetic Moment of the Nanoparticle

      In the case of a bulk paramagnetic, ferro‐, or ferrimagnetic material, the magnetism is due to the existence of the magnetic moment (total) at the atomic (or ionic/molecular) level (Kneller 1962; Jacobs and Bean 1963; Vonsovskii 1974; Caizer 2004a):

(1.1)

as a result of the spin–orbit coupling (vector summation of the spin magnetic moments (total) (

) and the orbital magnetic moments (total) (

): the vector model of the atom (

=

+

). In Eq. (1.1), g_J is the spectroscopic splitting factor (Lande factor) at the atomic level,

(1.2)

      m_J is the internal magnetic quantum number (total), which can take (2J + 1) values (according to quantum physics, respectively –J, …, 0, …, +J), and μ_B is the Bohr magnetone:

      (1.3)

with the observables: e is the electron charge (e = 1.6 × 10⁻¹⁹ C), m₀ is the resting electron mass (m₀ = 9.1 × 10⁻³¹ kg), and h is the Planck constant (h = 6.63 × 10⁻³⁴ Js). In Eq. (1.2), L is the internal orbital quantum number (total), and S is the internal spin quantum number.

      Macroscopically, the quantity that characterizes the bulk magnetic material, from a magnetic point of view, is the magnetization (

), defined as a numerical quantity equal to the resulting magnetic moment ( Скачать книгу