The goal of this chapter is to understand

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1 A photograph of a commercial highspeed maglev train that connects the Shanghai, China airport to the city center. Maglev trains do not run on wheels; instead, they are lifted from the track and propelled by magnetic fields. The highest speed for a train is 581 km/h set by a maglev train on an experimental track in Yamanashi, Japan. Photo Japan / Alamy The goal of this chapter is to understand The method for creating magnetic fields The response of materials to magnetic fields The intensity of magnetization of materials Diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic materials Hard and soft magnetic materials Magnetic materials for information storage Magnetoresistance and applications to magnetic data storage systems

2 Chapter 17 Magnetic Materials 17.1 Introduction The first recorded description of magnetic materials was in approximately 800 bce, when the Greeks wrote that lodestone (Fe 3 O 4 ) could attract iron. The first known use of magnetic materials was in China as early as 4000 bce, when the Chinese utilized elongated lodestones to orient important buildings with a south facing entrance. European explorers used an iron needle as a compass as early as 1190 ce for navigation, because it always pointed to magnetic north. Modern applications of magnetic materials include permanent magnets for industrial and electronic applications, magnetic materials in motors, electrical generators, electronic devices, magnetic recording tape, and hard disk memory and readout in computers. Superconducting materials also allow for interesting magnetic applications, such as magnetic levitation of trains.

3 W-70 CHAPTER Magnetic fields and material response Our first experience with magnetism comes from small magnets or by using a compass. The magnetic needle of a compass is always attracted to the magnetic north pole of the earth. We find by experiment that a magnet has a north pole and a south pole. The combination of a north pole and a south pole of a magnet is called a magnetic dipole. The north pole of one magnet attracts the south pole of another magnet, and the similar poles of two magnets repel each other. The magnetic poles act in a way similar to positive and negative electrical charges. The magnetic poles create a magnetic field, just as positive and negative electrical charges create an electrical field. The effect of the magnetic field of a magnet on the environment is observed by sprinkling iron powder onto a magnetic material, as shown in Figure 17.1a. The iron powder forms a pattern in response to the magnetic field that is shown for a bar magnet in Figure 17.1b. The magnetic field created by a current in a single loop is shown in Figure 17.1c. A coil that has N loops wound over a length L, and carries a current I, produces a magnetic field whose strength has a magnitude H, as shown in Equation H 5 NI L 17.1 The magnetic field strength produced by a coil is a vector (H) whose direction is given by the righthand rule, with the fingers curling in the direction of the positive current and the thumb pointing in the direction of the magnetic field. In this chapter, the magnitude of a vector is printed in italics and a vector N S (a) (b) (c) Figure 17.1 (a) A magnet with iron filings respond to a magnetic field. (b) A schematic of the magnetic field lines produced by a bar magnet. (c) A schematic of the magnetic field lines produced by a conducting wire loop with a current I. ((a) Magnet0873.png. (b) Based on (c) Based on

4 Magnetic Materials W-71 is printed in bold-roman type. The SI unit for magnetic field strength is amperes/meter (A/m). The term N/L is the number of turns per meter, and N/L has the units of m 21. Example Problem 17.1 Calculate the magnetic field strength inside a coil made of copper wire that has 100 turns over a length of 10 cm and carries a current of 10 A. Solution All of the information necessary to calculate the magnetic field strength with Equation 17.1 is given. H 5 IN L 5 10A s100d 0.1 m 5 10,000 A/m In Figure 17.1a, it is not the magnetic field (H) that is observed; what is observed is the response of the environment to the magnetic field. A mechanical analogy is that when a force is applied to a material, the deformation of the specimen is observed. The applied force is resisted by the atoms, but the force between the atoms cannot be seen by looking at the material. The machine that applies the force to a material can be seen, and the coil that produces the magnetic field also can be seen. The response of a material to an applied magnetic field (H) is the flux density (B). The flux density (B) is also called the magnetic induction, because B is the response induced into the material. If the material is a vacuum, the flux density (B 0 ), shown in Figure 17.2a, is given by Equation 17.2: B H 17.2 where 0 is the permeability of a vacuum ( Wb/A? m). The SI unit for the flux density is webers/m 2 (Wb/m 2 ), or a tesla (T). The vector H is the same in Figures 17.2a and 17.2b, but the vectors B 0 and B are different in Figures 17.2a and 17.2b. The coil of wire in Figures 17.2a and 17.2b are also called solenoids. B 0 = 0 H I L N I B = H L H H I (a) N TURNS I (b) Figure 17.2 (a) A coil in a vacuum, producing a magnetic field of H, with the response of the vacuum resulting in a magnetic flux density of B 0. (b) A coil with a material inside produces a magnetic flux density of B. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 770.)

5 W-72 CHAPTER 17 Example Problem 17.2 What is the magnitude of the flux density or inductance created by the coil in Example Problem 17.1 in a vacuum? Solution Because the coil is in a vacuum, the flux density is given by Equation B H Wb A? m 1 10,000 m2 A Wb m T If a material is placed in a magnetic field of strength H, as shown in Figure 17.2b, the flux density (B) inside the material is given by Equation 17.3: B 5 H 5 0 H 1 0 M 17.3 where is the magnetic permeability of the material. The intensity of magnetization of the material (M) is the magnetic field strength created by the material as a result of the applied magnetic field H. The magnetic field strength (H) and intensity of magnetization (M) have the same units of A/m. The flux density ( B) with a material is the sum of the flux density resulting from the applied magnetic field in a vacuum without the material ( B 0 ) and the flux density resulting from the intensity of magnetization of the material ( 0 M ). The relative magnetic permeability of a material is given by Equation r Values of the relative magnetic permeability for some materials are presented in Table The magnitude of the relative magnetic permeability depends upon the temperature, purity, and treatment of the material. Observe that the relative magnetic permeability goes from values slightly less than 1 for diamagnetic materials to a million for a ferromagnetic material. In this chapter, we explain the reason for the difference in relative magnetic permeability of different materials. The value of the relative magnetic permeability is high if the value of M is greater than H. In the magnetics literature the flux density (B) is emphasized, because flux density (B) is what is measured by instruments. If we study the flux density (B), the material and vacuum responses are combined, and the material response is not immediately obvious. In this textbook, our interest is in understanding the response of materials to the applied magnetic field H, and the material response is the intensity of magnetization of the material (M); as a result our focus is on M. Example Problem 17.3 The ferromagnetic material supermalloy listed in Table 17.1 is inserted into the coil in Example Problem What is the flux density created by the coil with this material inserted? Solution The flux density is given by Equation 17.3, and μ is calculated from Equation Wb 5 r B 5 H A? m2 Wb A? m Wb A? m 1 10,000 m2 A Wb T m 2

6 Magnetic Materials W-73 Table 17.1 Materials, the Type of Magnetic Response, and the Relative Permeability at Room Temperature Substance Group type Relative permeability r Bismuth Diamagnetic Silver Diamagnetic Lead Diamagnetic Copper Diamagnetic Water Diamagnetic Vacuum Nonmagnetic 1 (by definition) Air Paramagnetic Aluminum Paramagnetic Palladium Paramagnetic Permalloy powder (2 Mo, 81 Ni) Ferromagnetic 130 Cobalt Ferromagnetic 250 Nickel Ferromagnetic 600 Ferroxcube 3 (Mn-Zn-ferrite) Ferromagnetic 1500 Mild Steel (0.2 C) Ferromagnetic 2000 Iron (0.2 impurity) Ferromagnetic 5000 Silicon iron (4 Si) Ferromagnetic Permalloy (78.6 Ni) Ferromagnetic 100,000 Purified iron (0.05 impurity) Ferromagnetic 200,000 Supermalloy (5 Mo, 79 Ni) Ferromagnetic 1,000,000 Percentage composition. Remainder is iron and impurities. Used in power transformers. Based on data from Kraus, J. D., Electromagnetics, McGraw-Hill, N. Y. (1953), p Because the intensity of magnetization of the material (M) is created by the magnetic applied field strength (H), for many materials there is a proportionality between M and H called the magnetic susceptibility ( ), as shown in Equation M 5 H 17.5 The magnetic susceptibility ( ) in Equation 17.5 is dimensionless, because the intensity of magnetization (M) and the magnetic field strength (H) have the same units of A/m. The dimensionless susceptibility is also called the relative susceptibility, and is called the volume susceptibility, because as shown in Equation the intensity of magnetization (M) is also the dipole moment per unit volume. There are a variety of other magnetic susceptibilities utilized in the literature of magnetism. Magnetic materials are classified by their magnetic susceptibility as follows: 5 21: A perfect diamagnet or a superconductor, 0 and small in magnitude: Diamagnetic 5 0: A perfect vacuum. 0 and small: Paramagnetic and antiferromagnetic. 0 and large: Ferromagnetic and ferrimagnetic

7 W-74 CHAPTER 17 The magnetic susceptibility is determined from the relative magnetic permeability with Equation r As with relative magnetic permeability, the magnetic susceptibility depends upon the temperature, purity, and treatment of the material. Example Problem 17.4 What is the magnitude of the intensity of magnetization of the supermalloy in Example Problem 17.3? Solution The intensity of magnetization is given by Equation 17.5, and the magnetic susceptibility is given by Equation r ø 10 6 M 5 H A/m A/m 17.3 Diamagnetic Materials The magnetic susceptibility of diamagnetic materials is small and negative, as demonstrated by subtracting 1 from the relative magnetic permeability in Table 17.1 for the diamagnetic materials. The negative magnetic susceptibility of diamagnetic materials indicates that the intensity of magnetization in the material (M) is in the opposite direction to the applied magnetic field (H), as shown by Equation The negative magnetic susceptibility is due to Lenz s law that in a material subject to a magnetic field, a current is induced so that it always opposes the change in the applied magnetic flux. How are these currents induced in materials, and how do the currents result in an intensity of magnetization that is opposed to the applied magnetic field? The intensity of magnetization of a material (M) results from magnetic dipoles that are created in a volume of material as a result of applying the magnetic field H. The magnetic dipole moment (p m ) is the pole strength (m and 2m) times the separation of the two poles (d), as shown by Equation p m 5 md 17.7 The pole strength (m) in a magnetic material is analogous to an electrical charge in electrostatics. The direction of the vector p m is in the direction from 2m to m (south pole to north pole), and the units of a magnetic dipole moment are A? m 2. If the dipole moment is the dipole moment of an atom ( p a ), and the material is made up of N v identical atoms per unit volume, then the intensity of magnetization of the material is given by Equation M 5 N v p a 17.8

8 Magnetic Materials W-75 p e = I e A e p m = IA Electron Loop I e Ae Core Area A I (a) Figure 17.3 (a) An electron orbiting an atom, creating a current loop I e in the reverse direction to the electron orbit enclosing an area A e, producing a magnetic dipole moment of magnitude p e. (b) A current (I ) enclosing an area (A), producing a magnetic dipole moment of magnitude p m. (b) All materials have a diamagnetic contribution in their response to an applied magnetic field (H), because all atoms have orbiting electrons. As shown in Figure 17.3a, the magnitude of the dipole moment created by a single electron orbiting an atom ( p e ) is given by Equation 17.9: p e 5 I e A e 17.9 where I e is the current associated with the orbiting electron and A e is the area enclosed by the electron orbit. The direction of the vector p e is given by the right-hand rule, pointing the fingers in the direction of the positive current I e so that the thumb points in the direction of the dipole moment. The current direction is opposite to that of the orbiting electron. When there is no magnetic field applied to a diamagnetic material, the sum of the dipole moments on an atom created by the orbiting electrons is equal to 0, as indicated by the absence of any net magnetic moment (no arrow) in the individual atoms in Figure 17.4a. However, when a magnetic field is applied to any atom, the electron orbits on the atom are altered to oppose the applied magnetic field in compliance with Lenz s law, and an effective dipole moment ( p a ) is created on each atom, as shown in Figure 17.4b. The value of the dipole moment per atom ( p a ) is the sum of the values of p e from all of the electrons on the atom, and p a is in the direction opposite to the applied magnetic field (H). The intensity of magnetization ( M ) due to this diamagnetic effect is given by Equation In a diamagnetic material, when the applied magnetic field ( H ) is reduced to 0, the intensity of magnetization (M) also returns to 0, as is shown in Figure 17.4c, because p a is equal to 0. H = 0 H H = 0 (a) (b) (c) Figure 17.4 (a) In a diamagnetic material with no applied magnetic field (H 5 0), there is no dipole moment on individual atoms, and the intensity of magnetization (M) is 0. (b) When a magnetic field H is applied to a diamagnetic material, the response of the electrons on the atoms is to produce dipole moments that oppose the applied field H, resulting in a negative intensity of magnetization. (c) When H is removed from a diamagnetic material, the dipole moments on the individual atoms return to 0, and the intensity of magnetization (M) returns to 0. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 774)

9 W-76 CHAPTER 17 Some of the diamagnetic materials listed in Table 17.1 are metals, and metals have an additional diamagnetic contribution to the magnetic susceptibility. The free electrons in a metal form current loops (eddy currents) in compliance with Lenz s law that oppose an applied magnetic field. Eddy currents are also discussed in Section as a technique of nondestructive testing. Equation gives the magnitude of the dipole moment (p m ) created by a current (I) in amperes passing through a loop that encloses an area (A), as shown in Figure 17.3b. p m 5 IA The intensity of magnetization is the vector sum of all the dipole moments (p m ) in the material divided by the volume (V ), as shown in Equation o p m M 5 V From Equation the intensity of magnetization (M) is also the total dipole moment per unit volume of material. The eddy currents created in a metal by a rapidly alternating magnetic field result in joule heating. Induction furnaces or heaters use high-frequency alternating magnetic fields to induce eddy currents that heat and can even melt a metal. The orbital electron contribution to diamagnetism described by Equation 17.9 does not contribute to joule heating, because there is no resistance associated with the electron orbital Superconductors and Diamagnetism In a superconductor, there is no resistance to electrical current flow, and eddy current loops that are established as a result of applying a magnetic field ( H ) to a superconductor produce a magnetic field equal and opposite to the applied magnetic field ( H ). A superconductor is a diamagnet that has a magnetic susceptibility of 21, resulting in a value of M equal to 2H. If a magnet is placed over a superconducting material, the magnet is suspended in air or levitates, as shown in Figure Magnetic levitation occurs because the magnet induces in the superconductor magnetic field equal but opposite to itself. If a permanent magnet is oriented such that its south pole is pointing down toward the superconductor, the superconductor produces a magnetic field that has its south pole pointing up, as shown in Figure The south pole of the magnet and the south pole induced in the superconductor repel each other. Magnetic levitation (maglev) is used to lift and propel trains, allowing them to ride without any contact with the rails. The introductory photograph in this chapter is of commercial high-speed maglev train that connects the Shanghai, China airport to the city center, and Japan has the high-speed Linimo line. Lowspeed maglev trains are also under construction in Beijing, China and in Seoul, South Korea. Maglev trains are known for their high reliability and low maintenance. There is a limit to the magnitude of the magnetic field that can be applied to a superconductor and still have zero electrical resistivity. In a superconducting metal, the free electron spins are coupled into Cooper pairs of electron spin up and down, as discussed in Section However, when a magnetic field (H) is applied to an electron, there is a torque that rotates the electron spin axis into the direction of H. This torque is similar to the torque produced on a small magnet by a large magnet that aligns the small magnet s field to that of the large magnet. If the applied magnetic field (H) rotates the electron spins into the direction of H, then the coupling of Cooper electron pairs of the superconductor is destroyed, and the superconductivity is destroyed.

10 Magnetic Materials W-77 Figure 17.5 A photograph of a magnet levitating above a superconductor immersed in liquid nitrogen. ( Stonemeadow Photography / Alamy) N S Magnet S N Superconductor Figure 17.6 A schematic showing levitation of a magnet due to the magnetic field created in a superconductor that is equal and opposite to that of the original magnet.

11 W-78 CHAPTER Paramagnetism Paramagnetic materials have a small and positive magnetic susceptibility, typically from to 10 25, as demonstrated by subtracting 1 from the relative magnetic permeability of the paramagnetic materials in Table Paramagnetism is not of significant engineering use; however, the concepts developed for paramagnetic materials help us understand ferromagnetic materials that are of significant engineering importance. Why do diamagnetic materials have a negative magnetic susceptibility, whereas paramagnetic materials have a positive susceptibility? One reason for a positive magnetic susceptibility is that some atoms have a permanent net magnetic dipole moment (p m ). One way for an atom to have a net permanent dipole moment is for the atom to have a net electron spin. Hund s rule states that electrons on an atom with the same quantum numbers n and l tend to have their electron spins parallel. As electrons are added to the 3d shell with increasing atomic number, the first five electrons in the 3d shell all have parallel spins, as shown in Table Table 17.2 is for free atoms in a vapor. In solid or liquid metals, the number of parallel unpaired electron spins on atoms can be different than the number in Table 17.2, because the bonding has an effect on the electrons. One electron spinning about its axis creates a magnetic dipole moment, as shown in Figure 17.7, of 1 Bohr magneton (μ B ), where μ B A? m 2 and the direction of μ B is in the direction of the spin axis. Titanium has two electrons with parallel spins in the 3d shell, so each titanium atom produces a dipole moment (p a ) of two Bohr magnetons. When titanium atoms are subject to an applied magnetic field (H), the torque discussed in Section rotates the unpaired electron spins or dipole moments on the titanium atoms into the direction of H. The dipole moments on the individual titanium atoms due to the electron spins then produce an intensity of magnetization (M) that is in the same direction as H. Since M and H are in the same direction, this results in a positive magnetic susceptibility. Equation is used to calculate the magnitude of intensity of magnetization (M) resulting from parallel spins on an atom: M 5 n B B N v Table 17.2 Atoms in the First Transition Series and the Spin Orientation of the 3d and 4s Electrons Metal 3d Electron Spin Orientations 4s Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper

12 Magnetic Materials W-79 N e2 or e2 N Figure 17.7 A schematic of electron spin indicated by the curved arrow creating a dipole moment. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 768.) where n B is the average number of Bohr magnetons of magnitude B per atom pointing in the direction of H, and N v is the number of atoms per unit volume. For a paramagnetic material, the flux density (B) is linearly proportional to the applied magnetic field (H), as shown in Equation 17.3, and the intensity of magnetization (M) is linearly proportional to the applied magnetic field (H), as shown in Equation Figure 17.8a shows that M 5 0 when H 5 0 for a paramagnetic material, because there is a random orientation of electron spins on different atoms. As H is increased, the electron spins on the different atoms become oriented in the direction of H, as shown in Figure 17.8b, and the value of M increases linearly with H. When the H field is reduced, the intensity of magnetization follows the same slope as during the increase in H. When H is reduced to 0, M is equal to 0, as indicated by the return of the random orientations of the electron spins as shown in Figure 17.8c. The spins are randomized by lattice vibrations when H is reduced to 0. The magnetic susceptibility for a paramagnetic material decreases with increasing temperature, as expressed in the Curie law shown in Equation 17.13: 5 C T where C is a constant and the temperature (T ) is in kelvin. The susceptibility decreases with increases in temperature, because thermal vibrations disorder the electron spins. H = 0 H H = 0 (a) (b) (c) Figure 17.8 (a) In a paramagnetic material with no applied magnetic field, the dipole moments on individual atoms are in random directions, and there is no intensity of magnetization (M). (b) When a magnetic field (H) is applied, the atoms respond by producing dipole moments that are in the same direction as the applied field H, resulting in a positive intensity of magnetization (M). (c) When H is removed, the dipole moments on individual atoms return to random orientations, and there is no net intensity of magnetization (M) in the material. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 774)

13 W-80 CHAPTER 17 Example Problem 17.5 Titanium has a room-temperature magnetic susceptibility of Titanium is placed in a magnetic field of A/m at room temperature. (a) Determine the magnitude of the intensity of magnetization (M). (b) What is the average dipole moment per atom (p a ) in titanium that is parallel to the H of A/m? (c) The dipole moment per atom calculated in (b) corresponds to how many Bohr magnetons per atom? Solution a) M is calculated from the room-temperature susceptibility ( ) and H using Equation M 5 H M ( ) A/m A/m b) p a is calculated from Equation The number of atoms per unit volume (N v ) is calculated from the density ( kg/m 3 ) and the molar mass of titanium ( kg/mole). N v kg/m 3 atoms atoms kg/mole mole m 3 p a 5 M N v A/m A? m atoms/m atom c) Since one Bohr magneton ( B ) is equal to A? m 2, the number of Bohr magnetons (n B ) per atom is calculated as follows: n B 5 p a A? m 2 /atom Bohr magnetons B A? m /Bohr magneton atom Only 3.4 electron spins in 10,000 are parallel to the applied magnetic field H. Since titanium has two Bohr magnetons per atom, only a small fraction of the electron spins on titanium atoms are oriented in the direction of the applied magnetic field H Ferromagnetism The word ferro in Latin means iron. Iron was the first known ferromagnetic metal. There are other ferromagnetic metals, such as nickel, cobalt, and the rare earth metals gadolinium and neodymium. In ferromagnetic metals, the magnetic susceptibility is large and positive, as demonstrated by subtracting 1 from the relative permeability of ferromagnetic materials in Table It follows from Equation 17.5 that the intensity of magnetization is much greater than the applied magnetic field. The material develops more magnetic field than what is applied. How is this possible? Iron is a transition metal with six 3d electrons. Since there are a total of ten possible 3d electrons, according to Hund s rule the first five electrons have parallel spins, and the sixth 3d electron is antiparallel with the five parallel spins, as shown in Table As a result, an iron atom has four parallel electron spins that are unpaired. The difference in a paramagnetic and ferromagnetic material is demonstrated

14 Magnetic Materials W-81 M r M M s 2H s 2H c O H c H s H M s 2M r Figure 17.9 A schematic of a magnetic hysteresis loop for a ferromagnetic material, showing the magnitude of the intensity of magnetization (M) as a function of the magnitude of the applied magnetic field (H ). by subjecting the ferromagnetic material to a magnetic field. Figure 17.9 shows that for a ferromagnetic material the relationship between the applied magnetic field and the intensity of magnetization is not linear. In a ferromagnetic material, the intensity of magnetization increases rapidly as the applied magnetic field increases. The intensity of magnetization is greater than the applied magnetic field because the unpaired electron spins are rotated into the direction of H, and the unpaired electron spins produce an M that adds to H to produce a higher magnetic field. At some applied magnetic field, the intensity of magnetization is saturated at M s. At M s, the maximum number of individual atom unpaired electron spins is parallel to H, as shown in Figure 17.10a. Since the ferromagnetism of iron comes from oriented H = H s H = 0 H = 2H c (a) (b) (c) H = 2H s H = 0 H = H c (d) (e) (f) Figure The orientation of unpaired electron spins under various conditions in a ferromagnetic material. (a) In magnetic domains at saturation. (b) In magnetic domains with H 5 0. (c) In magnetic domains with H 5 2H c. (d) At reverse saturation. (e) In magnetic domains with H 5 0. (f) In magnetic domains with H 5 H c. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 774.)

15 W-82 CHAPTER 17 Figure A micrograph showing magnetic domains in a single grain of unmagnetized steel. The direction of magnetization is indicated by the arrows. (S. Zurek, C. Vardon, CC-BY-3.0, Encyclopedia Magnetica) unpaired electron spins on atoms, the average number of unpaired electron spins oriented in the direction of H is calculated from the saturation magnetization using Equation If the applied magnetic field is reduced to 0 from saturation in a ferromagnetic material, the intensity of magnetization only reduces to the remanent magnetization (M r ). A remanent magnetization indicates that the unpaired electron spins in the ferromagnetic material remain ordered in the former direction of H; however, there is some relaxation of unpaired electron spin orientations, as shown in Figure 17.10b. The remanent magnetization (M r ) is a result of the magnetic field created by the oriented unpaired electron spins, and this magnetic field is sufficient to maintain the unpaired electron spins on the atoms oriented in the initial direction of the applied magnetic field. Figure 17.9 shows that it is necessary to reverse the magnetic field to H c, the coercive field, to reduce the intensity of magnetization to 0. In a demagnetized material, when M is forced to 0 from the saturated state, the unpaired electron spins are not disordered. The unpaired electron spins are ordered into magnetic domains that have parallel unpaired electron spin orientations, and the sum of the unpaired electron spins in different domains cancel each other, as shown schematically in Figures 17.10c and in Figure 17.11, resulting in a net magnetization of 0. Figure shows that in a polycrystalline ferromagnetic material, the domain can be a single small grain, or a grain can contain several domains. Figure is an image of an unmagetized steel produced with a Kerr effect optical microscope. A Kerr effect microscope is capable of analyzing the polarization and intensity of light reflected from a surface that is dependent upon the direction of magnetization in the material. Small grain with a single domain A grain with domains Figure A schematic of magnetic domains in a ferromagnetic polycrystal. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 777.)

16 Magnetic Materials W-83 Domain Bloch wall Domain Direction of magnetic moments Figure The unpaired electron spin orientations change direction at the Bloch wall. (Based on Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p. 777.) The border between domains where unpaired electron spins rotate from one orientation to another is a Bloch wall, as shown in Figure Bloch walls can move under the effect of a magnetic field to allow a change in the net orientation of unpaired electron spins. When a change in H forces a change in M, Bloch wall motion is one way that the unpaired electron spin orientations can change. When the applied magnetic field is increased in the reverse direction until the intensity of magnetization reaches saturation (2M s ), the maximum number possible of magnetic domains are oriented with their magnetization in the reverse direction, as shown in Figure 17.10d. As the applied H is reduced again to 0, the intensity of magnetization changes to 2M r, and the magnetic domains continue to have their magnetization parallel to the reverse direction of H, as shown in Figure 17.10e. Increasing H again in the forward direction results in magnetic domains with magnetization oriented in the direction of H. At H c in the forward direction, M is equal to 0, and the magnetic domains are equally balanced to cancel each other, as shown in Figure 17.10f. The cycle from 1M s to 2M s and again to 1M s is a hysteresis loop. Example Problem 17.6 The saturation magnetization (M s ) of iron measured at room temperature is A/m. Calculate the average number of Bohr magnetons per iron atom, knowing that iron has a BCC structure at room temperature with a lattice parameter of nm. Solution The saturation magnetization is related to the number of Bohr magnetons in Equation 17.12: M s 5 n B B N v At room temperature the lattice parameter of iron is nm, and the lattice is BCC with an atom at the position 0, 0, 0. There are two atoms per BCC unit cell. The number of atoms per unit volume (N v ) is then calculated as follows: N v 5 2 atoms s md 5 2 atoms atoms m m 3 Since B A? m 2, everything in Equation is known except the number of Bohr magnetons (n B ). n B 5 M s A/m Bohr magnetons B N v A? m 2 /Bohr magneton s atoms/m 3 d atom

17 W-84 CHAPTER 17 On the average atom in metallic iron at room temperature, there are 2.20 parallel unpaired electron spins, as shown in Example Problem Table 17.2 shows that an iron atom has four parallel unpaired electron spins in the 3d shell for a free iron atom in the vapor at a temperature of absolute zero. The metallic bond in iron changes the unpaired electron spin orientations of the 3d electrons relative to those of the free atom, and thermal vibrations of the metal atoms at room temperature further reduce the number of atoms with unpaired electron spins parallel to the applied magnetic field relative to those at absolute zero. Example Problem 17.7 The rare earth element terbium (Tb) has one of the highest number of Bohr magnetons per atom of Calculate the saturation magnetization for terbium. Solution The saturation magnetization and the number of Bohr magnetons are related through Equation M s 5 n B B N v M s and N v are unknown, and we know both n B and B. Appendix B does not have any information about the crystal structure of terbium, but we can calculate the number of atoms per unit volume from data in the periodic table by using the molar mass of kg/mole, Avogadro s number, and the density of kg/m 3. N v kg/m 3 atoms atoms kg/mole mole m 3 Now substitute N v into Equation and solve for M s. M s 5 n B B N v Bohr magnetons atom A? m 2 atoms Bohr magneton m 3 M s A m Even though the number of Bohr magnetons in terbium is 4.2 times the number in iron, the saturation magnetization of terbium is only 1.5 times that of iron. The reason is the low number of atoms per unit volume in terbium. The saturation magnetization in a ferromagnetic material is a function of temperature, as shown in Figure At very low temperatures the unpaired electron spins are parallel, and at high temperatures thermal vibrations disorient the unpaired electron spins. At sufficiently high temperatures the unpaired electron spins cannot be oriented, because of thermal vibrations. At the Curie temperature (T c ) ferromagnetic materials change to paramagnetic with increasing temperature. Table 17.3 presents the Curie temperature of some ferromagnetic and ferrimagnetic materials. Is it possible to eliminate magnetic domains from a ferromagnet that has been in a strong magnetic field, and to demagnetize the material? Figure gives one answer. Heating the ferromagnet to above the Curie temperature in the absence of a magnetic field disorders the unpaired electron spins. On an individual atom, the unpaired electron spins will remain parallel; however, the magnetic domains are

18 Magnetic Materials W-85 Table 17.3 Material The Curie Temperature of Some Magnetic Materials Curie Temperature ( C) Gadolinium 16 Nd 2 Fe 12 B 312 Nickel 358 Co 5 Sm 747 Iron 771 Alnico Cunico 855 Alnico Cobalt 1117 Based on data from Askeland, D.R., Fulay, P.P., and Wright, W.J., The Science and Engineering of Materials, 6th ed., Cengage Learning, Stamford, CT. (2011), p eliminated by the heating. Subsequently cooling the ferromagnet in the absence of a magnetic field results in a demagnetized material without magnetic domains. Iron, cobalt, and nickel are ferromagnetic metals. Because they are metals, they have free electrons. If a ferromagnetic metal is subject to a rapidly alternating magnetic field (H), the free electrons in the metal form current loops (eddy currents) that create a diamagnetic response in the metal that opposes the application of H. The eddy currents produce joule heat in the metal, increasing the temperature. In an induction furnace, an alternating magnetic field is used to induce eddy currents that melt metals such as aluminum, copper, gold, iron, and silver. If the metal temperature in a magnet used in an alternating magnetic field exceeds the Curie temperature, the ferromagnetism is destroyed. Therefore, metallic ferromagnets are not suitable for applications in high frequency magnetic fields. M s T T c Figure A schematic for a ferromagnetic material of the magnitude of the saturation magnetization (M s ) for a magnetic field pointing to the right and the relative order in the unpaired electron spin orientations as a function of temperature up to the Curie temperature (T c ).

19 W-86 CHAPTER Ferrimagnetism Ferrimagnetic materials, or ferrites, such as Fe 3 O 4, have hysteresis loops and a magnetic susceptibility that are both similar to iron. However, ferrimagnetic materials are insulators. Whereas in metallic iron the two 4s electrons are free electrons, the two 4s electrons in Fe 3 O 4 are transferred to the oxygen, forming O 22 and Fe 21. There are no free electrons in the insulator Fe 3 O 4. The Fe 21 ion has four parallel unpaired electron spins after removal of the two 4s electrons from the Fe atom, as shown in Table For Fe 3 O 4 in a high-frequency alternating magnetic field, there is no joule heating due to induced eddy currents, because there are no free electrons. The ferrites are based upon Fe 3 O 4. Substitution of NiO or CoO for FeO in Fe 3 O 4 forms NiO:Fe 2 O 3 or CoO:Fe 2 O 3. Ferrimagnetic materials are utilized in high-frequency applications, such as televisions, communications equipment, and microwave devices. Table 17.4 lists the magnetic properties of some ferrites. Table 17.4 Some Soft Magnetic Materials and the Chemical Composition, Initial Relative Permeability, Maximum Relative Permeability, Coercivity, Retentivity, Maximum Inductance, and Electrical Resistivity of Each Permeability r Coercivity Retentivity B max Resistivity Name Composition Initial Maximum H c (A? m 21 ) B r (T) (T) ( V? m) Ingot Iron 99.8% Fe Low-carbon steel 99.5% Fe Silicon iron, unoriented Fe23% Si Silicon iron, Fe23% Si , grain-oriented 4750 alloy Fe248% Ni 11,000 80, permalloy Fe24% Mo279% Ni 40, , o.58 Superalloy Fe25% Mo280% Ni 80, , V-Permendur Fe22% V249% Co , Supermendur Fe22% V249% Co 100, Metglas a 2605SC Fe 81 B 13.5 Si 3.5 C 2 300, Metglas a 26052S2 Be 78 B 13 Si 9 600, MnZn Ferrite H5C2 b 10, MnZn Ferrite H5E b 18, NiZn Ferrite K5 b a Allied Corporation trademark. b TDK ferrite code. (Based on data from "Magnetic Materials: An Overview, Basic Concepts, Magnetic Measurements, Magnetostrictive Materials," by G.Y. Chin et al. In R. Bloor, M. Flemings, and S. Mahajan (eds.), Encyclopedia of Advanced Materials, Vol. 1, Peragamon Press. (1994), p. 1424, Table 1.)

20 Magnetic Materials W Soft and hard magnetic materials Both ferromagnetic and ferrimagnetic materials can be either soft or hard. Soft magnetic materials have a low H c and hard magnetic materials have a high H c, as shown in the hysteresis loops in Figure In a soft magnet, Bloch wall motion is easy, and the intensity of magnetization changes by the motion of the Bloch walls to increase the size of the domains oriented in the direction of the applied magnetic field. In hard magnetic materials, the Bloch wall motion is very difficult. If the Bloch walls do not move in response to the applied magnetic field, the unpaired electron spins must flip within the domains into the direction of the applied magnetic field to change the magnetization. Tables 17.4 and 17.5 list some soft and hard magnetic materials, respectively. In Table 17.4 the retentivity (B r ) is also called the remanence, and B r is equal to μ 0 M r. B max in Table 17.4 is equal to the maximum relative permeability (μ r ) times μ 0 M s. The electrical resistivity listed in Table 17.4 is important for soft magnetic materials that are to be utilized in alternating magnetic fields. A high electrical resistivity suppresses eddy currents that heat the magnetic material in an alternating magnetic field. The ferrites have the highest electrical resistivity of any materials in Table In soft magnetic materials, Bloch wall motion is made easy by having a uniform material without defects that would impede this motion. An example of a soft magnetic material is iron with 3 weight percent silicon. This material has a very low carbon content to prevent the formation of iron carbide. The silicon is added to increase the electrical resistivity. A high electrical resistivity reduces the magnitude of the eddy currents in a cyclic magnetic field. Iron-silicon alloys are used extensively in electrical motors and transformer cores that have the magnetic field reversed at a frequency of 60 Hz. Hard magnetic materials are used in applications where the intensity of magnetization is permanent, such as in magnetic separators, control devices for electron beams, and magnetic holding devices. In hard magnetic materials, domain walls are pinned by placing obstacles in the path of wall motion. The same defects that make metals mechanically hard also make metals magnetically hard. In hard magnetic M Hard Soft H Figure A schematic of the magnitude of the intensity of magnetization (M ) as a function of the magnitude of the applied magnetic field (H) for hard and soft ferromagnetic or ferrimagnetic materials.

21 W-88 CHAPTER 17 Table 17.5 Some Hard Magnetic Materials and the Retentivity (B r ), coercivity (H c ), (BH) max, and Curie Temperature (T c ) for each Material B r (Tesla) H c (10 5 A/m) BH max (kj? m 23 ) T c ( C) Co-steel Alnico BaFe 12 O SmCo Nd 2 Fe 14 B Based on data from from Permanent Magnetism, by R. Skomski and J. M. D. Coey. Edited by J. M. D. Coey and D. R. Tilley, Institute of Physics Publishing. (1999), p. 23, Table 1.2. materials, second-phase particles, such as borides in Nd 2 Fe 14 B or Ni 3 Al in alnico, are barriers to domain wall motion. Alnico is an acronym for a family of iron-based ferromagnetic alloys, that contain Al, Ni, and Co. Some of the hard magnetic materials, such as alnico, are of similar composition to hightemperature and high-mechanical-strength metal alloys. The magnetic properties of some hard magnetic materials are presented in Table Comparing the soft magnetic materials in Table 17.4 to the hard magnets in Table 17.5, the main difference is the value of the coercivity. The hard magnetic materials have a coercivity from three to five orders of magnitude larger than that of soft magnetic materials. The high coercivity is important for permanent magnets. In Table 17.5, the term (BH ) max is a measure of the energy density that is induced into a magnetic material by an applied magnetic field, as shown in Figure An area in a plot of B versus H using SI units is energy density in joules/m 3. This is analogous to the area under a stress-strain plot that is also energy density. The term (BH ) max is the area of the maximum-size rectangle that can be drawn in the second or fourth quadrant of the B versus H plot. Strong permanent magnets have a high (BH ) max. ( BH ) max Magnetic flux density Magnetic field Figure A schematic plot of the magnetic flux density (B) versus the applied magnetic field (H) and (BH) max. (Based on Permanent Magnetism, by R. Skomski and J. M. D. Coey. Edited by J. M. D. Coey and D. R. Tilley. Institute of Physics Publishing. (1999), p. 25, Fig )

22 Magnetic Materials W Magnetic recording Magnetic materials are utilized for recording information on magnetic recording tapes and hard disks for computers. Magnetic recording tapes are made in two ways. Small magnetic particles are embedded in a polymer tape, and the second method is by depositing thin films of magnetic material onto a polymer backing. The magnetic materials for thin film coatings are similar to the materials for hard disks that are discussed later in this section. The metal coating is deposited onto a polymer tape made of polyethylene terephthalate (PET) known by the trade name of Mylar TM. An advantage of magnetic particle tapes is that they are less expensive to produce. The cost of particle magnetic tape data storage is approximately $0.01 per gigabyte (GB). Some of the magnetic recording particle materials are shown in Table A recent magnetic particle is barium hexaferrite (BaFeO) that has a formula such as BaFe 12 O 19 ; however, several other compositions are also observed. The BaFeO particles in Table 17.6 are thin hexagonal platelets with a diameter of approximately 0.08 μm. With BaFeO tapes it is possible to store bits of data per square inch of tape. Magnetic tape materials have values of retentivity, as shown in Table 17.6, similar to both hard and soft magnetic materials and the coercivity of magnetic tape materials is higher than for soft magnetic materials but less than for hard magnetic materials. Magnetic tape is used for archival data storage, and the magnetic stripe on a credit card is a magnetic tape. The data are recorded onto the tape by applying a magnetic field that orients the unpaired electron spins along the long axis of the particle in the forward or reverse direction. This corresponds to a 1 or a 0 for digital data storage. The data storage is permanent, because after writing the data by producing saturation magnetization (M s ) in the material, the magnetization remains at the remanent magnetization (M r ) after removal of the magnetic field. The coercive field of the magnetic particles (H c ) must be sufficiently large that the unpaired electron spin orientations are not altered by stray magnetic fields; however, H c also must be sufficiently small that it can be changed by the magnetic field in the write heads of the data storage system. It is possible to erase the data by reversing the applied magnetic field and to rewrite new data by applying a new magnetic field. One disadvantage of tape is that tape must be wound to find the data; therefore, it is best utilized for archiving of data. Hard disks allow data to be located more quickly. The permanent data storage in most computers is on hard disks. The hard disk is a magnetic recording medium made of a fine-grained (approximately 30 nm) thin film of metal alloy such as Co-Cr-Pt or Co-Cr-Ta, and each grain of the metal film is a potential recording location. On a hard disk, magnetic thin film is deposited on a nonmagnetic substrate material, such as an aluminum alloy, and for magnetic Table 17.6 Properties of Some Magnetic Recording Particles, Including the Particle Length (L), Aspect Ratio (L/d ) Retentivity (B r ), Coercivity (H c ), and Curie Temperature (T c ) Material L (μm) L/d B r (tesla) H c (ka? t/m) T c ( C) g-fe 2 O / Co-g-Fe 2 O / CrO / Fe / BaFeO Based on data from The Complete Handbook of Magnetic Recording, Fourth Edition, by F. Jorgensen, The McGraw-Hill Companies. (1996), p. 324, Table 11.1.

23 W-90 CHAPTER 17 tape similar alloys are deposited on polymer tape. The direction of magnetization determines if the data is a 1 or a 0. The first hard disks introduced in 1956 could store 3 MB of information in a device the size of two refrigerators. Modern hard disks can store 3 TB in a device with a volume of approximately one cubic inch, and in the year 2012 each bit of data required approximately 800,000 atoms Antiferromagnetism Materials such as Cr, Mn, MnO, MnS, and NiO are antiferromagnetic. From Table 17.2 it might be expected that Cr and Mn would be ferromagnetic; however, they are antiferromagnetic at temperatures below the Neel temperature. At the Neel temperature, antiferromagnetic materials change to paramagnetic upon heating. In antiferromagnetic materials the unpaired electron spins on different atoms align antiparallel, and the magnetic moment from the paired spins cancel each other, as shown in the 2-D schematic in Figure In the simplest antiferromagnetic materials, such as BCC Cr and Mn, there are two sublattices A and B. The A sublattice atoms are at the BCC lattice cube corners, and the B sub lattice atoms are at the body centered atom positions. The unpaired electron spins in the A lattice behave as though they are ferromagnetic, and the unpaired electron spins on the B lattice also behave as though they are ferromagnetic. However, the electron spins on the A and B lattices oppose each other and cancel out the intensity of magnetization. The magnetic susceptibility ( ) for an antiferromagnetic material is positive and small. is positive because the magnetic field rotates electron spins into the direction of the applied magnetic field, and is small because of the opposed unpaired electron spins. in the antiferromagnetic state decreases as temperature decreases, because the unpaired electron spins on the two lattices more perfectly cancel each other out at lower temperatures. In the paramagnetic state, the magnetic susceptibility decreases as temperature increases, because thermal vibrations disorder the unpaired electron spins. At the Neel temperature, the magnetic susceptibility is at its maximum. Scientists at IBM have recently demonstrated the possibility of storing data with as few as 12 atoms of iron that are antiferromagnetic. Figure shows how 12 atoms of iron are aligned in 2 rows of 6 atoms each, in a stable cluster of iron atoms on a copper nitrate substrate. In the configuration shown, the iron atoms are antiferromagnetic and stable. If the magnetic state is changed to ferromagnetic, the clusters are not stable. Although iron is ferromagnetic at room temperature, it is possible for the magnetic state of materials to change with temperature and with lattice strain. For example, Fe 2 O 3 is ferrimagnetic at room temperature, and it is antiferrimagnetic at temperatures below 260 K. For computer information storage, the stable antiferromagnetic state of 12 antiferromagnetic Fe atoms could represent a 1, and the unstable ferromagnetic state could represent a 0. Each cluster of 12 Fe atoms would be one bit of information. Although this form of memory may never be practical, memory based upon parallel and antiparallel unpaired electron spins is already in use in magnetoresistance systems, discussed next in Section Figure The orientation of unpaired electron spins in 2-D schematic of an antiferromagnetic material. The oriented unpaired electron spins sum to 0.

24 Magnetic Materials W-91 Figure An STM image of eight clusters of iron atoms in an antiferromagnetic state, with each cluster containing 12 iron atoms in two rows of six atoms, on a copper nitrate surface. Each cluster of 12 atoms could be one bit of memory. The randomly placed atoms are xenon. (IBM) Magnetoresistance Magnetoresistance is when a change in the magnetization of a magnetic material changes the electrical resistivity. Disordered unpaired electron spin orientations on atoms in a metal scatter conduction electrons more frequently than do ordered unpaired electron spins. A ferromagnetic metal with unpaired electron spins all oriented in the same direction has a lower electrical resistivity than the same metal with unpaired electron spins oriented in different directions. Giant magnetorestistance (GMR) have been found in some layered magnetic materials, where it is possible to produce changes of 10% in the electrical resistivity by changing the magnetic state of the material. In one GMR material, layers of a ferromagnetic material (FM), such as Fe, and nonmagnetic (NM) spacers, such as of Cr, alternate, as shown schematically in Figure The layered material is produced by repeatedly depositing thin layers of material, and each layer is approximately 10-atoms thick. If a saturation magnetic field (H s ) is applied to the GMR material, all of the unpaired electron spins in the FM layers are oriented parallel, and the direction of magnetization (M) in each layer is parallel as shown by the large arrows in the FM material in Figure 17.19a. The conduction electrons in the FM metal Fe are primarily 4s electrons, and their spins are paired up and down. The up and down spin directions of the 4s electrons are indicated by the small up and down arrows on the left of each figure. Conduction electrons with spin opposite to M of the FM material are scattered more frequently by the vibrating iron atoms, as indicated by the irregular line crossing Figure 17.19, and conduction electrons with spin parallel to M are conducted, as indicated by the straight line. If the applied magnetic field is reversed to the coercive field (2H c ), then the direction of M alternates in the layers, as shown in Figure 17.19b. With layers of FM material having directions of M that alternate, both spin-up and spindown conduction electrons are scattered, and this material has a higher electrical resistivity than with parallel M. The GMR effect is an application of spintronics. Spintronics is the use of electron spin to produce electronic devices. Several applications of spintronics have been developed. GMR materials are used as read heads for magnetic recording systems. At the time of this writing, GMR read heads can read approximately bits per square meter. The magnetic field of a recorded bit that produces parallel unpaired electron spin layers in the GMR read head results in a low electrical resistivity, and a recorded bit that produces antiparallel unpaired electron spins in the read head results in a high electrical resistivity. The low and high electrical resistivity correspond to reading a 1 or a 0, respectively, from the hard disk.

25 W-92 CHAPTER 17 Spin FM NM FM Spin FM NM FM (a) (b) Figure A schematic of the structure of a GMR material, showing layers of ferromagnetic (FM) material and nonmagnetic (NM) material. In (a) the FM layers have parallel intensity of magnetization (M), as indicated by the large bold arrows. The path of conduction electrons is indicated by arrows crossing the layers, and the spin of the conduction electrons is indicated by the small arrows to the left of the figure. Conduction electrons with spin that is opposite to M are more likely scattered by vibrating FM atoms than conduction electrons with spin parallel to M. In (b) with alternating M, electrons with spin up and spin down are scattered in the FM material resulting in a higher resistivity than the material with parallel M. (Based on The GMR effect is also used for memory in magnetoresistive random access memory (MRAM). In MRAM the magnetic state of parallel unpaired electron spins, shown in Figure 17.19, is a 1; and the state with antiparallel unpaired electron spins is a 0. The magnetic state is switched with an applied magnetic field (H), and the magnetic state of the MRAM is determined by electrical resistivity. Summary A magnetic field is created by passing an electrical current through loops of conducting wire. The response of the environment to a magnetic field is called the magnetic flux density. The intensity of magnetization is the magnetic field created in a material by an external applied magnetic field. The intensity of magnetization of a material is a result of free electrons forming current loops, of the alteration of the electron orbitals on atoms, and of the orientation of unpaired electron spin. The ratio of the intensity of magnetization to the applied magnetic field is the magnetic susceptibility. Diamagnetic materials, other than superconductors, have a small negative magnetic susceptibility. All atoms have a diamagnetic response when a magnetic field is applied. The electron orbits on the atom are altered to oppose the applied magnetic field in compliance with Lenz s law. In a metal, free electrons form current loops or eddy currents in compliance with Lenz s law, which oppose an applied magnetic field. Superconductors have a magnetic susceptibility of 21. An applied magnetic field induces in a superconductor a magnetic field equal and opposite to the applied magnetic field. The induced

26 Magnetic Materials W-93 magnetic field in a superconductor results in interesting applications such as the magnetic levitation of trains. Paramagnetic materials have a small positive magnetic susceptibility that results from orienting electron spin in the direction of the applied magnetic field. Ferromagnetic materials are metals that have a large magnetic susceptibility dependent upon the magnitude of the applied magnetic field. Ferromagnetism results when there is a large number of parallel unpaired electron spins on the atoms. Applied magnetic fields (H) rotate the unpaired electron spins to produce an intensity of magnetization (M) that adds to H. At saturation, all unpaired electron spins are oriented parallel to H. When H is subsequently reduced to 0, there is a remanent M. To reduce M to 0 requires the application of the coercive magnetic field in the reverse direction. When M is reduced to 0, the unpaired electron spins are parallel within magnetic domains, and the sum of the unpaired electron spins over all of the magnetic domains is 0. When a ferromagnetic metal is heated above the Curie temperature, the metal becomes paramagnetic. An alternating magnetic field induces current loops in a ferromagnet that heat the metal. Ferrimagnetic materials, such as Fe 3 O 4, have hysteresis loops similar to those of a ferromagnetic material, but they are insulators. Ferrimagnetic materials are utilized in high-frequency applications, such as televisions, communications equipment, and microwave devices. Soft magnetic materials have a small coercivity, and hard magnetic materials have a large coercivity. Soft magnetic materials are used in applications with alternating magnetic fields, and hard magnetic materials are used in applications requiring permanent magnets. Magnetic recording tapes are made with magnetic particles that are embedded in a polymer tape and by depositing a thin film of magnetic material on the tape. The magnetic particles are usually elongated with an aspect ratio of 5/1 to 10/1, and the magnetic particles are so small that each particle is a single magnetic domain. The hard disk for computer permanent memory is a magnetic recording medium made of a fine-grained (approximately 30 nm) thin film metal alloy such as cobalt-chromium-platinum or cobalt-chromium-tantalum, and each grain of the metal film is a potential recording location. In antiferromagnetic materials, such as Cr, Mn, and MnO, the unpaired electron spins on different atoms align antiparallel below the Neel temperature, and above the Neel temperature the materials are paramagnetic. The magnetic susceptibility for an antiferromagnetic material is positive and small. Magnetoresistance is when a change in the magnetic state of a material changes the electrical resistivity of the material. Giant magnetorestistance (GMR) has been found in some multilayered magneticspacer materials, where it is possible to produce very large changes, such as 10%, in the electrical resistivity by changing the magnetic state of the material. GMR materials are now used for the read heads in magnetic recording systems and in magnetoresistance random access memory (MRAM). Supplemental Reading: Subjects and Authors Full references are listed at the end of the book. General: Askeland, Fulay, and Wright Electromagnetics: Kraus Magnetic materials: Chikazumi; Crangle

27 W-94 CHAPTER 17 Homework Concept Questions 1. The flux density divided by the applied magnetic field strength is equal to the magnetic. 2. The intensity of magnetization divided by the applied magnetic field strength is equal to the magnetic. 3. The dipole of a magnet is the pole strength times the separation distance of the two poles. 4. The relative magnetic permeability of a vacuum is equal to. 5. If the magnetic susceptibility of a material is , this material is. 6. A superconductor at temperatures below the critical temperature has a magnetic susceptibility equal to. 7. If the magnetic susceptibility of a material is , and the susceptibility decreases with an increase in temperature, this material is. 8. A positive magnetic susceptibility is due to an applied magnetic field orienting electron in the direction of the applied magnetic field. 9. In a paramagnetic material, if a large magnetic field is first applied and then reduced to 0, the intensity of magnetization is then equal to. 10. The applied magnetic field necessary to reduce the intensity of magnetization of a ferromagnetic material to 0 after saturation in the forward direction is the field. 11. In a ferromagnetic material, regions of parallel unpaired electron spin are magnetic. 12. To demagnetize a ferromagnetic metal, heat it to above the temperature in the absence of a magnetic field. 13. Materials that have a large magnetic susceptibility and are insulators are. 14. Ferromagnetic materials with a large are hard magnetic materials. 15. A(n) material has a small positive magnetic susceptibility that approaches 0 at 0 K, increases with increasing temperature, reaches a maximum, and then is paramagnetic with further increases in temperature. 16. At a wall, the unpaired electron spins orientation changes from one orientation to another. 17. occurs when there is a change in electrical resistivity in a ferromagnetic material resulting from an application of a magnetic field. Engineer in Training Style Questions 1. The magnetic field produced in a material resulting from an applied magnetic field is called the (a) Intensity of magnetization (b) Magnetic flux density (c) Magnetic permeability (d) Magnetic susceptibility

28 Magnetic Materials W If the relative magnetic permeability of a material is equal to , this material is (a) Diamagnetic (b) Paramagnetic (c) Ferromagnetic (d) Antiferromagnetic 3. Superconductivity is destroyed by a high magnetic field because the magnetic field (a) Heats the superconductor (b) Induces current in the superconductor (c) Rotates Cooper pair electron spins into the same direction (d) Alters the orbits of electrons on the atoms 4. In a paramagnetic material the magnetic susceptibility is (a) Linearly dependent upon temperature (b) Independent of temperature (c) A nonlinear function of temperature (d) Inversely dependent upon temperature 5. A given metal has a magnetic susceptibility of 100,000. This metal is (a) Diamagnetic (b) Antiferromagnetic (c) Ferromagnetic (d) Paramagnetic 6. When the applied magnetic field on a ferromagnetic material is reduced to 0 after saturation, the intensity of magnetization is equal to (a) 0 (b) The saturation magnetization (c) The remanent magnetization (d) The coercive field 7. The heating of a ferromagnet in an alternating magnetic field is due to (a) Induced free-electron current loops (b) Alterations of atomic electron orbitals (c) Switching of electron spin orientations (d) Friction created by Bloch wall motion 8. Which of the following materials is most appropriate for a design requiring a material with a high magnetic susceptibility that will be subjected to an alternating magnetic field of 10 6 Hz? (a) Fe23 weight percent Si (b) MnO (c) Alnico25 (d) Fe 3 O 4 9. Which of the following materials is most appropriate for a design requiring a material with a high magnetic susceptibility that will be subjected to an alternating magnetic field of 60 Hz? (a) Fe23 weight percent Si (b) MnO (c) Alnico25 (d) Fe 3 O 4

29 W-96 CHAPTER Which of the following materials is most appropriate for a design requiring a material with a permanent high intensity of magnetization? (a) Fe23 weight percent Si (b) MnO (c) Alnico25 (d) Fe 3 O The main difference between hard and soft magnetic materials is their (a) Remanence (b) Saturation magnetization (c) Coercivity (d) Electrical resistivity 12. Which of the following materials is most appropriate for a design of the magnetoresistance random access memory for a computer? (a) Layers of Fe and Ni (b) Layers of Fe and Cr (c) Layers of Fe 3 O 4 and MnO (d) Fe23 weight percent Si Problems Problem 17.1 Problem 17.2 Problem 17.3 Problem 17.4 Problem 17.5 Problem 17.6 (a) Calculate the magnetic field created by a coil made of copper wire that has 200 turns in 5 cm and carries a current of 5 A. (b) What is the magnitude of the flux density or inductance created by this coil in a vacuum? You are asked to design a coil that will produce a magnetic field of A/m. The maximum current for the coil wire is 1 A, and the space available for the coil limits the coil length to 1 cm. How many loops are required for the coil? You are asked to design a coil to operate in air that will produce a flux density of 0.01 T. The maximum current for the coil wire is 1 A, and the space available for the coil limits the length to 1 cm. How many loops are required for this coil? Round your answer to the nearest whole number. A coil to be operated in air has 200 loops in a length of 3 cm. What current is required to produce a flux density of 0.02 T? A solenoid made of copper wire has 100 turns in 3 cm and carries a current of 3 A in air. The ferromagnetic material 78 Permalloy (See Table 17.1) is inserted into the coil. What is the flux density created by the coil with this material inserted? A solenoid is available that has 100 loops in 2 cm of length with a supermalloy core (See Table 17.1), and the maximum current for the solenoid wire is 1A. What flux density is possible for this solenoid in air?

30 Magnetic Materials W-97 Problem 17.7 Problem 17.8 Problem 17.9 A solenoid must be produced that has a magnetic flux density of 25 Wb/m 2. The coil for the solenoid has 200 loops in a distance of 2 cm, and the maximum current for the wire is 1A. Select a suitable material for this solenoid from the materials listed in Table 17.1 that you expect to be cost effective. A solenoid must be produced that has a magnetic flux density of 25,000 T. The coil for the solenoid has 200 loops in a distance of 1 cm, and the maximum current for the wire is 1 A. Select a suitable material for this solenoid from the materials listed in Table For this design, performance is more important than cost. A magnetic field of 10 4 A/m is produced by a coil. What is the intensity of magnetization of the following materials placed into the coil? (a) Silver (b) Vacuum (c) Air (d) Palladium (e) Nickel Problem Prove that x 5 r 2 1. Problem Copper is usually the material of choice for the wire in a coil to produce a magnetic field and in wiring for electric motors. Copper wire is placed in a magnetic field (H) of A/m. The magnetic susceptibility of copper is (a) Determine the intensity of magnetization (M) in the copper. Is this M in the same direction or opposed to H? (b) What is the average dipole moment per atom (p a ) in copper that is parallel or antiparallel to H when subjected to the applied magnetic field? Problem Sodium metal is paramagnetic with a dimensionless magnetic susceptibility ( ) of The paramagnetism of sodium metal is due to the rotation of some of the spins of the metal s free electrons into the direction of the applied magnetic field. The applied magnetic field is equal to A/m. Sodium metal is BCC with a lattice parameter of m, and sodium is from Group 1 A of the periodic table. (a) What is the intensity of magnetization or the dipole moment per unit volume? (b) For sodium, what is the number of atoms per unit volume, and what is the number of free electrons per unit volume? (c) What is the dipole moment per sodium atom? (d) Assuming that all of the magnetic susceptibility is due to the orientation of free-electron spins, what is the net number of free electron spins per atom oriented in the direction of the applied magnetic field? Problem The number of Bohr magnetons per atom for cobalt is Calculate the saturation magnetization for cobalt.

31 W-98 CHAPTER 17 Problem The saturation magnetization of nickel measured at room temperature is A/m. (a) Calculate the average number of Bohr magnetons on a nickel atom, knowing that nickel has an FCC structure with an atom at 0, 0, 0. At room temperature, the lattice parameter is nm. (b) Compare your answer to part (a) with the theoretical number of Bohr magnetons based upon the atomic electron structure of nickel, and explain any possible difference. Problem The rare earth element gadolinium is ferromagnetic, and it has a saturation magnetization of A/m at low temperatures. (a) Calculate the number of Bohr magnetons per atom of gadolinium, knowing that the atomic mass is g/mole and the density is 7.89 g/cm 3. (b) What is the average number of parallel unpaired electron spins in the 4f shell per gadolinium atom?