# Classification of Magnetic Materials

Bohr Magneton

The Bohr magneton “μ”

B is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.

μB=$\frac{eh}{2me}$

where e is the elementary charge, ℏ is the reduced

Planck's constant, m

e is the electron rest mass.

The value of Bohr magneton in SI units is

9.27400968(20) ×10−24 JT−1

Relationship between Magnetic Permeability and Magnetic Susceptibility:

•       Magnetic susceptibility (χ) and magnetic permeability (μ) are related through the following equation: χ = μ - 1.
•       This equation signifies that magnetic susceptibility measures the deviation of a material's magnetic permeability from that of a vacuum (μ = 1).

Curie's law

According to Curie's law, the magnetization of a paramagnetic material is directly proportional to the applied field. When an object is heated, magnetization is considered to be inversely proportional to temperature.

The law was invented by the French physicist Pierre Curie.

Curie's law formula

Curie's law can be formulated as an equation.

M=C x (B/T)

where,

M=Magnetism

B=magnetic field (in Tesla)

T=absolute temperature (in Kelvin)

C=Curie's constant

Curie's law applies to high temperatures and not-so-strong magnetic fields.

Curie temperature:

The Curie temperature is the temperature at which a ferromagnetic material becomes paramagnetic when heated. This type of offset is used to delete and insert new data on optical media.

Hysteresis:

Definition: The meaning of hysteresisis "lag". Hysteresis is characterized by the lag of the magnetic flux density (B) after the magnetic field strength (H). All ferromagnetic materials exhibit the phenomenon of hysteresis. To better understand the concept, let's take an example where a ferromagnetic substance is placed inside a current carrying coil. Due to the existing magnetic field the matter becomes magnetized. When we change the direction of the current, the material is demagnetized and this process is called hysteresis. Systems with hysteresis are usually non-linear. Therefore, it can be mathematically difficult for some hysteresis models, such as the Preisach model and the Bouci-Wen model. In addition, there are phenomenological models of certain phenomena, such as the Jiles-Atherton model, which is used to describe ferromagnetism.

Types of hysteresis

There are two types of hysteresis.

Speed-Dependent Hysteresis: In this type of hysteresis, there is a delay between the input and the output. As an example, we can take a sinusoidal input X(t), which gives a sinusoidal output Y(t) with a phase delay φ:

X(t)=X0sin ωtY(t)=Y0sin (ωt-φ).

Rate-independent hysteresis: This hysteresis in systems tends to have a permanent memory of the past that persists even after transient disturbances have disappeared.

Hysteresis loop

The hysteresis loop shows the relationship between the magnetic flux density and the strength of the magnetizing field. The loop is formed by measuring the magnetic flux leaving the ferromagnetic material by changing the external magnetizing field.

Looking at the graph, when B is measured for different values of H and the results are plotted graphically, the graph shows a hysteresis loop.

The magnetic flux density (B) increases when the magnetic field strength (H) is increased from zero (zero). As the magnetic field increases, the value of magnetism increases and finally it reaches a point A, called the saturation point, where B is constant. As the value of the magnetic field decreases, the value of magnetism decreases. But when B and H are zero, when the substance or material retains some magnetism, it is called retentive or residual magnetism. As the magnetic field weakens towards the negative side, the magnetism also decreases. At point C, the substance is completely demagnetized. The force required to remove the restraint of the material is called the coercive force (C). In the opposite direction, the cycle is continued with saturation point D, retention point E and binding force F. Due to the forward and reverse process, the cycle is complete and this cycle is called the hysteresis loop.

Advantages of the hysteresis loop

1. A smaller area of the hysteresis loop indicates a smaller hysteresis loss.

2. The hysteresis loop provides the substance that has the meaning of restraint and coercion. Therefore, choosing the right material to make a permanent magnet is simplified thanks to the heart of the machines. 3. The residual magnetism can be calculated from the B-H diagram, and therefore the material selection of the electromagnets is easy.

Retentivity and Coercivity

If a ferromagnetic material is magnetized by an external magnetizing field, after magnetization, if we remove the external magnetizing field, the material will not relax back to the zero magnetization position.

Retentivity

The magnetization that occurs when the external magnetizing field is removed is called retentivity.

It is the ability of a material to retain a certain part of its magnetic properties when an external magnetizing field is removed. The value of B at point b of the hysteresis loop.

Coercive force

The magnitude of the reverse (-ve H) external magnetizing field required to completely demagnetize a substance is called the coercivity of the substance.

The value of H at point c in the hysteresis loop.

Applications of hysteresis:

Hysteresis is mostly found in chemistry, physics, engineering, economics, and biology. In addition, common examples include magnetic hysteresis, ferroelectric hysteresis, superconducting hysteresis, mechanical hysteresis, optical hysteresis, electron beam hysteresis, adsorption hysteresis, economic hysteresis, etc. Anyway, let's look at some important uses of hysteresis.

There are several hysteresis applications for ferromagnets. It is mostly used to store memory such as hard drives, magnetic tape and credit cards. Hysteresis is used in many artificial systems, such as thermostats and Schmitt triggers, designed to prevent unwanted repetitive or unwanted rapid switching. Hysteresis is sometimes an intentionally made part of computer algorithms. Hysteresis can be observed when reducing the angle of attack of the wing after stall in terms of lift and drag coefficients. The presence of bubble-like hysteresis has important implications for rheological experiments at interfaces involving bubbles. In biology, it is found in cell biology and genetics, immunology. neuroscience, respiratory physiology, speech and speech physiology, ecology, and epidemiology. Basically, hysteresis is encountered in many different disciplines and has many uses.

Energy loss due to hysteresis:

A transformer is the best example to study energy losses due to hysteresis, because we know that energy is required in the process of magnetization and demagnetization. The magnetization and demagnetization of magnetic materials consumes energy, and this consumed energy manifests itself in the form of heat. This heat loss is called hysteresis loss. The energy loss per unit volume of the substance is equal to the area of the hysteresis curve. Due to the constant magnetization and demagnetization process of transformers, energy is continuously lost in the form of heat; because of this, the energy loss efficiency of the transformer decreases. To stop this energy loss, transformers use a soft iron core because the energy loss or hysteresis loss of soft iron is much lower than other materials.

Diamagnetism

Diamagnetic substances tend to move from the stronger part of the external field to the weaker part. A magnet can also be said to repel diamagnetic substances.

A diamagnetic substance in a magnetic field

Consider the image above. We have a diamagnetic substance placed in an external magnetic field. We see that the material repels the field lines and the field inside the material decreases. If we place this substance in a non-uniform magnetic field, it will tend to move from a point with a strong electric field to a point with a low electric field.

Paramagnetism

Paramagnetic substances are substances that are weakly magnetized under the influence of an external magnetic field. In the presence of an external field, these substances tend to move from a region of weak field to a region of strong field. In other words, we can say that these substances are weakly attracted by a permanent magnet. In a paramagnetic material, individual atoms have a dipole moment, which, when placed in a magnetic field, interact with each other and spontaneously align in a common direction, leading to its magnetization. According to Curie's law, the magnetism of a paramagnetic substance is inversely proportional to the absolute temperature until it reaches saturation.

Ferromagnetism

Diamagnetism-paramagnetism-and-ferromagnetism

Ferromagnetic substances are substances that become strongly magnetized when placed in an external magnetic field. In addition, they tend to move from a weak region to a strong magnetic field and become strongly attracted to the magnet. In a ferromagnetic material, the dipole moment of individual atoms is similar to that of a paramagnetic material. When atoms are placed in a magnetic field, they interact with each other and spontaneously align in a common direction. The direction is common to the macroscopic volume, which we call the domain. The domain has a net magnetization, and each domain is self-directed, resulting in its strong magnetization.