**2.6.2 Paramagnetism**

Paramagnetic materials possess a permanent dipole moment due to incomplete cancellation of electron spin and/or orbital magnetic moments. In the absence of an applied magnetic field the dipole moments are randomly oriented; therefore the material has no net macroscopic magnetization. When a field is applied these moments tend to align by rotation towards the direction of the field and the material acquires a net magnetization (Figure 11) [3].

Fig. 11. Schematic of atomic dipoles for a paramagnetic material.

## **2.6.3 Ferromagnetism and ferrimagnetism**

Ferro and ferri-magnetic materials possess a permanent magnetic moment in the absence of an external field and a very large permanent magnetization [3]. In ferromagnetic materials, this permanent magnetic moment is the result of the cooperative interaction of large numbers of atomic spins in what are called domains, regions where all spins are aligned in the same direction (see section2.5).In ferrimagnetic materials, on the other hand, incomplete cancellation of the magnetic dipoles in a domain results in lower permanent magnetization (Figure 12) [5].

The macroscopic magnetization of ferro- and ferri-materials is the sum of the magnetizations of the domains which make up the sample [3]. Ferrimagnets are ionic solids meaning that they are electrically insulating, whereas most ferromagnets are metals (conductors) [4].

field, as illustrated in Figure 10), described by a negative susceptibility. These materials tend

Paramagnetic materials possess a permanent dipole moment due to incomplete cancellation of electron spin and/or orbital magnetic moments. In the absence of an applied magnetic field the dipole moments are randomly oriented; therefore the material has no net macroscopic magnetization. When a field is applied these moments tend to align by rotation towards the

Ferro and ferri-magnetic materials possess a permanent magnetic moment in the absence of an external field and a very large permanent magnetization [3]. In ferromagnetic materials, this permanent magnetic moment is the result of the cooperative interaction of large numbers of atomic spins in what are called domains, regions where all spins are aligned in the same direction (see section2.5).In ferrimagnetic materials, on the other hand, incomplete cancellation of the magnetic dipoles in a domain results in lower permanent magnetization (Figure 12) [5]. The macroscopic magnetization of ferro- and ferri-materials is the sum of the magnetizations of the domains which make up the sample [3]. Ferrimagnets are ionic solids meaning that they are electrically insulating, whereas most ferromagnets are metals

direction of the field and the material acquires a net magnetization (Figure 11) [3].

to move toward regions of weaker field [5, 15].

**2.6.2 Paramagnetism** 

(conductors) [4].

Fig. 10. Atomic dipole configuration for a diamagnetic material.

Fig. 11. Schematic of atomic dipoles for a paramagnetic material.

**2.6.3 Ferromagnetism and ferrimagnetism** 

Fig. 12. Ordering of the atomic dipoles in a) ferromagnetic and b) ferrimagnetic material.

## **2.6.4 Antiferromagnetism**

In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins (on different sublattices) pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. Generally, antiferromagnetic order may exist at sufficiently low temperatures, vanishing at and above a certain temperature, the Néel temperature (Neel temperature is the temperature at which an antiferromagnetic material becomes paramagnetic; hence losing its magnetic properties) [16].Above the Néel temperature, the material is typically paramagnetic. Figure13 shows ordering of the atomic dipoles in an antiferromagnetic material

Fig. 13. Ordering of the atomic dipoles in an antiferromagnetic material.

#### **2.6.5 Superparamagnetic**

Superparamagnetism is a phenomena by which magnetic materials may exhibit a behavior similar to paramagnetism at temperatures below the Neel or the Curie temperature (The Curie temperature is the temperature at which a ferromagnetic or a ferromagnetic material becomes paramagnetic; hence losing its magnetic properties).Normally, coupling forces in magnetic materials cause the magnetic moments of neighboring atoms to align, resulting in very large internal magnetic fields. At temperatures above the Curie temperature (or the Neel temperature for antiferromagnetic materials), the thermal energy is sufficient to overcome the coupling forces, causing the atomic magnetic moments to fluctuate randomly.

Crystalization in Spinel Ferrite Nanoparticles 361

High coercivity

Not important, but low High anisotropy Not important High Tc

High-energy product Not important

High saturation magnetization (0.3-1.6T)

Soft magnetic Hard magnetic

Table 2. The comparative properties of soft and hard magnetic materials

**3. Established methods for synthesis of nanocrystalline ferrites** 

There are two methods for the preparation of magnetic nanoparticles: physical and chemical. The methods of generation of magnetic nanoparticles in the gas or solid phase using high-energy treatment of the material are usually called physical, while the nanoparticle syntheses, which are often carried out in solutions at moderate temperatures are chemical methods. Different routes have become an essential focus of the related research and development activities. Various fabrication methods to prepare spinel ferrites nanocrystals have been reported, e.g., sol-gel methods [18], the ball-milling technique [19], co-precipitation [20], polymeric assisted route [21] the hydrothermal method [22], the reverse micelles process [23], and the micro-emulsion method [24]. Various precipitation agents have been used to produce specific size and shape spinel ferrites nanocrystals, e.g., metal hydroxide in the co-precipitation method, surfactant and ammonia in the reverse micelles process and various micro-emulsion methods, and organic matrices in the sol-gel method. Most of these methods have achieved particles of the required sizes and shapes, but they are difficult to employ on a large scale because of their expensive and complicated procedures, high reaction temperatures, long reaction times, toxic reagents and by-products,

In the present study, spinel ferrites nanocrystals with different structures were prepared from an aqueous solution containing metal nitrates, poly (vinyl pyrrolidon), and deionized water using a relatively low temperature thermal treatment method, followed by grinding and calcinations\*. No other chemicals were added to the solution. This method is environmentally friendly in that it neither uses nor produces toxic substances, and it offers the advantages of simplicity, low cost, and low reaction temperatures. The textural and morphological characteristics of the spinel ferrites nanocrystals we prepared were studied with various techniques to determine the influence of calcination temperature on the crystallization, morphology, and particle size distribution of the nanocrystals and to explore

This method was invented by Mahmoud Goodarz Naseri in university Putra Malaysia in 2011

High saturation magnetization (1-2T)

and their potential harm to the environment.

**3.1 Thermal treatment method** 

other parameters of interest.

 \* Low coercivity (Hc) High permeability Low anisotropy Low magnetostriction High Curie temperature (Tc)

High electrical resistivity

Low losses

Because there is no longer any magnetic order, the internal magnetic field no longer exists and the material exhibits paramagnetic behavior. Superparamagnetism occurs when the material is composed of very small crystallites (lower than 100 nm). In this case even though the temperature is below the Curie or Neel temperature and the thermal energy is not sufficient to overcome the coupling forces between neighboring atoms, the thermal energy is sufficient to change the direction of magnetization of the entire crystallite. The resulting fluctuations in the direction of magnetization cause the magnetic field to average to zero. The material behaves in a manner similar to paramagnetism, except that instead of each individual atom being independently influenced by an external magnetic field, the magnetic moment of the entire crystallite tends to align with the magnetic field. The energy required to change the direction of magnetization of a crystallite is called the crystalline anisotropy energy (see section 2.5) and depends both on the material properties and the crystallite size. As the crystallite size decreases, so does the crystalline anisotropy energy, resulting in a decrease in the temperature at which the material becomes superparamagnetic [17]. Ordering of the atomic dipoles in a superparamagnetic material is shown in Figure 14.

Fig. 14. Ordering of the atomic dipoles in a superparamagnetic material.

#### **2.7 Classification and applications of ferrites**

Ferrites are grouped into two types, soft and hard. This is the classification based on their ability to be magnetized and demagnetized, not their ability to withstand penetration or abrasion. Soft materials are easy to magnetize and demagnetize, so are used for electromagnets, while hard materials are used for permanent magnets. They can also be classified based on their coercive field strength into soft and hard materials [12]. With soft magnetic materials the hysteresis loop is small (low coercive field strength, independent of magnetic field amplitude); with hard magnetic however it is large (high coercive field strength). Table 2 gives a comparative account of both types.


Hard ferrite magnets are made in two different magnetic forms: isotropic and oriented. Isotropic magnets are formed to desired shapes, sintered and then magnetized. These exhibit a modest magnetic field and find applications in cycle dynamos and ring magnets. Oriented magnets are formed to shape under a strong magnetic field and then sintered. These exhibit a very strong magnetic field and find applications in loudspeakers, magnets of two wheelers like scooters, etc. [14].

Because there is no longer any magnetic order, the internal magnetic field no longer exists and the material exhibits paramagnetic behavior. Superparamagnetism occurs when the material is composed of very small crystallites (lower than 100 nm). In this case even though the temperature is below the Curie or Neel temperature and the thermal energy is not sufficient to overcome the coupling forces between neighboring atoms, the thermal energy is sufficient to change the direction of magnetization of the entire crystallite. The resulting fluctuations in the direction of magnetization cause the magnetic field to average to zero. The material behaves in a manner similar to paramagnetism, except that instead of each individual atom being independently influenced by an external magnetic field, the magnetic moment of the entire crystallite tends to align with the magnetic field. The energy required to change the direction of magnetization of a crystallite is called the crystalline anisotropy energy (see section 2.5) and depends both on the material properties and the crystallite size. As the crystallite size decreases, so does the crystalline anisotropy energy, resulting in a decrease in the temperature at which the material becomes superparamagnetic [17]. Ordering of the atomic dipoles in a superparamagnetic material is shown in Figure 14.

Fig. 14. Ordering of the atomic dipoles in a superparamagnetic material.

Ferrites are grouped into two types, soft and hard. This is the classification based on their ability to be magnetized and demagnetized, not their ability to withstand penetration or abrasion. Soft materials are easy to magnetize and demagnetize, so are used for electromagnets, while hard materials are used for permanent magnets. They can also be classified based on their coercive field strength into soft and hard materials [12]. With soft magnetic materials the hysteresis loop is small (low coercive field strength, independent of magnetic field amplitude); with hard magnetic however it is large (high coercive field

Hard ferrite magnets are made in two different magnetic forms: isotropic and oriented. Isotropic magnets are formed to desired shapes, sintered and then magnetized. These exhibit a modest magnetic field and find applications in cycle dynamos and ring magnets. Oriented magnets are formed to shape under a strong magnetic field and then sintered. These exhibit a very strong magnetic field and find applications in loudspeakers, magnets of

**2.7 Classification and applications of ferrites** 

Hc < 10 A/Cm: soft magnetic;

two wheelers like scooters, etc. [14].

strength). Table 2 gives a comparative account of both types.

Hc > 300 A/Cm: hard magnetic (permanent magnets).


Table 2. The comparative properties of soft and hard magnetic materials
