Magnetic Materials Chapter PDF

**[Magnetic Materials]** - **Introduction** - The phenomenon of magnetism is the one by which a material exerts either attractive or repulsive force on another. The fundamental source of magnetism is the rotation of electrically charged particles. Thus magnetic behavior of a materi...

**[Magnetic Materials]** - **Introduction** - The phenomenon of magnetism is the one by which a material exerts either attractive or repulsive force on another. The fundamental source of magnetism is the rotation of electrically charged particles. Thus magnetic behavior of a material can be drawn from the structure of atoms. - The electrons in atoms rotate around the nucleus in circular orbits. This orbital motion and its own spin cause magnetic moments on the atoms, which contribute to the magnetic behavior of materials. - Thus every material can respond to a magnetic field. However, the manner in which a material responds depends much upon its atomic structure, and determines whether the material will have strong or weak magnetic properties. - The first account of magnetism was given by the ancient Greeks. It originated from Magnesia, a Greek town and province in Asia Minor, the dialectal origin of the word \"magnet\" meaning \"the stone from Magnesia\" which consisted of magnetite (Fe~3~O~4~) and it was known that a piece of iron would become magnetized when rubbed with it. - For instance, it was seen in the 18th century that smaller pieces of magnetic materials were combined into a larger magnetic body that was found to have quite a substantial lifting power. - Progress inmagnetism was made after Oersted discovered in 1820 that a magneticfield could be generated using electric current. - Using this fact the first electromagnet was developed by Sturgeon in 1825. - Althoughmany scientists tackled the phenomenon of magnetism from the theoreticalside (Gauss, Maxwell and Faraday). It is mainlythe 20^th^ century physicists thosemust take the credit for giving a proper description of magnetic materialsand for laying the foundations of modern technology. - Many of our moderntechnological devices rely on magnetism and magnetic materials; - These include electrical power generators and transformers, electric motors, radio, television, telephones, computers, and components of sound and videoreproduction systems. - The permanent magnetic materials are essential in devices for storing energy in a static magnetic field. - The Major applications involve the conversion of mechanical energy to electrical energy and vice-versaor the exertion of a force on soft magnetic objects. - Curie and Weiss succeeded in clarifying the phenomenon of spontaneousmagnetization and its temperature dependence. - The existence of magneticdomains was postulated by Weiss to explain how a material could bemagnetized and nevertheless have a zero net magnetization. - The properties of the walls of such domains were studied in detail by Bloch,Landau and Neel. - Iron, some steels, and the naturally occurring mineral lodestone are well known examples of materials that exhibit magnetic properties. - Not so familiar, however, is the fact that all substances are influenced to one degree or another by the presence of a magnetic field. - **Terminology Related to Magnetism** - **Magnetic Dipoles** Magnetic dipoles are found to exist in magnetic materials, like the electric dipoles. A magnetic dipole is a small magnet composed of north and south poles instead of positive and negative charges. - **Magnetic Field Strength** The magnetic field strength is the externally applied magnetic field denoted by *H*. The magnetic field generated by means of a cylindrical coil (or solenoid) consisting of N closely spaced turns, having a length *l* and carrying a current *i*is given by*.* \ [\$\$\\mathbf{H}\\mathbf{=}\\mathbf{-}\\mathbf{\\ }\\frac{\\mathbf{\\text{Ni}}}{\\mathbf{l}}\$\$]{.math.display}\ The units of *H* are ampere-turns per meter, or just amperes per meter. - **Intensity of Magnetisation (I)** It is defined as the magnetic moment per unit volume of the magnetized substance \ [\$\$\\mathbf{I}\\mathbf{= \\ }\\frac{\\mathbf{M}}{\\mathbf{V}}\$\$]{.math.display}\ For a substance of length 2*l* and cross-sectional area a [\$\\mathbf{I}\\mathbf{= \\ }\\frac{\\mathbf{M}}{\\mathbf{V}}\$]{.math.inline}***=***[\$\\frac{\\mathbf{\\ }\\mathbf{m}\\mathbf{\\ }\\mathbf{\\times}\\mathbf{2}\\mathbf{l}}{\\mathbf{a}\\mathbf{\\ }\\mathbf{\\times}\\mathbf{2}\\mathbf{l}}\\mathbf{= \\ }\\frac{\\mathbf{m}}{\\mathbf{a}\\mathbf{\\ }}\$]{.math.inline} Thus, it can also be defined as pole-strength per unit area of cross-section. The intensity of magnetization is sometimes represented by M also. In that case, another symbol is used for the magnetic moment. - **Magnetic Susceptibility (**[**χ**~*m*~)]{.math.inline} It is the ratio of the magnetic moment per unit volume (I) to the magnetic field strength (H) of the magnetizing field. \ [\$\$\\mathbf{\\chi}\_{\\mathbf{m}}\\mathbf{= \\ }\\frac{\\mathbf{I}}{\\mathbf{H}}\$\$]{.math.display}\ It is positive for a paramagnetic material and negative for a diamagnetics. - **Relative Permeability (**µ~r~) It is the ratio of the magnetic permeability **(**µ) of the substance to thepermeability of the freespace **(**µ~0~). \ [\$\$\\mathbf{µ}\_{\\mathbf{r}}\\mathbf{= \\ }\\frac{\\mathbf{µ}}{\\mathbf{µ}\_{\\mathbf{0}}}\$\$]{.math.display}\ This can also be defined as the ratio of the magnetic flux density produced in the medium to that which would be produced in a vacuum by the same magnetizing force. - **Magnetic Flux Density** The magnetic induction, or magnetic flux density, denoted by B, represents the magnitude of the internal field strength within a substance that is subjected to an H field. The units for B are tesla or weber per square meter. Both B and H are magnetic field vectors. The relation between magnetic field strength and flux density is given by ***B* =** [**µ**]{.math.inline}***H*** Where [*µ* ]{.math.inline}is the permeability of a material which is a measure of the degree to which the material can be magnetized, or the ease with which a magnetic field (B) can be induced in the presence of an external field H. The magneticflux density due to magnetization in material can be written as below **B =** [**µ**~**0**~ **(H+I)**]{.math.inline}  - **Atom as a Magnetic Dipole** - Every current carrying coil behaves as a magnetic dipole and possesses a definite magnetic dipole moment like electric dipole moment of electric dipole. - In an atom electrons revolve around the nucleus in a closed orbit. Since electron is a chargedparticle, so it's orbiting around the nucleus is equivalent to a current carrying loop.Hence it behaves as a magnetic dipole. - The dipole moment (µ) of a magnetic dipole isequal to the product of pole strength (m) of any pole and the distance (l) between thepoles and it is directed from south pole to north pole i.e. **µ =*ml*** The unit of pole strength is A-m and of dipole moment is A-m^2^. - Since every current carrying coil behaves like a magnetic dipole and its dipole moment is given by µ =*NiA*, where N is the number of turns in the loop, *i* is the current through each turn, A is the area of each turn. - **Atomic Magnetic Moments** The **Magnetic Moment** on the atom arises due to (i) the orbital motion of the electrons and (ii) the electron spin. - **Orbital Magnetic Moment** - An electron circulating around the nucleus produces a small current like a coil, and generates a magnetic field. - This field can be considered as being produced or originated from a magnetic dipole with magnetic moment given by µ= *i x A*, where *i* is the current and A is the area of the orbit. - Let us consider that the electron moves in a circular path of radius rabout the nucleus. Then the current i.e. the charge passingthrough any point in theorbit per unit time will be given by \ [\$\$\\mathbf{i}\\mathbf{=}\\mathbf{-}\\mathbf{\\ }\\frac{\\mathbf{e}}{\\mathbf{T}}\\mathbf{= \\ }\\mathbf{-}\\frac{\\mathbf{\\text{ev}}}{\\mathbf{2}\\mathbf{\\text{πr}}}\$\$]{.math.display}\ Where *v* is the velocity of the electron in the orbit and T is time period of rotation in the orbit of the electron. The magnitude of magnetic dipole moment is given by **µ= *i X A*** [\$\\mathbf{= \\ }\\mathbf{-}\\frac{\\mathbf{\\text{ev}}\\mathbf{\\ }}{\\mathbf{2}\\mathbf{\\text{πr}}}\\mathbf{X}\\mathbf{\\ }\\mathbf{\\pi}\\mathbf{r}\^{\\mathbf{2}}\\mathbf{= \\ }\\mathbf{-}\\frac{\\mathbf{\\text{evr}}}{\\mathbf{2}}\$]{.math.inline} **Orbital Magnetic Moment of Revolving Electron and Angular Momentum** This magnetic dipole moment can be related with the angular momentum which is *L = mvr;* Accordingly \ [\$\$\\mathbf{µ}\\mathbf{= \\ }\\mathbf{-}\\frac{\\mathbf{\\text{ev}}}{\\mathbf{2}\\mathbf{m}}\\mathbf{L}\$\$]{.math.display}\ The --ve sign indicates that the dipole magnetic moment points in a direction opposite to the vector representing the angular momentum. In quantum mechanics of the angular momentum of the orbit is determined by the quantum number *l* and is expressed as[\$\\mathbf{\\ }\\frac{\\mathbf{h}}{\\mathbf{2}\\mathbf{\\pi}}\\mathbf{\\sqrt{}}\\mathbf{l}\\mathbf{(}\\mathbf{l}\\mathbf{+ 1)}\$]{.math.inline}; with ***l =* 0,1,2,..**.. The s electron (with ***l =* 0** ) always have zero angular momentum, hence zero magnetic momentum. For **(p, d, f, *l =* 1,2,3,\....** ); the electrons have non-zero angular momentum and thus magnetic moment can be given by [\$\\mathbf{µ}\_{\\mathbf{l}}\\mathbf{= \\ }\\mathbf{-}\\frac{\\mathbf{e}}{\\mathbf{2}\\mathbf{m}}\\frac{\\mathbf{h}}{\\mathbf{2}\\mathbf{\\pi}}\\mathbf{\\sqrt{}}\\mathbf{l}\\mathbf{(}\\mathbf{l}\\mathbf{+ 1) =}\\mathbf{-}\\mathbf{g}\_{\\mathbf{l}}\\mathbf{\\sqrt{}}\\mathbf{l}\\mathbf{(}\\mathbf{l}\\mathbf{+ 1)}\\mathbf{µ}\_{\\mathbf{B}}\$]{.math.inline}**;** Where, [**g**~**l**~ **=** **1,**  **µ**~**B**~]{.math.inline}+= [\$\\frac{\\mathbf{\\text{eh}}}{\\mathbf{4}\\mathbf{\\text{πm}}}\\ \\text{called}\\ the\\ \\text{Bo}hr\\ \\text{magneton}.\$]{.math.inline} It has value - **Spin Magnetic Moment** - The spin motion of the electrons around their own axis also contribution to the magnetic moment. - The electron has an intrinsic spin angular momentum of magnitude [\$\\frac{h}{2\\pi}\\sqrt{}s(s + 1)\$]{.math.inline}, where s is the spin quantum number, always equal to 1/2. - The spin magnetic moment associated with this angular momentum has magnitude \ [\$\$\\mathbf{µ}\_{\\mathbf{s}}\\mathbf{= \\ }\\mathbf{-}\\mathbf{g}\_{\\mathbf{s}}\\frac{\\mathbf{e}}{\\mathbf{2}\\mathbf{m}}\\frac{\\mathbf{h}}{\\mathbf{2}\\mathbf{\\pi}}\\mathbf{\\sqrt{}}\\mathbf{s}\\mathbf{(}\\mathbf{s}\\mathbf{+ 1)}\$\$]{.math.display}\ Where the coefficient *g~s~* is inserted because the ratio of the magnetic moment to the angular momentum differs from the classical value and very nearly equals to 2 and the negative sign shows that the magnetic moment is oppositely directed to the angular momentum vector. - **Classification of Magnetism** Magnetic materials can be classified mainly into three categories namely diamagnetic, paramagnetic and ferromagnetic.All these types of materials are discussed below in detail. **Diamagnetism (Zn, Bi, NaCl, Au)** - Diamagnetic materials are repelled weakly in the applied magnetic field. - They have even no. of electrons so no magnetic moment on the atom. - It is a very weak form of magnetism which exists only in the presence of large external field and is temporary. - When an external magnetic field is applied, there is a change in the orbital motion of electrons (i.e. their velocity of rotation in the orbit decreases, thereby increasing or decreasing the orbital current) which creates small magnetic dipoles within the atoms which oppose the applied field. - The magnitude of the induced magnetic moment is extremely small, and in a direction opposite to that of the applied field. - Thus, the relative permeability (µ) is slightly less than unity (-ve), and the magnetic susceptibility (**χ)** is negative; that is, the magnitude of the *B* field within a diamagnetic solid isless than that in a vacuum. - The volume susceptibility for diamagnetic solidmaterials is on the order of -10^-5^. - When placed between the poles of astrong electromagnet, diamagnetic materials are attracted toward regions where the field is weak. **Paramagnetism (Al, Pt, O, solutions of salts of iron)** - Paramagnetism is a slightly stronger phenomenon than diamagnetism. - Paramagnetic materials have partially filled p,d,f orbitals and unpaired electrons so a net magnetic moment on the atoms exists. - In the absence of external field, the orientations of atomic magnetic moments are random resulting in no net magnetization. - When a large external field is applied the atomic dipoles line-up with the field, resulting in a positive magnetization. However, the dipoles do not interact. - This type of magnetic materials exhibit a small positive magnetic susceptibility in the presence of a magnetic field. - However, because the dipoles do not interact, extremely large magnetic fields are required to align all of the dipoles. - In addition, the effect is lost as soon as the magnetic field is removed. - Since thermal agitation randomizes the directions of the magnetic dipoles, an increase in the temperature decreases the paramagnetism and [**χ**~*m*~ ]{.math.inline}decreases. Paramagnetic substances obey Curie Law is given as \ [\$\$\\mathbf{\\chi}\_{m} = - \\ \\frac{C}{T}\$\$]{.math.display}\ Where C is Curie constant and T is Temperature  **Ferromagnetism (**iron, nickel, cobalt) - Dia- and para- magnetic materials are considered as non-magnetic because these are very weak phenomenon and these are magnetized only in presence of large external field. - Certain materials possess permanent magnetic moments even in the absence of an external field. - This is the result of permanent dipoles formed from unpaired electrons or unfilled energy levels. - These dipoles can easily line-up with the magnetic field is imposed due to the exchange interaction or mutual reinforcement of the dipoles. These are characterized as *ferromagnetic materials.* **ParamagneticMaterials** **DiamagneticMaterials** **FerromagneticMaterials** --------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------- These materials have Very small but positive magnetic susceptibility (\~10^-6^) These materials have Very small but negative susceptibility (\~ 10^-6^) These materials have positive and large magnetic susceptibility (\~10^6^) The relative permeability is slightly more than unity (µ~r~˃1) µ~r~ is slightly less than unity (µ~r~˂1)(-ve) The µ*r* for a ferromagnetic material is of the order of few thousands The magnetic susceptibility depends strongly on temperature and varies inversely with temperature The magnetic susceptibility of diamagnetic materials is almost independent of temperature The magnetic susceptibility decreases with increase in temperature When a bar of a paramagnetic material is suspended between the poles of a magnet, it staysparallel to the lines of force. When a bar of these materials is suspended between the poles of a magnet, it stays parallel to the magnetic field When a bar of these materials is suspended between the poles of a magnet, itbehaves like a paramagneticmaterial If these materials areplaced in a non-uniformfield, they are attractedtowards the stronger field If these materials are placed in a non-uniform field, they are attracted towards the weaker field These materials behave like Paramagnetic substances, if placed in a nonuniform field - **CLASSICAL THEORY OF FERROMAGNETISM** - **Ferromagnetic materials** show spontaneous magnetization due to internal field arising as a result of mutual interactions between magnetic domains. When placed in external magnetic field they acquire very large and permanent magnetization in the direction of applied field. - Each atom of ferromagnetic material has a permanent magnetic moment like the paramagnetic substances. - The magnetic susceptibility of a ferromagnetic substance is a thousand times greater than that of a paramagnetic substance. - In general, a specimen of a ferromagnetic substance contains a number of small regions called domains. - These domains are typically very small (about 50 μm) or less and contain a large number of atoms, nearly 10^17^ to 10^22^, and have the dimensions of about 10^-6^ cm^3^ to 10^-2^cm^3^. - Each domain consists of magnetic moments that are aligned, giving rise to a permanent net magnetic moment per domain. - Each of these domains is separated from the rest by domain boundaries called *Bloch walls which* are about 100 nm thick. - Domains exist even in the absence of external field. In a material that has never been exposed to a magnetic field, the individual domains have a random orientation. This type of arrangement represents the lowest free energy. domainwallmotion.jpg Rotation of orientation and increase in size of magnetic domains in response to an externally applied field - When the bulk material is unmagnetized (no external magnetic field is applied), the net magnetization of these domains is zero, because adjacent domains are orientated randomly in any direction, effectively canceling each other's out figure (a). - When a magnetic field is applied on the material, domains that are nearly lined up with the field (favourable domains) grow at the expense of unaligned domains figure (b). - The Bloch walls move, the external field provides the force required for this movement and this process continues until only the most favorably oriented domains remains. - When the domain growth is completed, a further increase in the magnetic field causes the domains to rotate and align parallel to the applied field figure (c).  - At this instant material reaches saturation magnetization and no further increase in magnetizationwill take place on increasing the strength of the external field. - Under these conditions the permeability of these materials becomes quite small. The variation of magnetization with applied magnetic field H is shown is figure below. Materials with ferro-magnetism (e.g. Fe, Co, Ni, Gd) possess magnetic susceptibilities \~ 10^6^. Above the Curie temperature, ferro-magnetic materials behave as para-magnetic materials and their susceptibility is given by the Curie-Weiss law, defined as \ [\$\$\\mathbf{\\chi}\_{m} = \\ \\frac{C}{{\\mathbf{T}\\mathbf{-}\\mathbf{T}}\_{C}}\$\$]{.math.display}\ Where **C** is the Curie constant, **T** being temperature and Tc is called Curie temperature. - **FERRI MAGNETIC AND ANTI-FERROMAGNETICMATERIALS** **Ferrimagnetism** - **Ferrimagnetic materials are the oxides of metals i.e. ceramic magnetic materials.** - These materials exhibit net magnetization. e.g. Fe~3~O~4~(FeO.Fe~2~O~3~), NiFe~3~O~4~ (NiO.Fe~2~O~3~), (MnO/ MgO/ CaO/ ZnO/ MnO).Fe~2~O~3~ and are called soft ferrites. - Ferrites have hard magnetic properties also e.g. PbO.6Fe~2~O~3~, BaO.6Fe~2~O~3~, CdO.6Fe~2~O~3,~ NbO.6Fe~2~O~3,~ YIG- yttrium iron garnet Y~3~Fe~5~O~12~. - In applied magnetic field, the dipoles of a cation may line up with the field, while dipoles of other cation align opposite to the previous ones. - These ceramics are called ferrites, and the effect is known as *ferrimagnetism*. - Ferrimagnetism is similar to antiferromagnetism in that the spins of different atoms or ions line up anti-parallel. However, the spins do not cancel each other out, anda net spin moment exists. - Below the Neel temperature, ferimagnetic materials behave very much like ferromagnetic materialsand are paramagnetic above the Neel temperature. - These materials exhibit a large but field dependent magnetic susceptibility similar to ferromagnetics. They also show Curie-Weiss behavior. - As these ceramics are good insulators, electrical losses are minimal, and hence ferrites have lot of applications indevices such as high frequency transformers. - The hysteresis loop of the ferrites is so square shaped that these can easily be applied for memory storage devices. **Antiferromagnetism** - In antiferromagnetic materials the dipoles lineup, but in opposite directions, resulting in zero magnetization e.g., Mn, Cr, MnO, NiO, CoO, MnCl~2~. - Exchange interactions which are responsible for parallel alignment of spins is extremely sensitive to interatomic spacing and to the atomic positions. This sensitivity causes anti-parallel alignment of spins. - When the strength of antiparallel spin magnetic moments is equal, no net spin magnetic momentexists, and resulting susceptibilities are quite small. - One noticeable characteristic of antiferromagnets is, they attain maximum susceptibility at a critical temperature called *Neel temperature*. - At temperatures above *Neel temperature*, antiferromagnetic materials become paramagnetic. - The variation of susceptibility with temperature for ferromagnetic, antiferromagnetic and paramagnetic materials is shown in figure below.  - **Magnetic Hysteresis** - The magnetization behaviour of the ferromagnetic materials is described by the B-H curve (hysteresis loop) as shown in figure. - The hysteresis loop is generated by measuring the magnetic flux B in a ferromagnetic material by changing the magnetizing force H. - It shows that as the amount of field applied (H) to an unmagnetized or thoroughly demagnetized ferromagnetic material increases, the magnetic field (B) in the material increases. It will follow the dashed line. - At point "a" almost all of the magnetic domains are aligned and an additional increase in the magnetizing force will produce almost nil or very little increase in magnetic flux.The material has reached the point of magnetic saturation. - When H is reduced down to zero, the curve will move from point \"a\" to point "b". At this point, it can be seen that some magnetic flux remains in the material even though the magnetizing force is reduced to zero. This value of B is referred to as retentivity or remanence and indicates the amount of residual magnetism in the material. (Some of the magnetic domains still remain aligned but most have lost their alignment). - As the magnetizing force is reversed, the curve moves to point "c", at which the flux has been reduced to zero. This is called coercivity or coercive field. This is the field required to remove the residual magnetization from the material. - The reversed magnetizing force has flipped enough the domains so that the net flux within the material becomes zero. - As the magnetizing force is increased in the negative direction, the material will again become magnetically saturated but in the opposite direction (point "d"). - Reducing H to zero brings the curve to point "e". It will have a level of residual magnetism again, which is equal to that achieved in the other direction. - Increasing H back in the positive direction will return B to zero. - It should be noticed that the curve did not return to the origin of the graph because some force is required to remove the residual magnetism. - The curve will take a different path from point "f" back to the saturation point where it completes the loop. - The complete closed loop abcdefa is called hysteresis loop. From the hysteresis loop, a number of primary magnetic properties of a material can be determined. \(i) **Retentivity -** It is the ability of a material\' to retain a certain amount of residual magnetic field when the magnetizing force is removed after achieving saturation. \(ii) **Coercive force (field) -** The amount of reverse magnetic field which mustbe applied to a magnetic material to make the magnetic flux inside the material to return tozero. \(iii) **Permeability -** A property of a material that describes the ease withwhich a magnetic flux is established in the component. The hysteresis curve of a ferromagnetic material provides very usefulinformations regarding the magnetic properties of a material. - **Energy Loss Due to Hysteresis** During the process of magnetization and demagnetization, a loss of energy is always involved in aligning the domains (motion of domain walls and rotation of dipoles) in the direction of the applied magnetic field. When the direction of an external magnetic field is reversed, the absorbed energy is not completely recovered and rest energy in sample is lost in the form of heat. This loss of energy is called hysteresis loss. - **Calculation of Hysteresis Loss** It can be proved that the energy lost per unit volume of the substance in a complete cycle ofmagnetization is equal to the area of the hysteresis loop. We consider a unit volume of the ferromagnetic substance, which has N magnetic domains. Let M be the magnetic moment of each magnetic domain which makes an angle *θ* with the direction of the magnetic field H. So, the total magnetic moment per unit volume in the direction of magnetizing field   The size andshape of the hysteresis loop of ferromagnetic materials can be used to estimate retentivity, coercivity, susceptibility, permeability and energy loss per cycle of magnetization demagnetization. On the basis of these propertiesof the magnetic materials, it is possible to classify choose a particular magnetic material for aparticular application. - **Soft and Hard Magnetic Materials** The area of the hysteresis loop gives the energy loss per unit volume of a material for one cycle of magnetization and demagnetization. The hard magnetic materials are *difficult to magnetize and demagnetize.* They have a gradually rising magnetization curve, large hysteresis loop area and consequently large energy losses for each cycle of magnetization and demagnetization. In a hard magnetic material, it is difficult to align the domains. They have high saturation values, high coercive force, and high residual magnetism. The product of B and H for a hard magnetic material is high.\ \ Hard magnetic materials are used for making permanent magnets. e.g Carbon, Tungsten, Cobalt Steel, Alloys like ALNICO (Aluminium-nickel-iron cobalt), alloys basedon Co-Pt, Ta -Cr , Fe -Pt and Fe-Pd, etc. Materials which have relatively small and narrow hysteresis loop and consequently small energy losses for each cycle of magnetization and demagnetization are called **soft magnetic materials**. The commonest soft magnetic materials are pure annealed soft iron, iron silicon alloy, nickel-iron alloys, and soft ferrites. Soft magnetic materials are used for the construction of cores for electrical machines, transformers, electromagnets, electric motors, generators, and otherreactors, relays etc. The economic construction of such equipment demands that the magnetic flux should be produced in the minimum space and with minimum loss. To sum up, the **requirements of magnetic materials** for use in electrical machines and transformers are: - A small enclosed area of hysteresis loop, - low coercive forces, - High permeability, - High saturation value of flux density. - **Superparamagnetism** **It** is a form of magnetism which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time. In the absence of an external magnetic field, when the time used to measure the magnetization of the nanoparticles is much longer than the Néel relaxation time, their magnetization appears to be in average zero; they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles, similarly to a paramagnet. However, their magnetic susceptibility is much larger than that of paramagnets. When an external magnetic field *H* is applied to an assembly of superparamagnetic nanoparticles, their magnetic moments tend to align along the applied field, leading to a net magnetization. The magnetization curve of the assembly, i.e. the magnetization as a function of the applied field, is a reversible S-shaped increasing function.  Superparamagnetism sets a limit on the storage density of hard disk drives due to the minimum size of particles that can be used. This limit is known as the **superparamagnetic limit**. - - - ### The General applications of superparamagnetic materials include Ferrofluid: tunable viscosity, Contrast agents in magnetic resonance imaging (MRI), Magnetic separation: cell-, DNA-, protein- separation, RNA fishing and in Treatmentslike targeted drug delivery, magnetic hyperthermia, magnetofection