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’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/4pR 3 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 H f = 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 ? 2000 by CRC Press LLC 1.At a radius, r, between the conductors of a coaxial cable H f = I/2pr A/m 2.Between two infinite current sheets in which the current, K, flows in opposite directions H = K 2 a n where a n 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 · a f A/m Applying Stokes’ theorem to Ampère’s circuital law we find the point form of the latter. ? 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 Am 2 /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. ? 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 = e r e o E where e o is the permittivity of free space (e o = 8.854 ′ 10 –12 F/m) and e r is the (dimensionless) dielectric constant. For magnetic fields there is a magnetic flux density B(Wb/m 2 ) = m r m o H, where m o is the permeability of free space (m o = 4p 2 10 –7 H/m) and m r 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 10 6 A/m. TABLE 36.1Units in Magnetism Quality Symbol cgs Units 2 Factor = SI units B = H + 4pMB = m o (H + M) Magnetic flux density B gauss (G) 2 10 –4 = tesla (T), Wb/m 2 Magnetic flux F maxwell (Mx) 2 10 –8 = webers (Wb) G · cm 2 Magnetic potential difference (magnetomotive force) U gilbert (Gb) 2 10/4p = ampere (A) Magnetic field strength H oersted (Oe) 2 10 3 /4p = A/m Magnetization (per volume) M emu/cc 2 10 3 = A · m Magnetization (per mass) s emu/g 2 1 = A · m 2 /kg Magnetic moment m emu 2 10 –3 = A · m 2 Susceptibility (volume) c dimensionless 2 4p = dimensionless Susceptibility (mass) k dimensionless 2 4p = dimensionless Permeability (vacuum) m o dimensionless 2 4p.10 –7 = Wb/A · m Permeability (material) m dimensionless 2 4p.10 –7 = Wb/A · m Bohr magneton m B = 0.927 2 10 –20 erg/Oe 2 10 –3 =Am 2 Demagnetizing factor N dimensionless 2 1/4p = dimensionless ? 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, m r , of Some Diamagnetic, Paramagnetic, and Ferromagnetic Materials Material mrM s , A/m 2 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 Nos- trand, 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 ? 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 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 ? 2 E = dB/dt ? 2 H = J + dD/dt ? · D = r v ? · 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 ? 2000 by CRC Press LLC J = sE (current density = conductivity 2 electric field strength) J = r v V (current density = volume charge density 2 carrier velocity) D = e o E + P (displacement as function of electric field and polarization) B = m o (H + M) (magnetic flux density as function of magnetic field strength and magnetization) P = c e e o E (polarization = electric susceptibility 2 permittivity of free space 2 electrical field strength) M = c m m o H (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 = e o E and the magnetic moment M to the flux density B = m o 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 motion 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 applied magnetic field). Paramagnetics are magnetized in the same direction as the applied magnetic field, i.e., they FIGURE 36.3All 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. ? 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. Chro- mium and manganese in the elemental form narrowly miss being ferromagnetic. However, when manganese is alloyed with copper and aluminum (Cu 61 Mn 24 Al 15 ) 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. 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 g-Fe 2 O 3 and cobalt-impregnated iron oxides and to make barium ferrite, the most widely used material for permanent magnets. TABLE 36.3The 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 (Am 2 /kg) At 293 K — — 217.75 161 54.39 0 At 0 K — — 221.89 162.5 57.50 250 Curie point, Q c K — — 1,043 1,400 631 289 Néel temp., Q n K 475 100 — — — — ? 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 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 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 M s 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 temper- ature, and the “easy” directions of magnetization are those directions parallel to the cube edges [100], [010], and [001] or, collectively, <100>. 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 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 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 H c , 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 36.4Quantum 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. ? 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 (H 1 , M 1 ), 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 earth’s field FIGURE 36.5Ferro- and ferrimagnetic materials lose their spontaneous magnetic moment at temperatures above the Curie temperature, Q c . FIGURE 36.6In soft magnetic materials domains form such that the total magnetization is zero. By applying small magnetic fields, domain walls move and the magnetization changes. ? 2000 by CRC Press LLC and applying a field which is equal in magnitude but opposite in direction to the earth’s field in order to cancel its effects.) The magnetization of the sample in zero field may be macroscopically zero, but locally the material may be magnetized virtually to the saturation state. As shown in Fig. 36.6, which shows a greatly simplified domain structure, the net magnetization at the center of the loop is zero because the magnetization of the four “domains” cancels in pairs. A domain is a region (not necessarily square or even of a regular shape, although the shape often is regular in Ni–Fe thin films or sheets) over which the magnetization is constant in magnitude and direction. Thus, the sample in Fig. 36.6 consists of four domains, initially separated from each other by “domain walls.” If a magnetic field is applied in the direction of +H, that domain will grow whose direction of magne- tization is closest to the field direction and the domains will shrink if their magnetization is opposed to the field. For small applied fields, the movement of the walls is reversible, i.e., on reducing the applied field to zero, the original domain configuration will be obtained. Beyond a certain field the movement of the walls is irreversible, and eventually near the knee of the magnetization curve all the domain walls have been swept away by the applied field. The sample is not yet in the saturated state since the direction of M is not quite the same as the direction of the applied field. However, a small increase in the strength of the applied field finally achieves the saturated state by rotating the magnetization of the whole sample into the field direction. On removing the applied field, the sample does not retrace the magnetization curve, and when the applied field is zero, we can see that a considerable amount of magnetization remains, M r . Appropriately, this is referred to as the remanent state, and M r is the remanent magnetization. By reversing the original direction of the applied field, domains reappear and the magnetization is eventually reduced to zero at the coercive field, H c . It should be noticed that, at H c , although the net magnetization is clearly zero, the individual domains may be magnetized in directions that are different from those at the starting point. Figure 36.6 shows an incomplete hysteresis loop. If the field H were increased beyond +H c the loop would be completed. The differences between ideally magnetically soft materials (used in transformers and magnetic read/write heads) and magnetically hard materials (used in permanent magnets and in recording tapes and disks) are as follows: Magnetically soft materials: H c 0; M r 0; M s high value Magnetically hard materials: H c high value; M r /M s (“squareness”); M s high value Examples are given in Table 36.4. It is noticeable that the differences between hard and soft magnetic materials are confined to the extrinsic properties, M r , H c , and permeability, m. The latter is related to M and H as follows: TABLE 36.4“Hard” and “Soft” Magnetic Materials High M s Low H c Low M r High m Soft Fe 1700 emu/cc 1 Oe < 500 20,000 80 Ni 20 Fe 660 0.1 < 300 50,000 Mn Zn ferrite 400 0.02 < 200 5,000 Co 70 Fe 5 Si 15 B 10 530 0.1 < 250 10,000 High M s High H c High M r T c Hard Particles g-Fe 2 O 3 400 250–450 200–300 115–126 CrO 2 400 450–600 300 120 Fe 870–1100 1,100–1,500 435–550 768 BaO.6Fe 2 O 3 238–370 800–3,000 143–260 320 Alloys SmCo 5 875 40,000 690 720 Sm 2 Co 17 1,000 17,000 875 920 Fe 14 BNd 2 1,020 12,000 980 310 ? 2000 by CRC Press LLC B (G) = H (Oe) + 4pM (emu/cc) m = B/H = 1 + 4pk (cgs units) or B (Wb/m 2 ) = m o (H A/m + M A/m) = m o m r H = mH (SI units) Domain walls form in order to minimize the magnetic energy of the sample. The magnetic energy is mH 2 /8p cgs units or 1/2 mH 2 J/m 3 (SI units) and clearly depends on H, the magnetic field emanating from the sample. In the initial domain configuration shown in Fig. 36.6, there is no net magnetization of the sample and thus no substantial H exists outside the sample and the magnetostatic energy is zero. Thus, the establishment of domains reduces the energy associated with H but it increases the energy needed to establish domain walls within the sample. A compromise is reached in which domain walls are formed until the establishment of one more wall would increase, rather than decrease, the total magnetic energy of the sample. The wall energy depends on the area of the wall, i.e., L 2 , while the energy associated with the external magnetic field depends on L 3 , the volume of the sample. Clearly, as the size of single particles becomes small, terms in L 2 are more important than terms in L 3 , and so for small magnetic particles, the formation of domain walls may not be energetically feasible and a single-domain particle results. These are found in the particles of iron oxide, cobalt-modified iron oxide, chromium dioxide, iron, or barium ferrite, which are used to make magnetic recording tapes, and in barium ferrite, samarium cobalt, and neodymium iron boron, which are used to make powerful permanent magnets. In the latter cases, the very high coercivities are caused by domain walls being pinned at grain boundaries between the main phase grains and finely precipitated secondary phases. This is an example of nucleation-controlled coercivity. The amount of available energy that can be stored in a permanent magnet is the area of the largest rectangle that can be drawn in the second quadrant of the B vs. H hysteresis loop. The energy product has grown remarkably by a factor of about 50 since 1900 [Strnat, 1986]. We see from the graph in Fig. 36.7 of intrinsic coercive force, i.e., the coercive force obtained from the graph of M vs. H (in contrast to the smaller coercive force obtained by plotting B vs. H), that increases in H c (rather than increases in M r ) have been responsible for almost all the improvement in the energy product. The key attributes of technologically important magnetic materials are 1.Large, spontaneous atomic magnetic moments 2.Large, positive exchange integrals 3.Magnetic anisotropy and heterogeneity which are small for soft magnetic materials and large for hard magnetic materials. In single-domain materials, the magnetic particles are so small that reversal of the magnetization can only occur by rotation of the magnetization vector. This rotation can be resisted by combinations of three anisotro- pies: crystalline anisotropy, shape anisotropy, and magnetoelastic anisotropy (which depends on the magneto- strictive properties of the material). Crystalline Anisotropy Crystalline anisotropy arises from the existence of easy and hard directions of magnetization within the crystal structure of the material. For example, in iron the {100} directions are easy directions while the {111} directions are hard. In nickel crystals the reverse is true. In cobalt the hexagonal {00.1} directions are easy and the {10.0} directions in the basal plane are hard. Hard and easy directions in crystalline materials come about as a result of spin-orbit coupling. The spin, as usual, determines the occurrence of ferro- or ferrimagnetization, while the orbital motion of the electrons (3d in the case of Fe, Co, and Ni) responds to the structure of the crystal lattice. ? 2000 by CRC Press LLC The maximum value of coercivity resulting from crystalline anisotropy is given by H c = 2K 1 /M s , where K 1 is the first magnetocrystalline anisotropy constant and M s is the saturation magnetization. Shape Anisotropy A spherical particle has no shape anisotropy, i.e., all directions are equally easy (or hard). For particles (having low crystalline anisotropy) of any other shape, the longest dimension is the easy direction and the shortest dimension is the hardest direction of magnetization. Thus, a needle-shaped (acicular) particle will tend to be magnetized along the long dimension, whereas a particle in the form of a disk will have the axis of the disk as its hard direction, while any direction in the plane of the disk will be equally easy (assuming that shape is the dominant anisotropy). For an acicular particle, the maximum value of the particle’s switching field is [Stoner and Wohlfarth, 1948] H c = (N b – N a ) M s where N b is the demagnetizing factor in the shorter dimension and N a is the factor for the long axis of the particle. When the ratio b/a ? ￥ , then and H c for iron > 10,000 Oe (7.95 ′ 10 5 A/m), higher than has been achieved in the laboratory for single-domain iron particles. Particles of iron having H c ￡ 2000 Oe are widely used in high-quality audio and video tapes. The reason for the discrepancy is that the simplest single-domain model makes the assumption that the spins on all the atoms in a particle rotate in the same direction and at the same time, i.e., are coherent. This seems to be improbable since switching may begin at different places in the single-domain particle at the same time. Jacobs and Bean [1955] proposed an incoherent mode, fanning, in which different segments on a FIGURE 36.7 The development of magnetic materials for permanent magnets showing the increase in energy product and in intrinsic coercivity as a function of time. N N NNN a b abc ? ? ü y ? t ? ++o 0 2 4 p p ? 2000 by CRC Press LLC longitudinal chain of atoms rotate in opposite directions. Shtrikman and Treves [1959] introduced another incoherent mode, buckling. These incoherent modes of magnetization reversal within single-domain particles not only predicted values of coercivity closer to the observed values, but also they could explain why the observed coercivity values for single-domain particles increased with decreasing particle size [Bate, 1980]. Shape anisotropy also plays an important role in determining the magnetization direction in thin magnetic films. It, of course, favors magnetization in the film plane. Magnetoelastic Anisotropy Spin-orbit coupling is also responsible for magnetostriction (the increase or decrease of the dimensions of a body on becoming magnetized or demagnetized). The magnetostriction coefficient l s = fractional change of a dimension of the body. It can be positive or negative, and it varies with changes in the direction and magnitude of the applied stress (or internal stress) and of the applied magnetic field. It is highly sensitive to composition, to structure, and to the previous history of the sample. The maximum coercivity is given by the formula H c = 3l s T/M s where l s is the saturation magnetostriction coefficient, T is the tension, and M s the saturation mag- netization. Magnetostriction has been put to practical use in the generation of sonar waves for the detection of schools of fish or submarines. For samples made of single-domain particles, the maximum coercivity for three ferromagnetic metals and one ferrimagnetic oxide (widely used in magnetic recording) is calculated using the preceding formula. Table 36.5 shows maximum coercivity (Oe) for single-domain particles (coherent rotation). The assumption is made that all the spins rotate so that they remain parallel at all times. This is known as coherent rotation. In the case of g-Fe 2 O 3 , an incoherent mode of reversal probably occurs since the maximum observed coercivity is only 350 Oe. Several incoherent modes have been proposed, e.g., chain-of-spheres fanning [Jacobs and Bean, 1955], curling [Shtrikman and Treves, 1959]. Their characteristics and differences are discussed by Bate [1980]. The coercivity of particles of g-Fe 2 O 3 is increased (in order to make recording tapes of extended frequency response) by precipitating cobalt hydroxide on the surface of the particles. After gentle warming, the cobalt is incorporated on the surface of the particles and increases the coercivity to 650 Oe (51 · 73 kA/m). Figure 36.8 illustrates two additional extrinsic magnetic properties of importance. They are the remanence coercivity, H r , and the switching field distribution (SFD). These are of particular importance in magnetic particles used in magnetic tapes (audio, video, or data) or magnetic disks. The coercivity, H c , of a magnetic material is the value of the magnetic field (the major loop) at which M = 0. However, if the applied field is allowed to go to zero, a small magnetization remains. It is necessary to increase the applied field from H c > H r (Fig. 36.8) to achieve M r = 0. H r is the remanence coercivity and is more relevant than is H c in discussing the writing process in magnetic recording since it corresponds to the center of the remanent magnetization transition on the recording medium. Particles, for example, in a magnetic recording do not all reverse their magnetization at the same field; there is a distribution of switching fields, which can be found by differentiating M with respect to H around the point H c . The result is shown as the broken curve on Fig. 36.8, where the SFD = DH/H c , DH being the width at half the maximum of the curve. Typically, SFD = 0.2–0.3 for a high-quality particulate medium and smaller than this for thin-film recording media. Figure 36.8 also shows the construction used to find the parameter S*. The quantity 1 – S* is found to be very close to DH/H c , and it is quicker to evaluate. Either of these parameters can be used to determine the distribution of switching fields, small values of which are required to achieve high recording densities. TABLE 36.5Maximum Coercivity (Oe) for Single- Domain Particles (Coherent Rotation) Iron Cobalt Nickel g-Fe2O3 Crystalline 250 3,000 70 230 Strain 300 300 2,000 <10 Shape (10:1) 5,300 4,400 1,550 2,450 ? 2000 by CRC Press LLC Amorphous Magnetic Materials Before 1960, all the known ferro- and ferrimagnetic materials were crystalline. Because the occurrence of these magnetic states is known to depend on short-range interaction between atoms, there is no reason why amor- phous materials (which have only short-range order) should not have useful magnetic properties. This was found to be true in 1960, when thin, amorphous ribbons of Au 81 Si 19 were made by rapidly cooling the molten alloy through the melting point and the lower glass transition temperature. Because there is always at least one crystalline phase more stable than the amorphous state, the problem is to invent a production method that yields the amorphous phase rather than the crystalline one. Most methods involve cooling the molten mixture so rapidly that there is insufficient time for crystals to form. Cooling rates of 10 5 –10 6 degrees per second are needed and can be achieved in several ways: 1. Pouring the molten mixture from a silica crucible onto the edge of a rapidly rotating copper wheel. This yields a ribbon of the amorphous alloy, typically 1 mm wide and 25 mm thick. 2. Depositing a thin film from a metal vapor or a solution of metal ions. 3. Irradiating a thin sample of the metal with high-energy particles. Once an amorphous alloy is formed, it will remain indefinitely in the glassy state at room temperature. The problem is that only thin films are obtained, and large areas are required to make, for example, the core of a transformer. There are three main groups of amorphous films: 1. Metal-metalloid alloys, e.g., Au 81 Si 19 2. Late transition–early transition metal alloys, e.g., Ni 60 Nb 40 3. Simple metal alloys, e.g., Cu 65 Al 35 When normal metals freeze, crystallization begins at a fixed temperature, the liquidus, T e . In amorphous alloys configurational freezing occurs at a lower temperature, the glass temperature, T g , which is not as well defined as T e . There is an abrupt increase in the time required for the rearrangement of the atoms, from 10 –12 s for liquids to 10 5 s (a day) for glasses. Not surprisingly, this increase in atomic rearrangement time is associated with an abrupt increase in viscosity, from 10 –2 poise for liquids, e.g., water or mercury, to 10 15 poise for glasses. The principal difference between magnetic glasses and ferromagnetic alloys is that the glasses are completely isotropic (all directions of magnetization are very easy directions), and consequently, considering only the magnetic properties, soft amorphous alloys are almost ideally suited for use in the core of power transformers FIGURE 36.8 The switching field distribution (SFD) for a magnetic recording medium can be obtained in two ways: (1) SFD = DH/H c or (2) SFD = 1 – S*. ? 2000 by CRC Press LLC ? 2000 by CRC Press LLC MAGNETIC BEARING agnetic bearings support moving machinery without physical contact. For example, they can levitate a rotating shaft and permit relative motion without friction or wear. Long considered a promising advancement, magnetic bearings are now in actual service in such industrial applications as electric power generation, petroleum refining, machine tool operation, and natural gas pipelines. AVCON, Inc. worked initially with Lewis Research Center on the development of a magnetic bearing system for a cryogenic magnetic bearing test facility. The resulting AVCON development was extensively tested over a two-year span and these tests provided a wealth of data on the performance of magnetic bearings under severe conditions. In this program, AVCON developed the basic hybrid magnetic bearing approach in which both permanent magnets and electromagnets are employed to suspend a shaft; the permanent magnets provide suspension, the electromagnets provide control. Analyses of AVCON bearing tests showed that a hybrid magnetic bearing test was typically only one-third the weight, substantially smaller and dramatically less power-demanding than previous generations of magnetic bearings. In 1993, Marshall Space Flight Center awarded AVCON a contract to fabricate a set of magnetic bearings, install them in a fixture representing a Space Shuttle main engine turbopump, and test them under simulated shuttle mission conditions. AVCON has been able to develop a unique “homopolar” approach to permanent magnet type bearings that the company says are significantly smaller than prior designs, their control electronics are a fraction of the weight of previous systems, and power consumption is much lower than in all electromagnetic designs. Among other advantages cited are virtually zero friction and therefore no lubricant requirement, no wear, no vibration, longer service life, and very high reliability because single point failure modes are eliminated. (Courtesy of National Aeronautics and Space Administration.) This AVCON magnetic bearing permits motion without friction or wear. (Photo courtesy of National Aeronautics and Space Administration.) M or magnetic recording heads, where almost zero remanence and coercivity are desired at frequencies up to megahertz. The limit on their performance seems to be the magnetic anisotropy which arises from strains generated during the manufacturing process. When an amorphous material is required to store energy (as in a permanent magnet) or information (as in magnetic bubbles or thermomagneto-optic films), it must have magnetic anisotropy. This is generally produced by applying a magnetic field at high temperatures to the amorphous material. The field and temperature must be high enough to allow a local rearrangement of atoms to take place in order to create the desired degree of magnetocrystalline anisotropy. Amorphous materials will apparently play increasingly important roles as magnetic materials. To accelerate their use, we need to have answers to the questions “What governs the formation of amorphous materials?” and “What is the origin of their anisotropy and magnetostriction?”. Defining Terms Coercivity, H c (Oe, A/m): The property of a magnetized body enabling it to resist reversal of its magnetization. Compensation temperature, T c (°C, K): The temperature at which the magnetization of a material comprising ferromagnetic atoms (e.g., Fe, Co, Ni) and rare earth atoms (e.g., Gd, Tb) becomes zero because the magnetization of the sublattice of ferromagnetic atoms is canceled by the opposing magnetization of the rare earth sublattice. Curie temperature, Q c (°C, K): The temperature at which the spontaneous magnetization of a ferromagnetic or ferrimagnetic body becomes zero. Remanence, M r (emu/cc, A/m): The property of a magnetized body enabling it to retain its magnetization. Related Topics 1.3 Transformers ? 35.1 Maxwell Equations References G. Bate, in Recording Materials in Ferromagnetic Materials, vol. 2, Amsterdam: North-Holland, 1980, pp. 381–507. G. Bate, J. Magnetism and Magnetic Materials, vol. 100, pp. 413–424, 1991. F. Brailsford, Physical Principles of Magnetism, London: Van Nostrand, 1966. J. Crangle, “Ferromagnetism and antiferromagnetism in non-ferrous metals and alloys,” Metallurgical Reviews, pp. 133–174, 1962. I.S. Jacobs and C.P. Bean, Phys. Rev., vol. 100, p. 1060, 1955. K. Moorjani and J.M.D. Coey, Magnetic Glasses: Methods and Phenomena, Their Application in Science and Technology, vol. 6, Amsterdam: Elsevier, 1984. S. Shtrikman and D. Treves, J. Phys. Radium, vol. 20, p. 286, 1959. J.C. Slater, Phys. Rev., vol. 36, p. 57, 1930. E.C. Stoner and E.P. Wohlfarth, Phil. Trans. Roy. Soc., vol. A240, p. 599, 1948. K.J. Strnat, Proceedings of Symposium on Soft and Hard Magnetic Materials with Applications, vol. 8617-005, Metals Park, Ohio: American Society of Metals, 1986. Further Information A substantial fraction of the papers published in English on the technologically important aspects of magnetism appear in the IEEE Transactions on Magnetics or in the Journal of Magnetism and Magnetic Materials. The two major annual conferences are Intermag (proceedings published in the IEEE Transactions on Mag- netics) and the Magnetism and Magnetic Materials Conference, MMM (proceedings published in the American Physical Society’s Journal of Applied Physics). ? 2000 by CRC Press LLC 36.2 Magnetic Recording Mark H. Kryder Magnetic recording is used in a wide variety of applications and formats, ranging from relatively low-density, low-cost floppy disk drives and audio recorders to high-density videocassette recorders, digital audio tape recorders, computer tape drives, rigid disk drives, and instrumentation recorders. The storage density of this technology has been advancing at a very rapid pace. With a storage density exceeding 1 Gbit/in. 2 , magnetic recording media today can store the equivalent of about 50,000 pages of text on one square inch. This is more than 500,000 times the storage density on the RAMAC, which was introduced in 1957 by IBM as the first disk drive for storage of digital information. The original Seagate 5.25-inch magnetic disk drive, introduced in 1980, stored just 5 Mbytes. Today, instead of storing megabytes, 5.25-inch drives store tens of gigabytes, and drives as small as 2.5 inches store over a gigabyte. This astounding rate of progress shows no sign of slowing. Fundamental limits to magnetic recording density are still several orders of magnitude away, and recent product announcements and laboratory demonstrations indicate the industry is accelerating the rate of progress rather than approaching practical limits. Recently IBM demonstrated the feasability of storing information at a density of 3 Gbit/in. 2 [Tsang et al., 1996]. Similar advances can also be expected in audio and video recording. Fundamentals of Magnetic Recording Although magnetic recording is practiced in a wide variety of formats and serves a wide variety of applications, the fundamental principles by which it operates are similar in all cases. The fundamental magnetic recording configuration is illustrated in Fig. 36.9. The recording head consists of a toroidally shaped core of soft magnetic material with a few turns of conductor around it. The magnetic medium below the head could be either tape or disk, and the substrate could be either flexible (for tape and floppy disks) or rigid (for rigid disks). To record on the medium, current is applied to the coil around the core of the head, causing the high-permeability magnetic core to magnetize. Because of the gap in the recording head, magnetic flux emanates from the head and penetrates the medium. If the field produced by the head is sufficient to overcome the coercive force of the medium, the medium will be magnetized by the head field. Thus, a representation of the current waveform applied to the head is stored in the magnetization pattern in the medium. Readout of previously recorded information is typically accomplished by using the head to sense the magnetic stray fields produced by the recorded patterns in the medium. The recorded patterns in the medium cause magnetic stray fields to emanate from the medium and to flow through the core of the head. Thus, if the medium is moved with respect to the head, the flux passing through the coil around the head will change in a manner which is representative of the recorded magnetization pattern in the medium. By Faraday’s law of induction, a voltage representative of the recorded information is thus induced in the coil. FIGURE 36.9The fundamental magnetic recording configuration. ? 2000 by CRC Press LLC The Recording Process During recording the head is used to produce large magnetic fields which magnetize the medium. It was shown by Karlqvist [1954] that, in the case where the track width and length of the poles along the gap are both large compared to the gap length, the fields produced by a recording head could be described by (36.1a) (36.1b) where H x and H y are the longitudinal and perpendicular components of field, as indicated by the coordinates in Fig. 36.10, N is the number of turns on the head, I is the current driving the head, and g is the gap width of the head. In this approximation, the contours of equal longitudinal field are described by circles which intersect the gap corners as shown in Fig. 36.10. In digital or saturation recording, the recording head is driven with sufficiently large currents that a portion of the recording medium is driven into saturation. However, because of the gradient in the head fields, other portions of the medium see fields less than those required for saturation. This is illustrated in Fig. 36.10 where the contours for three different longitudinal fields are drawn. In this figure H cr is the remanence coercivity or the field required to produce zero remanent magnetization in the medium after it was saturated in the opposite direction, and H 1 and H 2 are fields which would produce negative and positive remanent magnetization, respectively. Note that the head field gradient is the sharpest near the pole tips of the head. This means that smaller head-to-medium spacing and thinner medium both lead to narrower transitions being recorded. Modeling the recording process involves convolving the head field contours with the very nonlinear and hysteretic magnetic properties of the recording medium. A typical M-H hysteresis loop for a longitudinal magnetic recording medium is shown in Fig. 36.11. Whether the medium has positive or negative magnetization depends upon not only the magnetic field applied but the past history of the magnetization. If the medium was previously saturated at –M s , then when the magnetic field H is reduced to zero, the remanent magnetization will be –M r ; however, if it was previously saturated at +M s , then the remanent magnetization would be +M r . FIGURE 36.10The constant longitudinal field contours in the gap region of a recording head. H NI g xg y xg y x = +? è ? ? ? ÷ - -? è ? ? ? ÷ é ? ê ù ? ú -- p tan tan 11 22// H NI g xg y xg y y = ++ -+ é ? ê ê ù ? ú ú 2 2 2 22 22 p ln () () / / ? 2000 by CRC Press LLC Similarly, if the medium was initially saturated to –M s , then magnetized by a field +H 1 , and finally allowed to go to a remanent state, the magnetization would go to value M 1 . This hysteretic behavior is the basis for the use of the medium for long-term storage of information but makes the recording process highly nonlinear. An additional complicating factor in determining the actual recorded pattern is the demagnetizing field of the medium itself. As shown in Fig. 36.9, transitions in the recorded magnetization direction produce effective magnetostatic charge given by (36.2) which in turn results in demagnetizing fields. The demagnetizing fields outside the medium are what is sensed by the head during readback, but demagnetizing fields also exist inside the medium and act to alter the total field seen by the medium during the recording process from that of the head field alone. Taking into account the head field gradients, the nonlinear M-H loop characteristics of the medium and the demagnetizing fields, Williams and Comstock [1971] developed a model for the recording process. This model predicts the width of a recorded transition, in a material with a square hysteresis loop, to be (36.3) where d is the medium thickness, d is the head-medium spacing, M r is the remanent magnetization of the medium, and H c is the coercivity of the medium. That the transition widens with the product M r · d is a result of the fact that the demagnetizing fields increase linearly with this quantity. Similarly, the transition narrows as H c is increased, because with high coercivity, the medium can resist the transition broadening due to the demagnetizing fields. The increase in transition width with d is due to the fact that a poorer head field gradient is obtained with larger head-medium spacing. The nonlinearities of the recording process can be largely removed by a technique referred to as ac bias recording. This is frequently used in analog recording in audio and video recorders. In this technique, a high- frequency ac bias is added to the signal to be recorded. This ac bias signal is ramped from a value much larger than the coercivity of the medium to zero. This removes the hysteretic behavior of the medium and causes it to assume a magnetization state which represents the minimum energy state determined by the amount of field produced by the signal to be recorded. FIGURE 36.11A remanent M-H hysteresis loop for a longitudinal recording medium. r M =-?× r M a Md H r c = d p ? 2000 by CRC Press LLC The Readback Process As opposed to the recording process, the readback process can usually be modeled as a linear process. This is because the changes in magnetization which occur in either the head or the medium during readback are typically small. The most common way to model the readback process is to use the principle of reciprocity, which states that the flux produced by the head through a cross section of an element of the medium, normalized by the number of ampere turns of current driving the head, is equal to the flux produced in the head by the element of medium, normalized by the equivalent current required to produce the magnetization of that element. For a magnetic recording head, which produces the longitudinal field H x (x,y) when driven by NI ampere turns of current, this principle leads to the following expression for the voltage induced in the head by a recording medium with magnetization M(x,y) and moving with velocity v relative to the head: (36.4) where W is the track width of the head. This expression shows that the readback voltage induced in the recording head is linearly dependent upon the magnitude of the magnetization in the recording medium being sensed and the relative head-to-medium velocity. The linearity of the readback process ensures that analog recordings such as those recorded on audio or video tapes are faithfully reproduced. Magnetic Recording Media A wide variety of magnetic recording media are available today. Different applications require different media, but furthermore, in many cases the same application will be able to utilize a variety of different competitive media. Just a decade ago, essentially all recording media consisted of fine acicular magnetic particles embedded in a polymer and coated onto either flexible substrates such as mylar for floppy disks and tapes or onto rigid aluminum-alloy substrates for rigid disks. Today, although such particulate media are still widely used for tape and floppy disks, thin-film media have almost entirely taken over the rigid disk business, and metal-evaporated thin-film media has been introduced into the tape marketplace. Furthermore, many new particle types have been introduced. The most common particulate recording media today are g-Fe 2 O 3 , Co surface-modified g-Fe 2 O 3 , CrO 2 , and metal particle media. All of these particles are acicular in shape with aspect ratios on the order of 5 or 10 to 1. The particles are sufficiently small that it is energetically most favorable for them to remain in a single- domain saturated state. Because of demagnetizing effects caused by the acicular shape, the magnetization prefers to align along the long axis of the particle. As was noted in the discussion of Eq. (36.3), to achieve higher recording densities requires media with higher coercivity. The coercivity of a particle is determined by the field required to cause the magnetization to switch by 180°. If the magnetization remained in a single-domain state during the switching process, then the coercivity should be given by H c = (N a – N b )M s (36.5) where N a and N b are the demagnetizing factors in the directions transverse and parallel to the particle axis, respectively. In practice the coercivity is measured to be less than this. This has been explained as being a result of the fact the magnetization does not remain uniform during the switching process, but switches inhomoge- neously [White, 1984]. In addition to the effects which the shape anisotropy of the particles has on the coercivity, crystalline anisotropy can also be used to control coercivity. e Wv I Mx xy x H x y dxdy ox d d x = ?- ? -￥ ￥+ òò m d (,) (, ) ? 2000 by CRC Press LLC The coercivity of the medium which is made from the particles is determined by the distribution of coer- civities of the particles from which it is made, their orientation in the medium relative to the fields from the head, and their interactions among each other. The coercivities of a variety of particulate recording media are summarized in Table 36.6. Although coercivity is indeed an important parameter for magnetic recording media, it is by no means the only one. Particle size affects the medium noise because, at any time, the head is sensing a fixed volume of the medium. Because the particles are quantized and there are statistical variations in their switching behavior, the medium power signal-to-noise ratio varies linearly with the number of particles contained in that volume. To reduce particulate medium noise, it is therefore generally desirable to use small particles. There is a limit, however, to how small particles may be made and still remain stable. When the thermal energy kT is comparable in magnitude to the energy required to switch a particle, M · H c , the particle becomes unstable and may switch because of thermal excitation. This phenomenon is known as superparamagnetism and can lead to decay of recorded magnetization patterns over time. The remanent magnetization of a medium is important because it directly affects the signal level during readback as shown by Eq. (36.4). The remanent magnetizations of several particulate media are listed in Table 36.6. Obtaining high remanent magnetization in particulate media requires the use of particles with high saturation magnetization and a high-volume packing fraction of particles in the polymer binder. Obtaining a high-volume packing fraction of particles in the binder, however, can lead to nonuniform distributions of particles and agglomerates of many particles, which switch together, also causing noise during readback. Generally, then, to obtain good high-density particulate recording media it is desired to have adequate coercivity (to achieve the required recording density), small particles (for low noise), with a very narrow switching field distribution (to obtain a narrow transition), to have them oriented along the direction of recording (to obtain a large remanence), and to have them uniformly dispersed (to obtain low modulation noise), with high packing density (to obtain large signals). TABLE 36.6Magnetic Material, Saturation Remanence M r (￥), Coercivity H c , Switching-Field Distribution Dh r , and Number of Particles per Unit Volume, N, of Various Particulate Magnetic Recording Media Mr (￥), Hc, kA/m kA/m N, Application Material (emu/cm 3 )(4p Oe) Dhr 10 3 /mm 3 Reel-to-reel audio tape g-Fe 2 O 3 100–120 23–28 0.30–0.35 0.3 Audio tape IEC I g-Fe 2 O 3 120–140 27–32 0.25–0.35 0.6 Audio tape IEC II CrO 2 120–140 38–42 0.25–0.35 1.4 g-Fe 2 O 3 + Co 120–140 45–52 0.25–0.35 0.6 Audio tape IEC IV Fe 230–260 80–95 0.30–0.37 3 Professional video tape g-Fe 2 O 3 75 24 0.4 0.1 CrO 2 110 42 0.3 1.5 g-Fe 2 O 3 + Co 90 52 0.35 1 Home video tape CrO 2 110 45–50 0.35 2 g-Fe 2 O 3 + Co 105 52–57 0.35 1 Fe 220 110–120 0.38 4 Instrumentation tape g-Fe 2 O 3 90 27 0.35 0.6 g-Fe 2 O 3 + Co 105 56 0.50 0.8 Computer tape g-Fe 2 O 3 87 23 0.30 0.16 CrO 2 120 40 0.29 1.4 Flexible disk g-Fe 2 O 3 56 27 0.34 0.3 g-Fe 2 O 3 + Co 60 50 0.34 0.5 Computer disk g-Fe 2 O 3 56 26–30 0.30 0.3 g-Fe 2 O 3 + Co 60 44–55 0.30 0.5 ? 2000 by CRC Press LLC Thin-film recording media generally have excellent magnetic properties for high-density recording. Because they are nearly 100% dense (voids at the grain boundaries reduce the density somewhat), they can be made to have the highest possible magnetization. Because of their high magnetization, they can be made extremely thin and still provide adequate signal during readback. This helps narrow the recorded transition since the head field gradient is sharper for thinner media, as was discussed in reference to Fig. 36.10. Thin-film media can also be made extremely smooth. To achieve the smallest possible head-to-medium spacing and therefore the sharpest head field gradient and the least spacing loss, smooth media are required. The coercivity of thin-film media can also be made very high. In volume production today are media with coercivities of 160 kA/m; however, media with coercivities to 250 kA/m have been made and appear promising [Velu and Lambeth, 1992]. Such high coercivities are adequate to achieve more than an order of magnitude higher recording density than today. Numerical models indicate that noise in thin-film media increases when the grains in polycrystalline films are strongly exchange coupled [Zhu and Bertram, 1988]. Exchange coupled films tend to exhibit zigzag tran- sitions, which produce considerable jitter in the transition position relative to the location where the record current in the head goes through zero. A variety of experimental studies have indicated that the introduction of nonmagnetic elements which segregate to the grain boundaries and careful control of the sputtering condi- tions to achieve a porous microstructure at the grain boundaries reduce such transition jitter [Chen and Yamashita, 1988]. Magnetic Recording Heads Early recording heads consisted of toroids of magnetically soft ferrites, such as NiZn-ferrite and MnZn-ferrite, with a few turns of wire around them. For high-density recording applications, however, ferrite can no longer be used, because the saturation magnetization of ferrite is limited to about 400 kA/m. Saturation of the pole tips of a ferrite head begins to occur when the deep gap field in the head approaches one-half the saturation magnetization of the ferrite. Because the fields seen by a medium are one-half to one-quarter the deep gap field, media with coercivities above about 80 kA/m cannot be reliably written with a ferrite head. High-density thin-film disk media, metal particle media, and metal evaporated media, therefore, cannot be written with a ferrite head. Magnetically soft alloys of metals such as Permalloy (NiFe) and Sendust (FeAlSi) have saturation magneti- zations on the order of 800 kA/m, about twice that of ferrites, but because they are metallic may suffer from eddy current losses when operated at high frequencies. To overcome the limitations imposed by eddy currents, they are used in layers thinner than a skin depth at their operating frequency. To prevent saturation of the ferrite heads, the high magnetization metals are applied to the pole faces of the ferrite, making a so-called metal-in-gap or MiG recording head, as shown in Fig. 36.12. Since the corners of the pole faces are the first parts of a ferrite head to saturate, the high magnetization metals enable these MiG heads to be operated to nearly twice the field to which a ferrite head can be operated. Because the layer of metal is thin, it can furthermore be less than a skin depth, and eddy current losses do not limit performance at high frequencies. Yet another solution to the saturation problem of ferrite heads is to use thin-film heads. Thin-film heads are made of Permalloy and are therefore metallic, but the films are made sufficiently thin that they are thinner than the skin depth and, consequently, the heads operate well at high frequencies. A diagram of a thin-film head is shown in Fig. 36.13. It consists of a bottom yoke of Permalloy, some insulating layers, a spiral conductor, and a top yoke of Permalloy, which is joined to the bottom yoke at the back gap but separated from it by a thin insulator at the recording gap. These thin-film heads are made using photolithography and microfabrica- tion techniques similar to those used in the manufacture of semiconductor devices. The thin pole tips of these heads actually sharpen the head field function and, consequently, the pulse shape produced by an isolated transition, although at the expense of some undershoot, as illustrated in Fig. 36.14. Because thin-film heads are made by photolithographic techniques, they can be made extremely small and to have low inductance. This, too, helps extend the frequency of operation. A relatively new head which is now being used for readback of information in high-density recording is the magnetoresistive (MR) head. MR heads are based on the phenomenon of magnetoresistance, in which the electrical resistance of a magnetic material is dependent upon the direction of magnetization in the material ? 2000 by CRC Press LLC relative to the direction of current flow. An unshielded MR head is depicted in Fig. 36.15. Current flows in one end of the head and out the other. The resistivity of Permalloy from which the head is made varies as r = r o + Dr cos 2 q (36.6) where q is the angle which the magnetization in the Permalloy makes relative to the direction of current flow, r o is the isotropic resistivity, and Dr is the magnetoresistivity. When the recording medium with a changing magnetization pattern moves under the MR head, the stray fields from the medium cause a change in the FIGURE 36.12A diagram of a metal-in-gap or MiG recording head. (Source: A.S. Hoagland and J.E. Monson, Digital Magnetic Recording, 2nd ed., New York: Wiley-Interscience, 1991, p. 127. With permission.) FIGURE 36.13A thin-film head. (Source: R.M. White, Ed., Introduction to Magnetic Recording, New York: IEEE Press, p. 28. ?1985 IEEE.) ? 2000 by CRC Press LLC direction of magnetization and, consequently, a change in resistance in the head. With a constant current source driving the head, the head will therefore exhibit a change in voltage across its terminals. Magnetoresistive heads are typically more sensitive than inductive heads and therefore produce larger signal amplitudes during readback. The increased sensitivity and the fact that the read head is independent of the write head can be used to make a write/read head combination in which the write head writes a wider track than the read head senses. Thus, adjacent track interference is reduced during the readback process. FIGURE 36.14 Pulse shapes for (curve A) long- and (curve B) short-pole heads normalized for equal amplitude. (Source: E.P. Valstyn and L.F. Shew, “Performance of single-turn film heads,” IEEETrans. Magnet., vol. MAG-9, no. 3, p. 317. ?1973 IEEE.) FIGURE 36.15 An unshielded magnetoresistive element. (Source: A.S. Hoagland and J.E. Monson, Digital Magnetic Record- ing, 2nd ed., New York: Wiley-Interscience, 1991, p. 131. With permission.) ? 2000 by CRC Press LLC Another advantage of the MR head is that it senses magnetic flux f, not the time rate of change of flux d(f)/dt as an inductive head does. Consequently, whereas the inductive head output voltage is dependent upon the head-to-medium velocity as was shown by Eq. (36.4), the output voltage of an MR head is independent of velocity. Conclusions Magnetic recording today is used in a wide variety of formats for a large number of applications. Formats range from tape, which has the highest volumetric packing density and lowest cost per bit stored, to rigid disks, which provide fast access to a large volume of data. Applications include computer data storage, audio and video recording, and collecting data from scientific instruments. The technology has increased storage density by more than a factor of 1,000,000 over the past 35 years since it was first used in a disk format for computer data storage; however, fundamental limits, set by superpara- magnetism, are estimated yet to be a factor of more than 1,000 from where we are today. Furthermore, recent product announcements and developments in research labs suggest that the rate of progress is likely to accelerate. Storage densities of over 5 Gbit/in. 2 are likely by the end of this decade and densities of 100 Gbit/in. 2 appear likely in the early twenty-first century. Defining Terms Coercive force or coercivity: The magnetic field required to reduce the mean magnetization of a sample to zero after it was saturated in the opposite direction. Demagnetizing field: The magnetic field produced by divergences in the magnetization of a magnetic sample. Magnetoresistance: The resistance change produced in a magnetic sample when its magnetization is changed. Remanence coercivity: The magnetic field required to produce zero remanent magnetization in a material after the material was saturated in the opposite direction. Remanent magnetization: The magnetic moment per unit volume of a material in zero field. Saturation magnetization: The magnetic moment per unit volume of a material when the magnetization in the sample is aligned (saturated) by a large magnetic field. Superparamagnetism: A form of magnetism in which the spins in small particles are exchange coupled but may be collectively switched by thermal energy. Related Topics 36.1 Magnetism ? 80.2 Basic Disk System Architectures References T. Chen and T. Yamashita, “Physical origin of limits in the performance of thin-film longitudinal recording media,” IEEE Trans. Magnet., vol. MAG-24, p. 2700, 1988. A.S. Hoagland and J.E. Monson, Digital Magnetic Recording, New York: John Wiley & Sons, 1991. O. Karlqvist, “Calculation of the magnetic field in the ferromagnetic layer of a magnetic drum,” Trans. Roy. Inst. Technol., Stockholm, No. 86, 1954. Reprinted in R. M. White, Ed., Introduction to Magnetic Recording, New York: IEEE Press, 1985. E. K?ster and T.C. Arnoldussen, “Recording media,” in Magnetic Recording, C. D. Mee and E.D. Daniel, Eds., New York: McGraw-Hill, 1987. M.-M. Tsang, H. Santini, T. Mccown, J. Lo, and R. Lee, “3 Gbit/in. 2 recording demonstration with dual element heads of thin film drives,” IEEE Trans Magnet., MAG-32, p. 7, 1996. E.P. Valstyn and L.F. Shew, “Performance of single-turn film heads,” IEEE Trans. Magnet., vol. MAG-9, p. 317, 1973. E. Velu and D. Lambeth, “High Density Recording on SmCo/Cr Thin Film Media,” Paper KA-01, Intermag Conference, St. Louis, April 1992; to be published in IEEE Trans. Magnet., vol. MAG-28, 1992. R.M. White, Introduction to Magnetic Recording, New York: IEEE Press, 1984, p. 14. ? 2000 by CRC Press LLC M.L. Williams and R.L. Comstock, “An analytical model of the write process in digital magnetic recording,” AIP Conf. Proc., part 1, no. 5, pp. 738–742, 1971. J-G. Zhu and H.N. Bertram, “Recording and transition noise simulations in thin film media,” IEEE Trans. Magnet., vol. MAG-24, p. 2706, 1988. Further Information There are several books which provide additional information on magnetic and magneto-optic recording. They include the following: R.M. White, Introduction to Magnetic Recording, New York: IEEE Press, 1984. C. D. Mee and E. D. Daniel, Magnetic Recording, New York: McGraw-Hill, 1987. A. S. Hoagland and J. E. Monson, Digital Magnetic Recording, New York: John Wiley & Sons, 1991. ? 2000 by CRC Press LLC