Magnetic Materials (Unit 3) PDF

# 3. Magnetic Properties of Materials ## Introduction A very large number of modern devices utilize magnetic properties of materials. Examples of such devices: - speakers - electrical power generators - electrical machines - transformers - television - data storage devices like magnetic tapes and...

# 3. Magnetic Properties of Materials ## Introduction A very large number of modern devices utilize magnetic properties of materials. Examples of such devices: - speakers - electrical power generators - electrical machines - transformers - television - data storage devices like magnetic tapes and disks - magnetic compass - MRI (Magnetic Resonance Imaging) scan- an important non-invasive diagnostic tool used in the medical field. An understanding of the origin of magnetism and the behavior of magnetic materials is valuable for: - selecting suitable materials for a particular application - proper utilization of such devices - designing new applications of these materials. ## Magnetism in Materials The origin of magnetism in materials stems from the magnetic moment or magnetic dipole of the magnetic materials. - **Orbital magnetic moment:** When an electron revolves around the positive nucleus, orbital magnetic moment arises. - **Spin magnetic moment:** Similarly, when the electron spins, spin magnetic moment arises. ## Materials Materials which can be magnetized by an external magnetic field are called magnetic materials. - **Magnetic field:** The space around the magnet or the current-carrying conductor where the magnetic effect is felt is called the magnetic field. - **Magnetic lines of force:** A continuous curve in a magnetic field, with the tangent at any point on the curve indicating the direction of resultant intensity at that point. All the molecules of a material contain electrons rotating around the nucleus. These orbits are equivalent to circulating currents, producing a magnetic motive force (m.m.f.). The force produces the magnetic effect. - In most molecules, each m.m.f. due to an individual orbit is neutralized by an opposite one. - In magnetic materials like iron and steel, there are a number of unneutralized orbits. - The resultant axis of m.m.f. produces a magnetic dipole. In unmagnetized specimens, the molecular m.m.f. axes line up along continuous closed paths resulting in no external magnetic effect. In magnetic specimens, the magnetic dipoles line up parallel with the exciting m.m.f. When the exciting m.m.f. is removed, the magnetic dipoles may remain aligned in the direction of the external field, thus leading to permanent magnetism. ## Basic Definitions Terms and definitions for understanding magnetic properties: - **Magnetic Pole Strength:** The magnetic pole strength of a pole is said to be unity when it experiences a force of 1 Newton when placed at a distance of 1 meter from a similar pole in air (or vacuum). - **Magnetic Dipole Moment (m):** The product of magnetic pole strength and the distance between the two poles. - **Magnetic Flux ($):** The total number of magnetic lines of force passing through a surface. Represented by the symbol $\phi$ and its unit is weber (Wb). - **Magnetic Flux Density (or) Magnetic Induction (B):** Magnetic flux density at a point in a magnetic field is defined as the magnetic field strength (Φ) passing normally through unit area of cross section (A) at that point. Represented by the symbol “B” and its unit is weber/metre² (Wb/m²) or tesla (T). $B=\frac{Φ}{A}$ weber/metre² or tesla(T) This is also called magnetic induction. - **Intensity of Magnetisation (I):** The process of converting a non-magnetic material into a magnetic material. Defined as the magnetic moment per unit volume of the material. $I=\frac{M}{V}$ weber/metre² where: - M → Magnetic moment of the substance - V→ Volume of the specimen - **Magnetic Field Intensity (or) Strength (H):** Magnetic field intensity at a point in a magnetic field is the force experienced by a unit north pole placed at that point. Represented by the symbol “H,” and its unit is newton per weber (N/Wb) or ampere turns per metre (A/m). - **Magnetic Permeability (μ):** Measures how easily a magnetic field can penetrate through the substance. $B=μH$ where μ is a constant of proportionality. Known as permeability or absolute permeability of the medium. $\mu=\frac{B}{H}$ Thus, the permeability of a substance is the ratio of magnetic flux density (B) inside the substance to magnetic field intensity (H). Absolute permeability of a medium or a material is defined as the product of the permeability of free space (μ₀) and the relative permeability (μᵣ) of the medium. $μ=μ₀×μᵣ$ $μᵣ=\frac{μ}{μ₀}$ The relative permeability is a dimensionless quantity, with a value of “1” for air and non-magnetic material. - **Magnetic Susceptibility (x):** A measure of how easily a specimen can be magnetized in a magnetic field. Defined as the intensity of magnetization produced in the substance per unit magnetic field strength (H). $x=\frac{I}{H}$ It is a dimensionless quantity. Magnetic induction in a given magnetic material for an applied field strength “H” is expressed as: - $B=μ₀(H+I)$ - $B=μ₀H(1+\frac{I}{H})$ - $B=μ₀(1+ x)H$ - $ x=\frac{I}{H} $ $= (μ-1)$ $B=μH= μ₀μᵣH$ ….(2) $μr = 1 + x $ …..(4) $x=μ-1$ - **Atomic Magnetic Moments:** The response of a material to an external magnetic field stems from the atoms’ possession of magnetic moments. Each atom acts like a tiny magnet. - **Orbital Magnetic Moment:** The motion of electrons in orbits around the nucleus, i.e., due to orbital angular momentum. This is called the orbital magnetic moment. - **Spin Magnetic Moment:** The spin of the electrons, i.e., due to spin angular momentum. This is called spin magnetic moment. In addition to the above two contributions, there is a small contribution due to the spin angular momentum of the nucleus, called the nuclear magnetic moment. However, the nuclear magnetic moments are significantly smaller (the magnitude of the nuclear magnetic moment is about 10³ times less than the electronic magnetic moment) and their interaction with the external field is masked by the interaction of the electronic magnetic moment. The nuclear magnetic moment can be detected by a technique called nuclear magnetic resonance. - **Orbital Motion of Electron:** The orbital motion of electron revolving about a nucleus is akin to a tiny current loop. This produces a magnetic moment perpendicular to the plane of the orbit. - **Derivation:** Let us consider an electron moving with a constant speed ‘v’ in a circular orbit of radius r. - Let T be the time taken for one revolution, and ‘e’ be the magnitude of charge on the electron. - Current I across any point in the orbit (charge of the electron/time) : $I= \frac{e}{T}$ …(1) - Magnetic moment associated with the orbit: $μL= Current × Area of the orbital (loop)$ $μL= IA = \frac{-e}{T} × πr²$ …(2) - The time taken for one complete revolution is T, so the distance travelled (angular displacement) by the electron in time T is 2πr (circumference of the orbit). - Velocity v = 2πr/T (or) T = 2πr/v - Substituting T in equation (2), we obtain: $μL = \frac{-e × 2πr}{2πr/v}πr²$ $μL = \frac{evr}{2}$ ……(4) - Dividing and multiplying the R.H.S. of equation (4) by m (mass of the electron), we get: $μL = \frac{-evr}{2} × \frac{m}{m}$ $μL = \frac{emuvr}{2m}=\frac{eL}{2m}$ …(5) where L = mur is the orbital angular momentum of the electron. Equation (5) expresses the magnetic moment associated with orbital electron motion. The negative sign indicates that the magnetic moment vector and angular momentum vector are in opposite directions (Fig. 3.2 (c)). - **Bohr Magneton:** The magnetic moment contributed by an electron with angular momentum quantum number $n=1$ is known as Bohr magneton. $μL = \frac{- eL}{2m}$ …(1) According to quantum theory, orbital angular momentum: $L = nh = n × \frac{h}{2π}$ where n is the orbital angular momentum quantum number. Substituting L in equation (1) we get: $μL = \frac{e}{2m} × \frac{nh}{2π}$ For n = 1, the electron is in the ground state (Bohr orbit): $μL = \frac{eh}{4 πm}$ …(2) The negative sign is often omitted because it simply indicates the opposite directions of the magnetic moment and angular momentum. This magnetic moment is defined as one Bohr magneton (μB): $μB = \frac{eh}{ 4 πm}$ …(3) Substituting the values of the constants in the above equation: $μB = \frac{ 1.6 × 10^{-19} × 6.625 × 10^{-34}}{4 × 3.14 × 9.1 × 10^{-31}}$ $μB = 9.274 × 10^{-24} ampere metre^2 $ $or Am^2 $. $1μB = 9.274 × 10^{-24} \frac{Am^2}{electron} $ -**Magnetic Moment due to Spin of Electron:** Similar to orbital motion, the magnetic moment due to spin motion of the electron (Fig. 3.3(a)) is given by: μS = $\frac{e}{m}$ $(S)$ Where S is the spin momentum. The spin quantum number (s) takes the values of +1/2 or -1/2. ## Classification of Magnetic Materials Magnetic materials are categorized into two types: (i) **Diamagnetic materials:** no permanent magnetic moment (ii) **Paramagnetic, ferromagnetic antiferromagnetic and ferrimagnetic materials:** having permanent magnetic moment. Diamagnetic materials have a very weak response to an external magnetic field and are termed “non-magnetic materials.” ## Diamagnetism Diamagnetism is exhibited by all materials. - **Diamagnetic materials:** Atoms in diamagnetic materials lack a permanent magnetic moment. - **Magnetic field effect:** When a diamagnetic material is placed in an external magnetic field, electrons in the atomic orbits counter theexternal magnetic field. As a result, the material becomes magnetized with an induced magnetic moment opposite to the direction of the externally applied magnetic field. - **Repulsion:** The diamagnetic material is very weakly repelled in the magnetic field. This phenomenon is known as diamagnetism. The schematic illustration in Fig. 3.4 illustrates this concept. - **Properties of Diamagnetic materials:** - Diamagnetic materials repel the magnetic lines of force. - The behavior of a perfect diamagnetic material in the presence of the magnetic field is shown in fig. 3.5. - No permanent dipole moment. - Magnetic effects are very small in these materials. - The magnetic susceptibility is negative. - Its value depends on neither temperature nor applied magnetic field strength. - Examples: gold, germanium, and silicon ## Paramagnetism Certain materials possess a permanent dipole moment even in the absence of an external magnetic field. - **Paramagnetic materials:** Atoms in paramagnetic materials have a net permanent magnetic moment. The magnetic moment is randomly oriented which results in a net zero magnetic moment and zero magnetization in the absence of an external magnetic field (Fig. 3.6 (a)). - When an external magnetic field is applied, magnetic dipoles align themselves in the direction of the magnetic field (Fig. 3.6(b)), leading to an increase in magnetization of the material, known as paramagnetism. - **Properties of Paramagnetic Materials:** - Paramagnetic materials attract the magnetic lines of force. - They possess permanent dipole moments. - The value of susceptibility is positive and depends on the temperature. - The magnetic susceptibility varies inversely with temperature, expressed as: $x = \frac{C}{T}$ - This is known as Curie’s law of paramagnetism. C is a constant known as Curie’s constant. - The spin alignment is shown in fig. 3.7. - Examples: Manganous sulphate, ferric oxide, ferrous sulphate, and nickel sulphate ## Ferromagnetism Certain metals, like iron (Fe), cobalt (Co), nickel (Ni), and certain alloys, exhibit a high degree of magnetization. - **Ferromagnetic materials:** Ferromagnetic materials exhibit spontaneous magnetization, meaning their atomic magnetic moments are aligned even in the absence of an external magnetic field. This characteristic arises from the strong internal field within the material, aligning atomic magnetic moments. - **Origin of Ferromagnetism:** The ferromagnetic property is exhibited by transition elements seperti iron, cobalt, and nickel at room temperature and rare earth elements like gadolinium and dysprosium. - **Parallel alignment:** Ferromagnetic materials have parallel alignment of dipoles. This parallel alignment is not attributed to the magnetic force existing between any two dipoles. The reason for parallel alignment is the very low magnetic potential energy compared to the thermal energy. - **Electronic Configuration:** Let's take the example of iron, whose electronic configuration is $1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 3d^6, 4s^2$. - The $3d$ subshell lacks filled orbitals. There are five orbitals in this subshell. - Six electrons occupy the 3d subshell. This arrangement results in four unpaired electrons and two paired electrons (Fig. 3.8). - These four unpaired electrons contribute a magnetic moment of $4μB$. This arrangement demonstrates the parallel alignment of four unpaired electrons. - The parallel alignment of dipoles in iron is not rooted in magnetic interaction. It stems from the Pauli's exclusion principle and electrostatic interaction energy. - **Exchange Interaction:** Pauli's exclusion principle and electrostatic interaction energy combine to create a new kind of interaction called exchange interaction. This interaction is a quantum mechanical concept. - The exchange interaction between any two atoms depends on the interatomic separation between the two interacting atoms and the relative spins of the two outer electrons. - The expression for the exchange interaction between any two atoms is: $E_{ex}=-J_{e}S_{1}S_{2}$ where: - $J_{e}$ is the numerical value of the exchange integral. - $S_{1}$ and $S_{2}$ are the spin angular momenta of the first and second electrons, respectively. The exchange integral value is negative for certain elements. - The minimal energy configuration occurs when the spin angular momentum $S_{1}$ and $S_{2}$ are in opposite directions. This explains the antiparallel alignment of dipoles favored in antiferromagnetic materials. In iron, cobalt, and nickel, the exchange integral value becomes positive. The exchange energy becomes negative when the spin angular momentum is in the same direction causing the parallel alignment of magnetic dipoles. - A plot of the exchange integral versus the ratio of interatomic separation to the radius of 3d orbital (r/rd) (Fig. 3.9) illustrates this concept. - The positive value of the exchange integral signifies ferromagnetic material, whereas the negative value signifies antiferromagnetic materials. Generally, if the ratio r/rd > 3, the material is ferromagnetic. - For manganese, it is observed that antiferromagnetic material can be suitably alloyed so that r/rd > 3, leading to the material exhibiting ferromagnetism. - **Saturation Magnetisation:** The maximum magnetization in a ferromagnet when all the atomic magnetic moments are aligned, termed saturation magnetization (Msat). - **Curie Temperature (Tc):** Magnetic behavior disappears at a critical temperature called Curie temperature. At Curie temperature, the thermal energy of lattice vibrations overwhelms the potential energy of exchange interaction, destroying the spin alignment of ferromagnetic materials. Above Curie temperature, ferromagnetic materials behave like paramagnetic materials. Saturation magnetization decreases from its maximum value (Msat(0) at absolute zero temperature) to zero at Curie temperature. Fig. 3.10 shows the dependence of Msat on temperature, with Msat (0) being the saturation magnetization at 0 Kelvin. - **Curie Weiss Law:** Susceptibility of Ferromagnetic material is given as: $x= \frac{C}{T-Tc} $ Where C represents the Curie constant. - Table 3.1 provides Curie temperature values (Tc) for various ferromagnetic substances, along with their saturation magnetization (Msat). ## Domain Theory of Ferromagnetism Weiss proposed the concept of domains to explain the properties of ferromagnetic materials. - **Magnetic domains:** Tiny bounded regions in the ferromagnetic materials containing a group of atomic dipoles (atoms with permanent magnetic moments) aligned in the same direction and exhibiting a net magnetic moment. Each domain serves as a magnet, having its own magnetic moment and axis. - **Demagnetized ferromagnetic materials:** Domains are randomly aligned, resulting in zero net magnetization (Fig. 3.11 (a)). - **Magnetized ferromagnetic materials:** When an external magnetic field is applied, domains align themselves with the field (fig. 3.11 (b)), which results in a large net magnetization of the material. - **Bloch walls:** The domain walls are also known as Bloch walls. ## Process of Domain Magnetisation Initially, in an unmagnetized specimen, domains are randomly oriented, and net magnetization is zero. When an external magnetic field is applied, domains align with the field direction leading to a large net magnetisation of the material. - **Domain wall motion:** Two mechanisms govern this alignment process: - **Motion of domain walls:** The domain walls move, expanding the domains aligned with the field at the expense of other domains (Fig. 3.12 (b)). - **Rotation of domains:** When a large external magnetic field is applied (near saturation), further domain growth becomes impossible, causing domain rotation to align with the field direction. This rotation brings the domains into alignment with the field direction (Fig. 3.12 (c)). - **Origin of Domains:** The free energy of a solid tends to reach a minimum. The domain structure arises to minimize the total free energy of a ferromagnetic solid. - **Types of Energy:** The total energy involved in the domain growth process: - **Exchange energy:** The quantum mechanical coupling that aligns individual atomic dipoles within a single domain stemming from the interaction of electron spins. It depends on the interatomic distance. Figure 3.13 (a) depicts a single domain structure in a ferromagnetic crystal. - **Magnetostatic energy:** The potential energy in a ferromagnetic material arises from the external magnetic field produced by the material. Its presence is due to the resultant dipole moment in the material, even without an external magnetic field. - The magnetic energy of the specimen can be reduced by dividing a single domain into two domains (Fig. 3.13 (b)). - Dividing a single domain into N domains (fig. 3.13(c)) reduces the magnetic energy to 1 / N of the magnetic energy of the material with a single domain. - The introduction of triangular domains at the bottom and the top of the crystal (Fig. 3.13 (d) & (e)), called closure domains, helps to minimize the magnetic energies. - **Crystal anisotropy energy:** The energy of magnetisation that depends on the crystal orientation. - Magnetization curves for iron with an applied field along different crystallographic directions are plotted in fig. 3.14. This graph demonstrates the dependence of magnetic saturation on direction. - The energy variation required to achieve saturation in easy [100] direction compared to the hard [1, 1, 1] direction is referred to as crystal anisotropic energy. - **Magnetostrictive energy:** When a material is magnetised, it undergoes a change in dimensions known as magnetostriction. This deformation varies based on the crystal direction. The domains in the material are magnetized in different directions. These domains expand or shrink, causing work to be done against restoring forces. This work is known as magneto-elastic energy or magnetostrictive energy. ## Hysteresis – M vs. H Behaviour Hysteresis refers to the lagging effect that occurs when a ferromagnetic material is subjected to a magnetization cycle. Magnetization intensity and magnetic induction lag behind the magnetizing field. - **Lagging:** Even when the magnetizing field is reduced to zero, a residual magnetic property remains in the material, leading to a tendency for magnetization to persist (I and B lag behind H). This phenomenon is called hysteresis. - **Hysteresis loop:** This lagging effect is represented by a closed loop (or) curve, known as a hysteresis loop. - Figure 3.15 illustrates a hysteresis loop obtained by plotting magnetic field strength (H) along the X-axis and magnetic induction (B) along the Y-axis. - The magnetic induction (B) increases along curve OA with the magnetic field (H). - When the magnetic field (H) increases beyond point A, the magnetic induction stays constant even as the magnetic field increases, signifying the saturation of the specimen with magnetization. - As the magnetic field (H) decreases, the magnetic induction also decreases but at a slower rate. - When the magnetic field (H) reaches zero, the magnetic induction (B) takes on a specific value, represented by OB, known as retentivity. - When the magnetic field (H) is reversed and increased, the magnetic induction (B) increases along the curve, reaching zero at point C. - Point C represents the coercivity. - Upon further increase in the magnetic field (H), the magnetic induction increases along CD in the reverse direction. - If the magnetic field is reversed, the magnetic induction follows curve DEFA, completing a cycle of magnetization. - The curve ABCDEFA is called the hysteresis loop. - **Key observations from the hysteresis loop:** - The magnetic induction (B) lags behind the applied magnetic field strength (H), even when the field strength is zero. This lagging effect is called magnetic hysteresis. - **Retentivity or Residual magnetism:** At zero magnetic field strength, the magnetic induction (B) is not zero. This remnant magnetization is known as retentivity or residual magnetism. Represented by OB in the B-H curve (Fig. 3.15). - **Coercivity or Coercive force:** The magnetic field strength (H) required to reduce the residual magnetization to zero is called coercivity or coercive force. It is represented by OC in the B-H curve (Fig. 3.15). - **Hysteresis loss:** The area of the hysteresis loop represents the energy loss per cycle per unit volume of the specimen during the magnetization cycle. - **Explanation of Hysteresis Based on Domain Theory:** When a ferromagnetic material is placed in an external magnetic field, the domain walls move, and domains rotate, increasing the value of the resultant magnetic moment of the specimen. - **Domain wall motion:** When a small external magnetic field is applied, domain walls shift slightly along the direction of magnetization, leading to small magnetization, as shown in the initial part of the hysteresis curve (OA) in fig. 3.16. - **Domain wall return:** When the applied magnetic field is removed, reversible domains return to their original position. - **Domain wall growth:** If the magnetic field strength increases, a larger number of domains contribute to the magnetization, causing a rapid increase in magnetization (B) with H. - **Irreversible domain wall motion:** The displacement of domain walls due to a large magnetic field causes the domain boundary to move a significant distance, failing to return to the original position after the magnetic field is removed. - **Domain rotation:** Further increase of magnetic field causes domains to rotate in the field direction, enhancing the anisotropic energy stored in the hard direction as shown in fig 3.16 (BC). - At this point, the specimen reaches maximum magnetisation. - When the external magnetic field is removed, the specimen continues to exhibit magnetization due to residual (retentivity), represented by OD in fig. 3.16. - To reduce magnetization to zero requires a reverse magnetic field to overcome the effects of impurities, lattice imperfections, etc., which is known as coercivity (OE in fig. 3.16). ## Ferromagnetic Materials Ferromagnetic materials exhibit the ferromagnetism. - **Properties of Ferromagnetic materials:** - The magnetic dipoles align in parallel due to magnetic interaction between the dipoles. - Presence of permanent dipole moment. - They attract strongly to a magnetic field. - Exhibit spontaneous magnetization, i.e magnetisation occurs even in the absence of an external magnetic field. - Exhibit hysteresis, leading to a lag in magnetization with the applied magnetic field. - They lose their magnetization slowly upon heating. - Their dipole alignment is depicted in fig. 3.17. - The magnetic susceptibility is very high and depends on temperature. - $χ= \frac{C}{T-Θ} $ - Where C is the Curie constant and Θ is the ferromagnetic Curie temperature. - T>Θ, paramagnetic behavior. - T<Θ, ferromagnetic behaviour. - Examples: iron, cobalt, nickel, certain alloys. ## Antiferromagnetism Antiferromagnetic materials are magnetic materials that exhibit a small positive susceptibility of the order of 10⁻³ to 10⁻⁵. - **Sublattice Structure**: In antiferromagnetism, the magnetic moments of two sublattices in a crystal cell are equal in magnitude but in opposite directions, resulting in zero magnetization. - **Antiferromagnetic Materials:** These materials are referred to as antiferromagnetic materials. Examples: Manganese, chromium, ionic compounds like MnO, MnS, Cr₂O₃, NiCr. - **Properties of antiferromagnetic materials:** - Adjacent magnetic dipoles are antiparallel (Fig. 3.19) - Magnetic susceptibility primarily depends on temperature. - The magnetic susceptibility of antiferromagnetic materials is small and positive. - $χ=\frac{C}{T+Θ}$ (T>TN) Where TN is Neel temperature. - $χ \propto \frac{1}{T}$ ( T<TN) - The magnetic susceptibility initially increases slightly with the temperature. After surpassing the Neel temperature, it decreases with temperature. ## Ferrimagnetism Certain materials have magnetic moments in opposite directions but not with equal magnitude. These materials exhibit most of the properties of ferromagnetic materials. This uncompensated antiferromagnetic behaviour, known as ferrimagnetism, is evident. - **Ferrimagnetic materials/ Ferrites:** Materials exhibiting ferrimagnetism are known as ferrimagnetic materials or ferrites. - **Properties of Ferrites:** - Ferrites have a net magnetic moment. - Above Curie temperature (Tc), they behave like paramagnetic materials. Below Tc, they behave as ferrimagnetic materials. - Susceptibility of Ferrites is very large and positive. It depends on temperature. $χ= \frac{C}{T±Θ}$ (T> TN). - The spin alignment is antiparallel with different magnitudes (Fig. 3.20). - Mechanically, they are pure iron. - They exhibit high permeability and high resistivity. - They feature low eddy current loss and low hysteresis loss. - **Applications of Ferrites:** - Used for manufacturing permanent magnets. - Super-high frequency technology. - Production of cores for inductors and transformers used in telecommunication and low-power transformers. - Magnetic films for demagnetization processes. - Information storage devices like magnetic tapes and disks. - Producing ultrasonics. - Increasing sensitivity and selectivity in radio receivers - Microwave devices (gyrator, circulator, isolator) ## Types of Magnetic Materials Magnetic materials fall into two categories: - **Soft magnetic Materials:** Easy to magnetize and demagnetize. - They do not retain the alignment of magnetic domains after the removal of the external magnetic field. - Properties: - Can be easily magnetized and demagnetised. - High permeability. - Low residual magnetism. - Low coercivity. - Low hysteresis loss (Fig 3.21). - Low magnetic energy storage. - Examples: - Pure or ingot iron. - Cast iron (carbon content > 2.5 percent) - Carbon steel. - Silicon steel. - Manganese and nickel steel. - Permalloy. - Mumetal. - Perminvar. - Soft ferrites - Applications: - Designing of electrical machinery, DC machines, transformers and other devices. - Making turbo-alternator motors. - Construction of telecommunication equipment. - **Hard Magnetic Materials:** Retain their magnetism. Hard to demagnetize. - They retain the aligned magnetic domains even after removing the external magnetic field. - Properties: - Low permeability. - Strong magnetic repulsion. - High coercivity. - High retentivity - High magnetizing force is needed for magnetic saturation. - Large hysteresis loop area and energy loss (Fig 3.22). - High BH- product. - Examples: - Tungsten steel. - Cobalt steel. - Alini. - Alnico. - Cunife. - Hypernic. - Applications: - Making permanent magnets. - Motors and generators. - Heavy-duty instruments. - Portable and light-weight instruments. - Loudspeakers. - Electrical measuring instruments. Table 3.3 summarizes the key differences between soft and hard magnetic materials. ## Energy Product The energy product of a permanent magnet is the product of retentivity (B) and coercivity (H). This value represents the maximum amount of energy stored in the specimen. - For permanent magnets, higher energy product is desired. - Figure 3.23 illustrates the energy product for permanent magnets.