Magnetic properties

Substance is composed of nucleus, which contains protons and neutrons, electrons. An atom has magnetic moments that originate from nucleus spins and electron spins. Magnetic moments from nucleus can be ignored because it is substantially less than the magnetic moments producing electrons. Every substance has different magnetize property. This section provides a brief description of five magnetisms.

1.5.1 Diamagnetism

Diamagnetism is a very weak form of magnetism and the volume susceptibility (χ) for diamagnetic solid materials is on the order of -10^-5 (Table 1.2). When a diamagnetic material is placed in a magnetic field, the induced magnetization in the material is in a direction opposite to that of the applied magnetizing field. Thus, χ is negative and it can be interpreted as the substance trying to expel the applied field out from the material. Atoms of a diamagnetic material show no net magnetic moment in the absence of an applied magnetic field. In the presence of an applied magnetic field, a net magnetic moment is induced. It is aligned opposite to the field direction (Figure 1.8). Diamagnetism is found in all materials, but because it is so weak, it can be observed only when other types of magnetism are totally absent.

Figure 1.8 The atomic dipole configuration for a diamagnetic material with and without a magnetic field.³⁵

1.5.2 Paramagnetism

Susceptibilities for paramagnetic materials have values varying from 10^-5 to 10^-2 (Table 1.2). In the absence of an external magnetic field, the orientation of these magnetic moments are random. The result is that a piece of the material possesses no net macroscopic magnetization. These atomic magnetic moments are free to rotate.

Without an external field, these magnetic dipoles are acted individually with no mutual interaction between adjacent dipoles as shown in Figure 1.9. In the presence of an applied magnetic field, the dipoles align somewhat along the field, thus, χ is positive (Figure 1.9).

Figure 1.9 Atomic dipole configuration with and without an external magnetic field for a paramagnetic material.³⁵

Table 1.2 Room-temperature magnetic susceptibilities for diamagnetic and paramagnetic materials.³⁵

1.5.3 Ferromagnetism

Certain metallic materials possess a large magnetic moment even in the absence of an external magnetic field. The succeptibility χ is very large ~ 10⁶ (even infinite) and further depends on the applied field intensity. Every piece of ferromagnetic material should have a strong magnetic field, but ferromagnets are often found in an

"unmagnetized" state. The reason for this is that a bulk piece of ferromagnetic material is divided into many tiny magnetic domains. Within each domain, the spins are aligned, but (if the bulk material is in its lowest energy configuration, i.e.

"unmagnetized"), the spins of separate domains point in different directions and their magnetic fields cancel out, so the object has no net large scale magnetic field (Figure 1.10a). Ferromagnetic materials tend to divide into magnetic domains because this is a lower energy configuration. Thus, an ordinary piece of iron generally has little or no net magnetic moment. However, if it is placed in a strong external magnetic field, the domains will re-orient in parallel with that field, and will remain oriented when the field is turned off, thus creating a "permanent" magnet. The domains do not go back to their original minimum energy configuration when the field is turned off because the domain walls tend to become 'pinned' or 'snagged' on defects in the crystal lattice, preserving their parallel orientation (Figure 1.10b).^35,36

Figure 1.10 (a) Domain in a ferromagnetic material, arrows represent atomic magnetic dipoles. (b) The mutual alignment of atomic dipoles for a ferromagnetic material, which will exist even in the absence of an external magnetic field.³⁵

1.5.4 Antiferromagnetism

In one such group, spin coupling results in an antiparallel alignment i.e.

alignment of spin moments of adjacent atom or ions in opposite directions is termed as antiferromagnetism. Antiferromagnetic materials with atoms at alternate positions have their spins aligned in opposite directions. This results in complete cancellation of the magnetic moments and net zero magnetization. Manganese oxide (MnO) exhibits antiferromagnetic behavior as shown in Figure 1.11. No net magnetic moment is associated with the O^2- ions. The magnetic moment of Mn²⁺ ions at corners of a cubic unit cell are aligned in one directions while those at face centers are in opposite directions thereby leading to complete cancellation of the magnetic moments and resulting in net zero magnetic moment.

Figure 1.11 Schematic representation of antiparallel alignment of spin magnetic moments for antiferromagnetic manganese oxide.³⁵

1.5.5 Ferrimagnetism

The phenomenon of ferrimagnetism is similar to antiferromagnetism but there is no complete cancellation of spin of adjacent atoms because of different type of atoms/ions occupying these positions and a spontaneous magnetization remains. The macroscopic magnetic characteristics of ferromagnets and ferrimagnets materials are similar. The difference is in the magnitude of magnetic moments. The prototype

ferrite is Fe₃O₄. Fe₃O₄ is basically FeOFe₂O₃ [Fe²⁺O^2-(Fe³⁺)₂(O^2-)₃] in which Fe ions exists in both +2 and +3 valence states in the ratio of 1:2 (Figure 1.12). According to Table 1.3, we know that net magnetic moments are not zero.

Figure 1.12 The spin magnetic moment configuration for Fe²⁺ and Fe³⁺ iron in Fe3O4.³⁵

Table 1.3 The distribution of spin magnetic moments for Fe²⁺ and Fe³⁺ ions in a unit cell of Fe3O4.³⁵

1.5.6 Superparamagnetism

Superparamagnetism is similar to paramagnetism. In small enough nanoparticles, magnetization can randomly flip direction under the influence of temperature (Figure 1.13). When the nanoparticle size decreases towards critical particle diameter (Dcritical), the coercivity increases toward maximum value and the multi-domain structure changes into the single domain one. When the nanoparticle size continues to decrease below the single domain value, the coercivity decreases to zero and the system becomes superparamagnetic with no hysteresis (Figure 1.14).

Different magnetic nanoparticles have various critical sizes shown in Figure 1.15.

Figure 1.13 Schematic representation of spin magnetic moments for superparamagnetism.³⁷

Figure 1.14 Qualitative illustration of the behavior of the coercivity in ultrafine particle system as the particle size changes.³⁷

Figure 1.15 Single domain size, Dcrit and magnetic stability size or the superparamanetic limit at room temperature, Dsp for some common ferromagnetic materials.³⁷

1.5.7 Hysteresis curve

A hysteresis loop shows the relationship between the induced magnetic flux density (B) and the magnetizing force (H). It is often referred to as the B-H loop. An example hysteresis loop is shown in Figure 1.16.

Figure 1.16 Hysteresis loop of ferromagnetic material.³⁵

A ferromagnetic material is initially unmagnetized then it will follow the dashed line as H is increased. At point "S" almost all of the magnetic domains are aligned and the material has reached the point of magnetic saturation. When H is reduced to zero, the curve will move from point "S" to point "R". At this point, there exists a residual B field that is called the remanence, or remanent flux density, B_r, the material remains magnetized in the absence of an external H field. As the magnetizing force is reversed, the curve moves to point "C", where the flux has been reduced to zero. This is called the point of coercivity on the curve. The force required to remove the residual magnetism from the material is called the coercive force or coercivity of the material (Hc). As the magnetizing force is increased in the negative direction, the material will again become magnetically saturated but in the opposite direction (point

"S’"). A second reversal of the field to the point of the initial saturation (point S) completes the symmetrical hysteresis loop and also yields both a negative romance (-Br) and a positive coercivity (+Hc).