MAGNETIC MATERIALS

1) Magnetic Induction or Magnetic Flux density (B): The magnetic induction or magnetic flux density is the number of lines of magnetic force passing through unit area perpendicularly. Where Φ is the magnetic flux and A is the area of cross section. Units: Weber/m2 or Tesla. 2) Magnetic Field Intensity or Intensity of Magnetic Field (H): Magnetic Field Intensity at any point in the magnetic field is the force experienced by an unit north pole placed at that point. Units: A/m.

3) Magnetic Permeability (µ): It describes the nature of the material i.e. it is a material property. It is the ease with which the material allows magnetic lines of force to pass through it or the degree to which magnetic field can penetrate a given medium. Mathematically it is equal to the ratio of magnetic induction B inside a material to the applied magnetic field intensity H. Units: H/m.

4) Magnetization: Process of converting a non magnetic material into magnetic sample. 5) Intensity of Magnetization (M): It is a material property. It is defined as magnetic moment per unit volume in a material. Units: A/m.

Sources of Magnetic Fields

Magnetic Field Strength 22-11-2018 Magnetic Field Strength • Created by current through a coil: magnetic field H current I N = total number of turns L = length of the coil • Relation for the applied magnetic field, H: applied magnetic field units = (ampere-turns/m) current

Response to a Magnetic Field • Magnetic induction results in the material current I B = Magnetic Induction (tesla) inside the material

Origin of Magnetic Moment Magnetism arises from the Magnetic Moment or Magnetic dipole of Magnetic Materials. When the electrons revolves around the nucleus Orbital magnetic moment arises, similarly when the electron spins, spin Magnetic moment arises. The permanent Magnetic Moments can arise due to the 1.The orbital magnetic moment of the electrons 2.The spin magnetic moment of the electrons, and 3.The spin magnetic moment of the nucleus

Origin of Magnetic Moment A moving electric charge, macroscopically or “microscopically” is responsible for Magnetism Nuclear spin Very Weak effect Unpaired electrons required for net Magnetic Moment Origin of Magnetism Spin of electrons Orbital motion of electrons Weak effect. Magnetic Moment resultant from the spin of a single unpaired electron → Bohr Magneton = 9.273 x 1024 A/m2

Origin of magnetic dipoles The spin of the electron produces a magnetic field with a direction dependent on the quantum number ml.

Origin of magnetic dipoles The spin of the electron produces a magnetic field with a direction dependent on the quantum number ms.

Electrons orbiting around the nucleus create a magnetic field around the atom.

Classification of magnetic Materials Permanent Dipoles No Yes Para, Ferro, Anti ferro, Ferri magnetic materials Dia magnetic materials Alignment of dipoles Random Uniform Ferro, Anti ferro, Ferri Para Same Direction of dipoles Opposite Ferro Anti ferro, Ferri Magnitudes of dipoles Different Same Ferri Anti ferro

Diamagnetic Materials

Properties It is a weak form of magnetism Diamagnetism is because of orbital magnetic moment. No permanent dipoles are present so net magnetic moment is zero. Persists only when external field is applied. The number of orientations of electronic orbits is such that the vector sum of the magnetic moments is zero. Dipoles are induced by change in orbital motion of electrons due to applied magnetic field.

Applied No Applied Magnetic Field (H = 0) Magnetic Field (H) opposing none opposing

External field will cause a rotation action on the individual electronic orbits. The external magnetic field produces induced magnetic moment which is due to orbital magnetic moment. Induced magnetic moment is always in opposite direction of the applied magnetic field. So magnetic induction in the specimen decreases. Magnetic susceptibility is small and negative. Repels magnetic lines of force.

Diamagnetic susceptibility is independent of temperature and applied magnetic field strength. Susceptibility is of the order of -10-5. Relative permeability is less than one. It is present in all materials, but since it is so weak it can be observed only when other types of magnetism are totally absent. Examples: Bi, Zn, gold, H2O, alkali earth elements (Be, Mg, Ca, Sr), superconducting elements in superconducting state.

Paramagnetic Materials

Properties Possess permanent dipoles. If the orbital's are not completely filled or spins not balanced, an overall small magnetic moment may exist. i.e. paramagnetism is because of orbital and spin magnetic moments of the electron. In the absence of external magnetic field all dipoles are randomly oriented so net magnetic moment is zero. Spin alignment is random. The magnetic dipoles do not interact

Paramagnetic Materials No Applied Magnetic Field (H = 0) Applied Magnetic Field (H) random aligned

In presence of magnetic field the material gets feebly magnetized i.e. the material allows few magnetic lines of force to pass through it. Relative permeability µr >1 (barely, ≈ 1.00001 to 1.01). The orientation of magnetic dipoles depends on temperature and applied field. Susceptibility is independent of applied mag. field & depends on temperature C is Curie constant

With increase in temperature susceptibility decreases. Susceptibility is small and positive. These materials are used in lasers. Paramagnetic property of oxygen is used in NMR technique for medical diagnose. The susceptibility range from 10-5 to 10-2. Examples: alkali metals (Li, Na, K, Rb), transition metals, Al, Pt, Mn, Cr etc.

Ferromagnetic Materials 22-11-2018 Ferromagnetic Materials

Properties Permanent dipoles are present so possess net magnetic moment Origin for magnetism in Ferro mag. Materials is due to Spin magnetic moment of electrons. Material shows magnetic properties even in the absence of external magnetic field. Possess spontaneous magnetization. Spontaneous magnetization is because of interaction between dipoles called EXCHANGE COUPLING.

aligned No Applied Magnetic Field (H = 0) Applied Magnetic Field (H)

Magnetic susceptibility is as high as 106. So H << M. thus Bs = µoMs Magnetic induction B (tesla) Strength of applied magnetic field (H) (ampere-turns/m) Ferromagnetic

When placed in external mag When placed in external mag. field it strongly attracts magnetic lines of force. All spins are aligned parallel & in same direction. Susceptibility is large and positive, it is given by Curie Weiss Law C is Curie constant & θ is Curie temperature. When temp is greater than curie temp then the material gets converted in to paramagnetic. Material gets divided into small regions called domains. They possess the property of HYSTERESIS. Examples: Fe, Co, Ni.

Ferro magnetic Materials Even when H = 0, the dipoles tend to strongly align over small patches. When H is applied, the domains align to produce a large net magnetization.

Thermal energy can randomize the spin Tcurie Ferromagnetic Paramagnetic Heat Tc for different materials: Fe=1043 K, Ni=631 K, Co=1400 K, Gd= 298 K

Curie Temperature The temperature above (Tc) which ferromagnetic material become paramagnetic. Below the Curie temperature, the ferromagnetic is ordered and above it, disordered. The saturation magnetization goes to zero at the Curie temperature.

Antiferro magnetic Material

Properties The spin alignment is in antiparallel manner. So net magnetic moment is zero. Susceptibility depends on temperature. Susceptibility is small and positive. Initially susceptibility increases with increase in temperature and beyond Neel temperature the susceptibility decreases with temperature. At Neel temperature susceptibility is maximum. Examples: FeO, MnO, Cr2O3 and salts of transition elements.

Ferri-magnetic Materials

Ferrimagnetic Materials Classification of Ferri-magnetic Materials Ferrimagnetic Materials Cubic Ferrites MFe2O4 Hexagonal Ferrites AB12O19 Garnets M3Fe5O12

Properties Special type of ferro and antiferromagnetic material. Generally oxides in nature. Ionic in nature Ceramic in nature so high resistivity (insulators) The spin alignment is antiparallel but different magnitude. So they possess net magnetic moment. Also called ferrites. General form MFe2O4 where M is a divalent metal ion. Susceptibility is very large and positive. Examples: ferrous ferrite, nickle ferrite

Ion Spin Orientation Net Spin S Magnetic Moment E.C Mn2+ 3d5 5/2 5µB Fe2+ 3d6 2 4µB Co2+ 3d7 3/2 3µB Ni2+ 3d8 1 2µB Cu2+ 3d9 1/2 1µB

Net magnetic moment atom crystal Na 3s1 1 B 4 B 2.2 B Fe 3d64s2 Unpaired electrons give rise to ferromagnetism in alkali metals Ms = m. N Net magnetic moment N = ρ NA/A atom crystal Na 3s1 1 B 4 B 2.2 B Fe 3d64s2 3 B Co 3d74s2 1.7 B Ni 3d84s2 2 B 0.6 B

Ferrimagnetism All Fe2+ have a spin magnetic moment. Half of Fe3+ have a spin moment in one direction, the other half in the other (decreasing the overall moment to just that contributed by the Fe2+ ions). Simpler picture showing a net magnetic moment.

Ferrimagnetism-Structure

Domain Theory of Ferromagnetic Materials 22-11-2018 Domain Theory of Ferromagnetic Materials

Domain Theory of Ferromagnetism The domain in ferromagnetic solid is understandable from the thermo dynamical principle (i.e,) in equilibrium the total energy of the system is minimum. Total Energy of the domains comprises the sum of Exchange Energy (or) Magnetic Field Energy Anisotropic Energy => Easy and Hard direction Domain Wall Energy => Thick wall and Thin Wall Magneto-strictive Energy

Exchange Energy or Magnetic Field Energy The interaction energy that makes the adjacent dipoles to align themselves is known as Exchange Energy. It establishes a single domain in the ferromagnetic material. It is the energy required in assembling the atomic magnets into a single domain and this work done is stored as potential energy.

Anisotropy Energy Two types of directions of magnetization Easy Direction Hard Direction Along easy direction weak field. Along hard direction strong field. For producing same amount of magnetisation. The excess of energy required to magnetize the specimen along hard direction over that required to magnetize the specimen along easy direction is called crystalline anistropy energy.

Domain Wall Energy or Bloch Wall Energy Bloch is a transition layer which separates the adjacent domains, magnetized in different directions. Based on the spin alignments Thick Wall & Thin Wall Thick Wall: When the spins at the boundary are misaligned and if the direction of the spins changes gradually. The misalignment of spins is associated with exchange energy. Thin Wall: When the spins at the boundaries changes abruptly, then the anistropic energy becomes very less. Ansitropy energy is directly proportional to the thickness of the wall.

Domain Structure and the Hysteresis Loop Bloch walls - The boundaries between magnetic domains. The entire change in spin direction between domains does not occur in one sudden jump across a single atomic plane rather takes place in a gradual way extending over many atomic planes. Bloch Wall The magnetic moments in adjoining atoms change direction continuously across the boundary between domains.

Magnetostrictive Energy When the domains are magnatised in different directions, they will either expand or shrink this leads to deformation of the material, when magnetised. This phenomenon is known as magnetostriction. Energy produced in this effect is called Magnetostriction Energy. The deformation is different along different crystal directions & the change in dimension depends on nature of the material.

Ferromagnetism Materials that retain a magnetization in zero field Quantum mechanical exchange interactions favour parallel alignment of moments Examples: iron, cobalt

According to Becker, there are two independent processes which take place and lead to magnetization when magnetic field is applied. Domain wall moment or Domain growth Domain rotation

Domain wall moment or Domain wall growth Volume of favorably oriented domains will increase. Occurs at low magnetic field. It is a reversible process. Rotation of Domains Rotation of less favorably oriented domains takes place. Occurs at large magnetic field. It is a irreversible process.

Domain Structure and the Hysteresis Loop Domain growth: Each domain is magnetized in a different direction 2. Applying a field changes domain structure. Domains with magnetization in direction of field grow. 3. Other domains shrink Domain rotation: Finally by applying very strong fields can saturate magnetization by creating single domain

Magnetic domains Applying very strong fields can saturate magnetization by creating single domain

Hysteresis Curve Means lagging or retarding of an effect behind the cause of the effect. Here effect is B & cause of the effect is H. Also called B H curve. Hysteresis in magnetic materials means lagging of magnetic induction (B) or magnetization (M) behind the magnetizing field (H).

Domain Structure and the Hysteresis Loop • “Domains” with aligned magnetic moment grow at expense of poorly aligned ones!

Domain Structure and the Hysteresis Loop When a magnetic field is first applied to a magnetic material, magnetization initially increases slowly, then more rapidly as the domains begin to grow. Later, magnetization slows, as domains must eventually rotate to reach saturation. Notice the permeability values depend upon the magnitude of H.

Hysteresis Loop Hysteresis loop - The loop traced out by magnetization in a ferromagnetic or ferrimagnetic material as the magnetic field is cycled. OR Removing the field does not necessarily return domain structure to original state. Hence results in magnetic hysteresis. B 2. apply H, cause alignment 3. remove H, alignment stays! => permanent magnet! 4 Negative H needed to demagnitize! . Coercivity, HC Applied Magnetic Field (H) 1. initial (unmagnetized state)

Ferromagnetism: Magnetic hysteresis 22-11-2018 Ferromagnetism: Magnetic hysteresis M H Mrs Hc Ms Ms – Saturation magnetization Mrs – Saturation remanent magnetization Hc – Coercive force (the field needed to bring the magnetization back to zero)

remanent magnetization = M0 coercivity = Hc

Hysteresis Loop Magnetization by domain rotation Domain growth irreversible boundary displacements. Means lagging or retarding of an effect behind the cause of the effect. Here effect is B & cause of the effect is H. Also called B H curve. Hysteresis in magnetic materials means lagging of magnetic induction (B) or magnetization (M) behind the magnetizing field (H). Domain growth reversible boundary displacements.

Hysteresis, Remanence, & Coercivity of Ferromagnetic Materials

“hard” ferromagnetic material has a large M0 and large Hc. “soft” ferromagnetic material has both a small M0 and Hc.

Hard versus Soft Magnets Characteristics of soft magnetic materials: High initial permeability. Low coercivity. Reaches to saturation magnetization with a relatively low applied magnetic field. It can be easily magnetized and demagnetized. Low Hysteresis loss. Applications involve, generators, motors, dynamos, Cores of transformers and switching circuits.

Importance of Soft Magnetic Materials: Saturation magnetization can be changed by altering composition of the materials. Ex:- substitution of Ni2+ in place of Fe2+ changes saturation magnetization of ferrous-Ferrite. Susceptibility and coercivity which also influence the shape of the Hysteresis curve are sensitive to the structural variables rather than composition. Low value of coercivity corresponds to the easy movement of domain walls as magnetic field changes magnitude and/ or direction.

Hard versus Soft Magnets Hard Magnets: Characteristics of Hard magnetic materials: Low initial permeability. High coercivity and High remanence. High saturation flux density. Reaches to saturation magnetization with a high applied magnetic field. It can not be easily magnetized and demagnetized. High Hysteresis loss. Used as permanent magnets.

Importance of Hard magnetic material Two important characteristics related to applications of these materials are (i) Coercivity and (ii) energy product expressed as (BH)max with units in kJ/m3. This corresponds to the area of largest B-H rectangle that can be constructed within the second quadrant of the Hysteresis curve. Larger the value of energy product harder is the material in terms of its magnetic characteristics. Schematic magnetization curve that displays hysteresis. Within the second quadrant are drawn two B–H energy product rectangles; the area of that rectangle labeled (BH)max is the largest possible, which is greater than the area defined by Bd–Hd

Who to get larger area of (BH)max i.e., who to produce Hard magnets? 22-11-2018 Who to get larger area of (BH)max i.e., who to produce Hard magnets? Energy product represents the amount of energy required to demagnetize a permanent magnet. Hysteresis behaviour depends upon the movement of domain walls. The movement of domain walls depends on the final microstructure. Ex: the size, shape and orientation of crystal domains and impurities. Microstructure will depend upon how the material is processed. In a hard magnetic material, impurities are purposely introduced, to make it hard. Due to these impurities domain walls cannot move easily. Finally the coercivity can increase and susceptibility can be decrease. So large external field is required to demagnetization i.e., difficult to move the domain walls.

Hard Magnetic Material Soft Magnetic Material Have large hysteresis loss. Have low hysteresis loss. Domain wall moment is difficult Domain wall moment is relatively easier. Coercivity & Retentivity are large. Coercivity & Retentivity are small. Cannot be easily magnetized & demagnetized Can be easily magnetized & demagnetized. Magneto static energy is large. Magneto static energy is small. Have small values of permeability and susceptibility Have large values of susceptibility and permeability. Used to make permanent magnets. Used to make electromagnets. Iron-nickel-aluminum alloys, copper-nickle-iron alloys, copper–nickel– cobalt alloys Iron- silicon alloys, ferrous- nickel alloys, ferrites, garnets.

Applications of Magnetic Materials

Magnetic materials applications 1) Ferrite Applications 2) Magnetic Storage Reading Process Writing Process Storage of data( Tapes, Floppy and Magnetic Disc Drives) 3) Transformer 4) Motors

Magnetic materials applications FERRITE APPLICATIONS Ferrites Being Ferro-magnetic but high resistivity Used as transformer cores eddy currents less effective Used as induction cores, antennas for medium and long wave broad casting, electronic tuning, auto frequency control, FM, switching etc. Since ferrites have a domains & hysteresis loop they are used as memory elements for rapid storage and retrieval of digital information by switching the direction of magnetization in very small toroidal cores. Garnets (Y3Fe5O12) are useful in microwave applications. Magnetic recording uses ferrite material in powder form. Ferrites can be used as magnets. Confidential 86

Transformer Core Properties: Should be ceramic in nature. Should have very high permeability. The material should have very high susceptibility. The material should have low coresive field and low remeanent field. Magnetostriction should be small. --Best example is Iron-Silicon alloy (97% Fe & 3% Si) --Fe-Si (alloy) anisotropic poly crystalline materials can develop via plastic deformation, for example by rolling. http://www.marktec.co.jp/e/product/ndt/ect/et.html

M V V K Srinivas Prasad; K L University -- For body centred cubic alloys including Fe-Si alloy, the rolling texture is (1 1 0) [0 0 1]. 11/22/2018 M V V K Srinivas Prasad; K L University

Magnetic Storage Devices • Information is stored by magnetizing material due to high retentivity. • Head can... --apply magnetic field H & align domains (i.e., magnetize the medium). --detect a change in the magnetization of the medium. Recording Head: Soft Magnetic Materials Ex: Fe-Ni, Fe-Al-Si alloy, Mn-Zn ferrite, Ni-Zn ferrite

Recording Principle (Digital)

How Magnetic Storage Works A magnetic disk's medium contains iron particles, which can be polarized—given a magnetic charge—in one of two directions. Each particle's direction represents a 1 (on) or 0 (off), representing each bit of data that the CPU can recognize. A disk drive uses read/write heads containing electromagnets to create magnetic charges on the medium. 

Magnetic Storage Devices

Magnetic Storage Devices There are two types of magnetic storage media. Those are particulate and thin film. Particulate media consist of very small needle like or acicular particles. Ex: γ-Fe2O3 ferrite, Co- γ- Fe2O3 ferrite and CrO2 .

Magnetic Storage Devices Thin film: It provides higher storage capacities at lower costs. Ex: Co-Pt-Cr alloy, Co-Cr-Ta alloy (thickness 10 to 50 nm).Domains are ~ 10-30nm! (hard drive) The thin film is a poly crystalline material. Each grain within the thin film is a single magnetic domain. The grain shape and size must be uniform.

Magnetic Storage Devices Thin film:

Magnetic Tapes

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MOTORS Hard magnetic materials are used. Motor converts electrical energy into mechanical energy. No heat is generated during operation. Motors using permanent magnets are much smaller than their electromagnets motors. http://www.animations.physics.unsw.edu.au/jw/electricmotors.html