Bate, G, Kryder, M.H. Magnetism and Magnetic Fields The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Bate, G., Kryder, M.H. “Magnetism and Magnetic Fields” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
36 Magnetism and Magnetic Fields 36.1 Magnetism Static Magnetic Fields. Time-Dependent Electric and Magnetic Fields. Magnetic Flux Density. Relative Permeabilities. Forces on a Moving Charge. Time-Varying Magnetic Fields. Maxwell ' Equations. Dia- and Paramagnetism.Ferromagnetism and Geoffrey Bate Ferrimagnetism. Intrinsic Magnetic Properties. Extrinsic Magnetic Properties. Amorphous Magnetic Materials 6.2 Magnetic Recording Fundamentals of Magnetic Recording. The Recording Mark H. Kryder Process. The Readback Process. Magnetic Recording Carnegie Mellon University Meda· Magnetic Recording heads· Conclusions 36.1 Magnetism Geoffrey bate Static Magnetic Fields To understand the phenomenon of magnetism we must also consider electricity and vice versa. A stationary electric charge produces, at a point a fixed distance from the charge, a static(i.e, time-invariant)electric field A moving electric charge, i.e., a current, produces at the same point a time-dependent electric field and a magnetic field, dH, whose magnitude is constant if the electric current, L, represented by the moving electric charge, is constant Fields from Constant Currents Figure 36. 1 shows that the direction of the magnetic field is perpendicular both to the current I and to the line, R, from the element dL of the current to a point, P where the magnetic field, dH, is being calculated or measured. dh =I dL x r/4Tr3 A/m when I is in amps and dL and r are in meters If the thumb of the right hand points in the direction of the current, then the fingers of the hand curl in the direction of the magnetic field. Thus, the stream lines of H, i.e. the lines representing at any point the direction of the H field, will be an infinite set of circles having the current as center. The magnitude of the field Ho /2R A/m. The line integral of H about any closed path around the current is H dL= I. This relationship lown as Ampere's circuital law) allows one to find formulas for the magnetic field strength for a variety of symmetrical coil geometries, e.g c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 36 Magnetism and Magnetic Fields 36.1 Magnetism Static Magnetic Fields • Time-Dependent Electric and Magnetic Fields • Magnetic Flux Density • Relative Permeabilities • Forces on a Moving Charge • Time-Varying Magnetic Fields • Maxwell’s Equations • Dia- and Paramagnetism • Ferromagnetism and Ferrimagnetism • Intrinsic Magnetic Properties • Extrinsic Magnetic Properties • Amorphous Magnetic Materials 36.2 Magnetic Recording Fundamentals of Magnetic Recording • The Recording Process • The Readback Process • Magnetic Recording Media • Magnetic Recording Heads • Conclusions 36.1 Magnetism Geoffrey Bate Static Magnetic Fields To understand the phenomenon of magnetism we must also consider electricity and vice versa. A stationary electric charge produces, at a point a fixed distance from the charge, a static (i.e., time-invariant) electric field. A moving electric charge, i.e., a current, produces at the same point a time-dependent electric field and a magnetic field, dH, whose magnitude is constant if the electric current, I, represented by the moving electric charge, is constant. Fields from Constant Currents Figure 36.1 shows that the direction of the magnetic field is perpendicular both to the current I and to the line, R, from the element dL of the current to a point, P, where the magnetic field, dH, is being calculated or measured. dH = I dL 2 R/4pR3 A/m when I is in amps and dL and R are in meters If the thumb of the right hand points in the direction of the current, then the fingers of the hand curl in the direction of the magnetic field. Thus, the stream lines of H, i.e., the lines representing at any point the direction of the H field, will be an infinite set of circles having the current as center. The magnitude of the field Hf = I/2pR A/m. The line integral of H about any closed path around the current is rH · dL = I. This relationship (known as Ampère’s circuital law) allows one to find formulas for the magnetic field strength for a variety of symmetrical coil geometries, e.g., Geoffrey Bate Consultant in Information Storage Technology Mark H. Kryder Carnegie Mellon University
FIGURE 36.1 a current I flowing through a small segment dl of a wire produces at a distance r a magnetic field whose direction dH is perpendicular both to R and dL. At a radius, P, between the conductors of a coaxial cable I12πpA/ 2. Between two infinite current sheets in which the current, K, flows in opposite directions H=K×an where a. is the unit vector normal to the current sheets 3. Inside an infinitely long, straight solenoid of diameter d, having N turns closely wound h= Nilda/m 4. Well inside a toroid of radius p, having N closely wound turns H=N2rp·aA/m Applying Stokes' theorem to Ampere's circuital law we find the point form of the latter. V×H where J is the current density in amps per square meter. Time-Dependent Electric and Magnetic Fields A constant current I produces a constant magnetic field H which, in turn, polarizes the medium containing H. While we cannot obtain isolated magnetic poles, it is possible to separate the" poles"by a small distance to reate a magnetic dipole (i. e, to polarize the medium), and the dipole moment(the product of the pole strength and the separation of the poles) per unit volume is defined as the magnetization M. The units are emu/cc in the cgs system and amps per meter in the SI system of units. Because it is usually easier to determine the ma of a sample than to determine its volume, we also have a magnetization per unit mass, o, whose units are emu/g or Am /kg. The conversion factors between cgs and SI units in magnetism are shown in Table 36.1 The effects of the static and time-varying currents may be summarized as follows Static I。→[H]。→[M]。 Time-varying 山→[H]→[M]r where the suffixes"o"and"t"signify static and time-dependent, respectively e 2000 by CRC Press LLC
© 2000 by CRC Press LLC 1. At a radius, r, between the conductors of a coaxial cable Hf = I/2pr A/m 2. Between two infinite current sheets in which the current, K, flows in opposite directions H = K 2 an where an is the unit vector normal to the current sheets 3. Inside an infinitely long, straight solenoid of diameter d, having N turns closely wound H = NI/d A/m 4. Well inside a toroid of radius r, having N closely wound turns H = NI/2pr · af A/m Applying Stokes’ theorem to Ampère’s circuital law we find the point form of the latter. ¹ 2 H = J where J is the current density in amps per square meter. Time-Dependent Electric and Magnetic Fields A constant current I produces a constant magnetic field H which, in turn, polarizes the medium containing H. While we cannot obtain isolated magnetic poles, it is possible to separate the “poles” by a small distance to create a magnetic dipole (i.e., to polarize the medium), and the dipole moment (the product of the pole strength and the separation of the poles) per unit volume is defined as the magnetization M. The units are emu/cc in the cgs system and amps per meter in the SI system of units. Because it is usually easier to determine the mass of a sample than to determine its volume, we also have a magnetization per unit mass, s, whose units are emu/g or Am2 /kg. The conversion factors between cgs and SI units in magnetism are shown in Table 36.1. The effects of the static and time-varying currents may be summarized as follows: where the suffixes “o” and “t ” signify static and time-dependent, respectively. FIGURE 36.1 A current I flowing through a small segment dL of a wire produces at a distance R a magnetic field whose direction dH is perpendicular both to R and dL
TABLE 36.1 Units in Magnetism Symbol cgs Units x Factor SI units B=H+4TM Magnetic flux density B tesla(T), wb/m2 maxwell (Mx) webers(wb) magnetomotive force) UHM 10/4兀 (Oe) Magnetization(per volume) Magnetization(per mass Magnetic moment xKμμ sss xxxxxxxx dimensionless dimensionless 4π Wb/A·m Permeability(material) Wb/A Bohr m =0.927×10erg/Oex103 Am Demagnetizing factor n dimensionless 14 dimensionless tic flux density In the case of electric fields there is in addition to E an electric flux density field d, the lines of which be on positive charges and end on negative charges. D is measured in coulombs per square meter and is associated with the electric field E(V/m)by the relation D=EE E where e, is the permittivity of free space(E,=8.854 x 10-12 F/m)and E, is the(dimensionless)dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m2)=A,u, H, where u, is the permeability of free space(u,=4T X 10 H/m) andu, is the(dimensionless)permeability. In contrast to the lines of the D field, lines of B are closed, having no beginning or ending. This is not surprising when we remember that while lated positive and negative charges exist, no magnetic monopole has yet been discovered Relative permeabilities The range of the relative permeabilities covers about six orders of magnitude(Table 36. 2)whereas the range of dielectric constants is only three orders of magnitude Forces on a Moving Charge A charged particle, g, traveling with a velocity v and subjected to a magnetic field experiences a force This equation reveals how the Hall effect can be used to determine whether the majority current carriers sample of a semiconductor are(negatively charged) electrons flowing, say, in the negative direction or (positively charged)holes flowing in the positive direction. The(transverse)force( Fig. 36. 2)will be in the same direction in either case, but the sign of the charge transported to the voltage probe will be positive for holes and negative for electrons. In general, when both electric and magnetic fields are present, the force experienced by the carriers is given by F=q(E+v×B) The Hall effect is the basis of widely used and sensitive instruments for measuring the intensity of magnetic fields over a range of 10to2×10°A/m. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Magnetic Flux Density In the case of electric fields there is in addition to E an electric flux density field D, the lines of which begin on positive charges and end on negative charges. D is measured in coulombs per square meter and is associated with the electric field E (V/m) by the relation D = er eoE where eo is the permittivity of free space (eo = 8.854 ¥ 10–12 F/m) and er is the (dimensionless) dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m2 ) = mrmoH, where mo is the permeability of free space (mo = 4p 2 10–7 H/m) and mr is the (dimensionless) permeability. In contrast to the lines of the D field, lines of B are closed, having no beginning or ending. This is not surprising when we remember that while isolated positive and negative charges exist, no magnetic monopole has yet been discovered. Relative Permeabilities The range of the relative permeabilities covers about six orders of magnitude (Table 36.2) whereas the range of dielectric constants is only three orders of magnitude. Forces on a Moving Charge A charged particle, q, traveling with a velocity v and subjected to a magnetic field experiences a force F = qv 2 B This equation reveals how the Hall effect can be used to determine whether the majority current carriers in a sample of a semiconductor are (negatively charged) electrons flowing, say, in the negative direction or (positively charged) holes flowing in the positive direction. The (transverse) force (Fig. 36.2) will be in the same direction in either case, but the sign of the charge transported to the voltage probe will be positive for holes and negative for electrons. In general, when both electric and magnetic fields are present, the force experienced by the carriers is given by F = q (E + v 2 B) The Hall effect is the basis of widely used and sensitive instruments for measuring the intensity of magnetic fields over a range of 10–5 to 2 2 106 A/m. TABLE 36.1 Units in Magnetism Quality Symbol cgs Units 2 Factor = SI units B = H + 4pM B = mo(H + M) Magnetic flux density B gauss (G) 2 10–4 = tesla (T), Wb/m2 Magnetic flux F maxwell (Mx) 2 10–8 = webers (Wb) G · cm2 Magnetic potential difference (magnetomotive force) U gilbert (Gb) 2 10/4p = ampere (A) Magnetic field strength H oersted (Oe) 2 103 /4p = A/m Magnetization (per volume) M emu/cc 2 103 = A · m Magnetization (per mass) s emu/g 2 1 = A · m2 /kg Magnetic moment m emu 2 10–3 = A · m2 Susceptibility (volume) c dimensionless 2 4p = dimensionless Susceptibility (mass) k dimensionless 2 4p = dimensionless Permeability (vacuum) mo dimensionless 2 4p.10–7 = Wb/A · m Permeability (material) m dimensionless 2 4p.10–7 = Wb/A · m Bohr magneton mB = 0.927 2 10–20 erg/Oe 2 10–3 = Am2 Demagnetizing factor N dimensionless 2 1/4p = dimensionless
TABLE 36.2 Relative Permeability, H, of Some Diamagnetic, Material Na cygan(s t.p.) permalloy: 79% Ni, 15% Fe Permendur: 49% Fe, 49% Ca, 2%6V Source: F Brailsford, Physical Principles of Magnetism, London: Van Nos- and, 1966. With permission. (b) FIGURE 36.2 Hall effect. A magnetic field B applied to a block of semiconducting material through which a current I is flowing exerts a force F=VX B on the current carriers(electrons or holes)and produces an electric charge on the right face of the block. The charge is positive if the carriers are holes and negative if the carriers are electrons Time-Varying Magnetic Fields In 1831, 11 years after Oersted demonstrated that a current produced a magnetic field which could deflect a compass needle, Faraday succeeded in showing the converse effect-that a magnetic field could produce a current. The reason for the delay between the two discoveries was that it is only when a etic field is anging that an emf is produce dΦ e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Time-Varying Magnetic Fields In 1831, 11 years after Oersted demonstrated that a current produced a magnetic field which could deflect a compass needle, Faraday succeeded in showing the converse effect—that a magnetic field could produce a current. The reason for the delay between the two discoveries was that it is only when a magnetic field is changing that an emf is produced. TABLE 36.2 Relative Permeability, mr , of Some Diamagnetic, Paramagnetic, and Ferromagnetic Materials Material mr Ms , A/m2 Diamagnetics Bismuth 0.999833 Mercury 0.999968 Silver 0.9999736 Lead 0.9999831 Copper 0.9999906 Water 0.9999912 Paraffin wax 0.99999942 Paramagnetics Oxygen (s.t.p.) 1.000002 Air 1.00000037 Aluminum 1.000021 Tungsten 1.00008 Platinum 1.0003 Manganese 1.001 Ferromagnetics Purified iron: 99.96% Fe 280,000 2.158 Motor-grade iron: 99.6% Fe 5,000 2.12 Permalloy: 78.5% Ni, 21.5% Fe 70,000 2.00 Supermalloy: 79% Ni, 15% Fe, 5% Mo, 0.5% Mn 1,000,000 0.79 Permendur: 49% Fe, 49% Ca, 2% V 5,000 2.36 Ferrimagnetics Manganese–zinc ferrite 750 0.34 1,200 0.36 Nickel–zinc ferrite 650 0.29 Source: F. Brailsford, Physical Principles of Magnetism, London: Van Nostrand, 1966. With permission. FIGURE 36.2 Hall effect. A magnetic field B applied to a block of semiconducting material through which a current I is flowing exerts a force F = V ¥ B on the current carriers (electrons or holes) and produces an electric charge on the right face of the block. The charge is positive if the carriers are holes and negative if the carriers are electrons. emf d d = - V F t
where p =BS= flux density(in gauss)x area S. The time-changing flux, dap/dt, can happen as a result of 1. A changing magnetic field within a stationary circuit 2. A circuit moving through a 3. A combination of 1 and 2 The electrical circuit may have n turns and ther emf =-N We can write emf=E. dL and in the presence of changing magnetic fields or a moving electrical circuit E.dL no longer required to be equal to 0 as it was for stationary fields and circuits. Maxwell's Equations Because the flux d can be written JB. ds we have emf=E dl=-d/dt B. ds, and by using Stokes'theorer (V×E)·ds=-dB/dtds V×E=-dB/dt That is, a spatially changing electric field produces a time-changing magnetic field. This is one of Maxwells equations linking electric and magnetic fields By a similar argument it can be shown that V×H=J+dDdt This is another of Maxwells equations and shows a spatially changing magnetic field produces a time-changing electric field. The latter dD/dt can be treated as an electric current which flows through a dielectric, e.g., in a capacitor, when an alternating potential is applied across the plates. This current is called the displacement current to distinguish it from the conduction current which flows in conductors. The conduction current involves the movement of electrons from one electrode to the other through the conductor (usually a metal). The displacement current involves no translation of electrons or holes but rather an alternating polarization through out the dielectric material which is between the plates of the capacitor From the last two equations we see a key conclusion of Maxwell: that in electromagnetic fields a time-varying magnetic field produces a spatially varying electric field and a time-varying electric field produces a spatially varying magnetic field. Maxwell's equations in point form, then, are V×E=dB/dt V×H=J+dD/d These equations are supported by the following auxiliary equations: D=EE (displacement permittivity x electric field intensity) B= uh (flux density permeability x magnetic field intensity) e 2000 by CRC Press LLC
© 2000 by CRC Press LLC where F = BS = flux density (in gauss) ¥ area S. The time-changing flux, dF/dt, can happen as a result of 1. A changing magnetic field within a stationary circuit 2. A circuit moving through a steady magnetic field 3. A combination of 1 and 2 The electrical circuit may have N turns and then We can write emf = E · dL and in the presence of changing magnetic fields or a moving electrical circuit E · dL is no longer required to be equal to 0 as it was for stationary fields and circuits. Maxwell’s Equations Because the flux F can be written eB · ds we have emf = E · dL = –d/dt B · ds, and by using Stokes’ theorem (— 2 E) · ds = –dB/dt ds or — 2 E = –dB/dt That is, a spatially changing electric field produces a time-changing magnetic field. This is one of Maxwell’s equations linking electric and magnetic fields. By a similar argument it can be shown that — 2 H = J + dD/dt This is another of Maxwell’s equations and shows a spatially changing magnetic field produces a time-changing electric field. The latter dD/dt can be treated as an electric current which flows through a dielectric, e.g., in a capacitor, when an alternating potential is applied across the plates. This current is called the displacement current to distinguish it from the conduction current which flows in conductors. The conduction current involves the movement of electrons from one electrode to the other through the conductor (usually a metal). The displacement current involves no translation of electrons or holes but rather an alternating polarization throughout the dielectric material which is between the plates of the capacitor. From the last two equations we see a key conclusion of Maxwell: that in electromagnetic fields a time-varying magnetic field produces a spatially varying electric field and a time-varying electric field produces a spatially varying magnetic field. Maxwell’s equations in point form, then, are — 2 E = dB/dt — 2 H = J + dD/dt — · D = rv — · B = 0 These equations are supported by the following auxiliary equations: D = eE (displacement = permittivity 2 electric field intensity) B = mH (flux density = permeability 2 magnetic field intensity) emf d d = -N t F
ALL MATTER Paramagnetic Antiferromagnetic Ferrimagnetic Ferromagnetic e.g. Mno 8.g-1- Fe2 0. FIGURE 36.3 All matter consists of diamagnetic material (atoms having no permanent magnetic dipole moment) aramagnetic material (atoms having magnetic dipole moment). Paramagnetic materials may be further divided into J =oE (current density conductivity X electric field strength) J=P, V (current density volume charge density x carrier velocity) D=EE +P(displacement as function of electric field and polarization) B=H(H M)(magnetic flux density as function of magnetic field strength and magnetization) P=xe E(polarization electric susceptibility x permittivity of free space x electrical field strength) M=x,uH (magnetization magnetic susceptibility x permeability of free space X magnetic field strength) The last two equations relate, respectively, the electric polarization P to the displacement D =E,E and the magnetic moment M to the flux density B=u H. They apply only to "linear"materials, i.e, those for which P is linearly related to E and M to H. For magnetic materials we can say that nonlinear materials are usually of greater practical interest. Dia- and Paramagnetism The phenomenon of magnetism arises ultimately from moving electrical charges(electrons). The movement may be orbital around the nucleus or the other degree of freedom possessed by electrons which, by analogy with the notion of the planets, is referred to as spin. In technologically important materials, i.e., ferromagnetics and ferri magnetics, spin is more important than orbital motion. Each arrow in Fig. 36.3 represents the total spin of an atom. An atom may have a permanent magnetic moment, in which case it is referred to as belonging to a paramagnetic material, or the atom may be magnetized only when in the presence of a magnetic field, in which case it is called diamagnetic. Diamagnetics are magnetized in the opposite direction to that of the applied magnetic field, i.e., they display negative susceptibility(a measure of the induced magnetization per unit of applie magnetic field). Paramagnetics are magnetized in the same direction as the applied magnetic field, i. e, they e 2000 by CRC Press LLC
© 2000 by CRC Press LLC J = sE (current density = conductivity 2 electric field strength) J = rvV (current density = volume charge density 2 carrier velocity) D = eoE + P (displacement as function of electric field and polarization) B = mo(H + M) (magnetic flux density as function of magnetic field strength and magnetization) P = ceeoE (polarization = electric susceptibility 2 permittivity of free space 2 electrical field strength) M = cmmoH (magnetization = magnetic susceptibility 2 permeability of free space 2 magnetic field strength) The last two equations relate, respectively, the electric polarization P to the displacement D = eoE and the magnetic moment M to the flux density B = moH. They apply only to “linear” materials, i.e., those for which P is linearly related to E and M to H. For magnetic materials we can say that nonlinear materials are usually of greater practical interest. Dia- and Paramagnetism The phenomenon of magnetism arises ultimately from moving electrical charges (electrons). The movement may be orbital around the nucleus or the other degree of freedom possessed by electrons which, by analogy with the motion of the planets, is referred to as spin. In technologically important materials, i.e., ferromagnetics and ferrimagnetics, spin is more important than orbital motion. Each arrow in Fig. 36.3 represents the total spin of an atom. An atom may have a permanent magnetic moment, in which case it is referred to as belonging to a paramagnetic material, or the atom may be magnetized only when in the presence of a magnetic field, in which case it is called diamagnetic. Diamagnetics are magnetized in the opposite direction to that of the applied magnetic field, i.e., they display negative susceptibility (a measure of the induced magnetization per unit of applied magnetic field). Paramagnetics are magnetized in the same direction as the applied magnetic field, i.e., they FIGURE 36.3 All matter consists of diamagnetic material (atoms having no permanent magnetic dipole moment) or paramagnetic material (atoms having magnetic dipole moment). Paramagnetic materials may be further divided into ferromagnetics, ferrimagnetics, and antiferromagnetics
TABLE 36.3 The Occurrence of Ferromagnetism omic number 25 262728 64 1.631.821.971.57 Ferromagnetic moment/mass (Am2/kg) 2177516154.390 Curie point, e K Neel temp, e,K have positive susceptibility. All atoms are diamagnetic by virtue of their having electrons. Some atoms are also paramagnetic as well, but in this case they are called paramagnetic since paramagnetism is roughly a hundred times stronger than diamagnetism and overwhelms it. Faraday discovered that paramagnetic are attracted by magnetic field and move toward the region of maximum field, whereas diamagnetic are repelled and move wara a s The total magnetization of both paramagnetic and diamagnetic materials is zero in the absence of an app ld, i. e, they have zero remanence. Atomic paramagnetism is a necessary condition but condition for ferro- or ferrimagnetism, i.e., for materials having useful magnetic properties not a suffici Ferromagnetism and Ferrimagnetism To develop technologically useful materials, we need an additional force that ensures that the spins of the outermost(or almost outermost)electrons are mutually parallel. Slater showed that in iron, cobalt, and nickel this could happen if the distance apart of the atoms(D)was more than 1. 5 times the diameter of the 3delectron shell(d).(These are the electrons, near the outside of atoms of iron, cobalt, and nickel, that are responsible for the strong paramagnetic moment of the atoms. Paramagnetism of the atoms is an essential prerequisite for ferro-or ferrimagnetism in a material. Slater's result suggested that, of these metals, iron, cobalt, nickel, and gadolinium should be ferromagnetic at room temperature, while chromium and manganese should not be ferromagnetic. This is in accordance with experiment. Gadolinium, one of the rare earth elements, is only weakly ferromagnetic in a cool room. Chro mium and manganese in the elemental form narrowly miss being ferromagnetic. However, when manganese is alloyed with copper and aluminum( Cu Mn2 Als)to form what is known as a Heusler alloy [Crangle, 1962 it becomes ferromagnetic. The radius of the 3d electrons has not been changed by alloying, but the atomic e. ing has been increased by a factor of 1.53/1.47. This small change is sufficient to make the difference ween positive exchange, parallel spins, and ferromagnetism and negative exchange, antiparallel spins, and antiferromagnetism. For all ferromagnetic materials there exists a temperature(the Curie temperature)above which the thermal disordering forces are stronger than the exchange forces that cause the atomic spins to be parallel. From Table 36.3 we see that in order of descending Curie temperature we have Co, Fe, Ni, Gd. From Fig. 36.4 we find that this is also the order of descending values of the exchange integral, suggesting that high positive values of the exchange integral are indicative of high Curie temperatures rather than high magnetic intensity in ferromagnetic materials. Negative values of exchange result in an antiparallel arrangement of the spins of adjacent atoms and in antiferromagnetic materials(Fig. 36.3). Until 5 years ago, it was true to say that antiferromagnetism had no practical application. Thin films on antiferromagnetic materials are now used to provide the bias field which is used to linearize the response of some magnetoresistive reading heads in magnetic disk drives. Ferrimag- netism, also illustrated in Fig. 36.3, is much more widely used. It can be produced as soft, i.e., low coercivity ferrites for use in magnetic recording and reading heads or in the core of transformers operating at frequencies up to tens of megahertz. High-coercivity, single-domain particles(which are discussed later )are used in very large quantities to make magnetic recording tapes and flexible disks - O, and cobalt-impregnated iron oxides and to make barium ferrite, the most widely used material for permanent magnets. e 2000 by CRC Press LLC
© 2000 by CRC Press LLC have positive susceptibility. All atoms are diamagnetic by virtue of their having electrons. Some atoms are also paramagnetic as well, but in this case they are called paramagnetics since paramagnetism is roughly a hundred times stronger than diamagnetism and overwhelms it. Faraday discovered that paramagnetics are attracted by a magnetic field and move toward the region of maximum field, whereas diamagnetics are repelled and move toward a field minimum. The total magnetization of both paramagnetic and diamagnetic materials is zero in the absence of an applied field, i.e., they have zero remanence. Atomic paramagnetism is a necessary condition but not a sufficient condition for ferro- or ferrimagnetism, i.e., for materials having useful magnetic properties. Ferromagnetism and Ferrimagnetism To develop technologically useful materials, we need an additional force that ensures that the spins of the outermost (or almost outermost) electrons are mutually parallel. Slater showed that in iron, cobalt, and nickel this could happen if the distance apart of the atoms (D) was more than 1.5 times the diameter of the 3d electron shell (d). (These are the electrons, near the outside of atoms of iron, cobalt, and nickel, that are responsible for the strong paramagnetic moment of the atoms. Paramagnetism of the atoms is an essential prerequisite for ferro- or ferrimagnetism in a material.) Slater’s result suggested that, of these metals, iron, cobalt, nickel, and gadolinium should be ferromagnetic at room temperature, while chromium and manganese should not be ferromagnetic. This is in accordance with experiment. Gadolinium, one of the rare earth elements, is only weakly ferromagnetic in a cool room. Chromium and manganese in the elemental form narrowly miss being ferromagnetic. However, when manganese is alloyed with copper and aluminum (Cu61Mn24Al15) to form what is known as a Heusler alloy [Crangle, 1962], it becomes ferromagnetic. The radius of the 3d electrons has not been changed by alloying, but the atomic spacing has been increased by a factor of 1.53/1.47. This small change is sufficient to make the difference between positive exchange, parallel spins, and ferromagnetism and negative exchange, antiparallel spins, and antiferromagnetism. For all ferromagnetic materials there exists a temperature (the Curie temperature) above which the thermal disordering forces are stronger than the exchange forces that cause the atomic spins to be parallel. From Table 36.3 we see that in order of descending Curie temperature we have Co, Fe, Ni, Gd. From Fig. 36.4 we find that this is also the order of descending values of the exchange integral, suggesting that high positive values of the exchange integral are indicative of high Curie temperatures rather than high magnetic intensity in ferromagnetic materials. Negative values of exchange result in an antiparallel arrangement of the spins of adjacent atoms and in antiferromagnetic materials (Fig. 36.3). Until 5 years ago, it was true to say that antiferromagnetism had no practical application. Thin films on antiferromagnetic materials are now used to provide the bias field which is used to linearize the response of some magnetoresistive reading heads in magnetic disk drives. Ferrimagnetism, also illustrated in Fig. 36.3, is much more widely used. It can be produced as soft, i.e., low coercivity, ferrites for use in magnetic recording and reading heads or in the core of transformers operating at frequencies up to tens of megahertz. High-coercivity, single-domain particles (which are discussed later) are used in very large quantities to make magnetic recording tapes and flexible disks g-Fe2O3 and cobalt-impregnated iron oxides and to make barium ferrite, the most widely used material for permanent magnets. TABLE 36.3 The Occurrence of Ferromagnetism Cr Mn Fe Co Ni Gd Atomic number 24 25 26 27 28 64 Atomic spacing/diameter 1.30 1.47 1.63 1.82 1.97 1.57 Ferromagnetic moment/mass (Am2 /kg) At 293 K — — 217.75 161 54.39 0 At 0 K — — 221.89 162.5 57.50 250 Curie point, Qc K — — 1,043 1,400 631 289 Néel temp., Qn K 475 100 — — — —
FIGURE 36.4 Quantum mechanical exchang es cause a parallel arrar of materials for which the ratio of atomic separation, D, is at least 1.5 x d, the diamter of the 3d orbita Intrinsic Magnetic Properties Intrinsic magnetic properties are those properties that depend on the type of atoms and their composition and rystal structure, but not on the previous history of a particular sample. Examples of intrinsic magneti properties are the saturation magnetization, Curie temperature, magnetocrystallic anisotropy, and magneto- striction Extrinsic magnetic properties depend on type, composition, and structure, but they also depend on the previous history of the sample, e.g., heat treatment. Examples of extrinsic magnetic properties include the technologically important properties of remanent magnetization, coercivity, and permeability. These properties can be substantially altered by heat treatment, quenching, cold-working the sample, or otherwise changing the ze of the magnetic particle A ferromagnetic or ferrimagnetic material, on being heated, suffers a reduction of its magnetization(per unit mass, i. e, O, and per unit volume, M). The slope of the curve of M, vS. T increases with increasing temperature as shown in Fig. 36.5. This figure represents the conflict between the ordering tendency of the exchange interaction and the disordering effect of increasing temperature. At the Curie temperature, the order no longer exists and we have a paramagnetic material. The change from ferromagnetic or ferrimagnetic materials to paramagnetic is completely reversible on reducing the temperature to its initial value. Curie temperatures are always lower than melting points le crystal of iron has the body-centered structure at room temperature. If the magnetization as a function of applied magnetic field is measured, the shape of the curve is found to depend on the direction of ature, and the"easy" directions of magnetization are those directions parallel to the cube edges [100],[010 and [001] or, collectively, . The hard direction of magnetization for iron is the body diagonal [111].At higher temperatures, the anisotropy becomes smaller and disappears above 300C 3. Nickel crystals(face-centered cubic) have an easy direction of [111] and a hard direction of [100]. Cobalt has the hexagonal close-packed (HCP)structure and the hexagonal axis is the easy direction at room temperature Magnetocrystalline anisotropy plays a very important part in determining the coercivity of ferro- or ferri- magnetic materials, i.e., the field value at which the direction of magnetization is reversed. Many magnetic materials change dimensions on becoming magnetized: the phenomenon is known a magnetostriction and can be positive, i. e, length increases, or negative. Magnetostriction plays an important role in determining the preferred direction of magnetization of soft, i. e, low H, films such as those of alloys of nickel and iron, known as Permalloy The origin of both magnetocrystalline anisotropy and magnetostriction is spin-orbit coupling. The magnitude of the magnetization of the film is controlled by the electron spin as usual, but the preferred direction of that e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Intrinsic Magnetic Properties Intrinsic magnetic properties are those properties that depend on the type of atoms and their composition and crystal structure, but not on the previous history of a particular sample. Examples of intrinsic magnetic properties are the saturation magnetization, Curie temperature, magnetocrystallic anisotropy, and magnetostriction. Extrinsic magnetic properties depend on type, composition, and structure, but they also depend on the previous history of the sample, e.g., heat treatment. Examples of extrinsic magnetic properties include the technologically important properties of remanent magnetization, coercivity, and permeability. These properties can be substantially altered by heat treatment, quenching, cold-working the sample, or otherwise changing the size of the magnetic particle. A ferromagnetic or ferrimagnetic material, on being heated, suffers a reduction of its magnetization (per unit mass, i.e., s, and per unit volume, M). The slope of the curve of Ms vs. T increases with increasing temperature as shown in Fig. 36.5. This figure represents the conflict between the ordering tendency of the exchange interaction and the disordering effect of increasing temperature. At the Curie temperature, the order no longer exists and we have a paramagnetic material. The change from ferromagnetic or ferrimagnetic materials to paramagnetic is completely reversible on reducing the temperature to its initial value. Curie temperatures are always lower than melting points. A single crystal of iron has the body-centered structure at room temperature. If the magnetization as a function of applied magnetic field is measured, the shape of the curve is found to depend on the direction of the field. This phenomenon is magnetocrystalline anisotropy. Iron has body-centered structure at room temperature, and the “easy” directions of magnetization are those directions parallel to the cube edges [100], [010], and [001] or, collectively, . The hard direction of magnetization for iron is the body diagonal [111]. At higher temperatures, the anisotropy becomes smaller and disappears above 300°C. Nickel crystals (face-centered cubic) have an easy direction of [111] and a hard direction of [100]. Cobalt has the hexagonal close-packed (HCP) structure and the hexagonal axis is the easy direction at room temperature. Magnetocrystalline anisotropy plays a very important part in determining the coercivity of ferro- or ferrimagnetic materials, i.e., the field value at which the direction of magnetization is reversed. Many magnetic materials change dimensions on becoming magnetized: the phenomenon is known as magnetostriction and can be positive, i.e., length increases, or negative. Magnetostriction plays an important role in determining the preferred direction of magnetization of soft, i.e., low Hc, films such as those of alloys of nickel and iron, known as Permalloy. The origin of both magnetocrystalline anisotropy and magnetostriction is spin-orbit coupling. The magnitude of the magnetization of the film is controlled by the electron spin as usual, but the preferred direction of that FIGURE 36.4 Quantum mechanical exchange forces cause a parallel arrangement of the spins of materials for which the ratio of atomic separation, D, is at least 1.5 ¥ d, the diamter of the 3d orbital
FIGURE 36.5 Ferro- and ferrimagnetic materials lose their spontaneous magnetic moment at temperatures above the Curie temperature, e saturation ment bie movement FIGURE 36.6 In soft magnetic materials domains form such that the total magnetization is zero. By applying small magnetic fields, domain walls move and the magnetization changes. magnetization with respect to the crystal lattice is determined by the electron orbits which are large enough to interact with the atomic structure of the film Extrinsic Magnetic Properties Extrinsic magnetic properties are those properties that depend not only on the shape and size of the sample, but also on the shape and size of the magnetic constituents of the sample. For example, if we measure the hysteresis loop like the one shown in Fig. 36.6 on a disk-shaped sample punched from a magnetic recording tape, the result will depend not only on the diameter and thickness of the disk coating but also on the distribution of shapes and sizes of the magnetic particles within the disk. They display hysteresis individually and collectively For a soft magnetic material, i e, one that might be used to make the laminations of a transformer, the dependence of magnetization, M, on the applied magnetic field, H, is also complex. Having once left a point described by the coordinates(H,, M), it is not immediately clear how one might return to that point. Alloys of nickel and iron, in which the nickel content is the greater, can be capable of a reversal of magne- tization by the application of a magnetic field, H, which is weaker than the earth's magnetic field(0.5 Oe, 40 A/m)by a factor of five. To avoid confusion caused by the geomagnetic field it would be necessary to screen the sample, for example, by surrounding it by a shield of equally soft material or by measuring the earths field e 2000 by CRC Press LLC
© 2000 by CRC Press LLC magnetization with respect to the crystal lattice is determined by the electron orbits which are large enough to interact with the atomic structure of the film. Extrinsic Magnetic Properties Extrinsic magnetic properties are those properties that depend not only on the shape and size of the sample, but also on the shape and size of the magnetic constituents of the sample. For example, if we measure the hysteresis loop like the one shown in Fig. 36.6 on a disk-shaped sample punched from a magnetic recording tape, the result will depend not only on the diameter and thickness of the disk coating but also on the distribution of shapes and sizes of the magnetic particles within the disk. They display hysteresis individually and collectively. For a soft magnetic material, i.e., one that might be used to make the laminations of a transformer, the dependence of magnetization, M, on the applied magnetic field, H, is also complex. Having once left a point described by the coordinates (H1, M1), it is not immediately clear how one might return to that point. Alloys of nickel and iron, in which the nickel content is the greater, can be capable of a reversal of magnetization by the application of a magnetic field, H, which is weaker than the earth’s magnetic field (0.5 Oe, 40 A/m) by a factor of five. (To avoid confusion caused by the geomagnetic field it would be necessary to screen the sample, for example, by surrounding it by a shield of equally soft material or by measuring the earth’s field FIGURE 36.5 Ferro- and ferrimagnetic materials lose their spontaneous magnetic moment at temperatures above the Curie temperature, Qc. FIGURE 36.6 In soft magnetic materials domains form such that the total magnetization is zero. By applying small magnetic fields, domain walls move and the magnetization changes
