Introduction

The shape of the B versus H characteristic of a material reveals whether its magnetism is based upon magnetocrystalline or shape anisotropy. In either case, the ideal characteristics described in Chapter 1 were founded on the concept of spontaneous magnetization, and this theory is certainly a good approximation for single crystals; measurements in the preferred [1,0,0] direction for iron shown in Figure 1.6 confirm this. However, practical materials do not follow this theoretical ideal, as shown for comparison by the initial magnetization curves for a real sample of iron in Figure 2.1. A measurable external applied field H is required to magnetize and saturate this material, so this sample does not exhibit spontaneous magnetization. The same is true for samples of nickel, cobalt and all alloys that are used to produce permanent magnets.

While the magnetization curves for the single crystal in Figure 1.6 are dependent upon the crystallographic direction, the curve for a bulk sample of iron is not. A simple ferromagnetic material such as this is therefore isotropic with no preferred axis, and any enhanced properties in a specific direction will only be imparted to a magnet during its production process. Spontaneous magnetization still exists in the crystal lattice structure, so it must be explained how the theory of magneto crystalline anisotropy must be modified to predict the actual characteristics of permanent magnets. To do this, the model of a magnetic material must first be enhanced.

Introduction

Earlier texts on permanent magnets have opened with historical reviews of these materials (Hadfield, 1962; McCaig, 1977; Parker, 1990; Parker and Studders, 1962). In this book the design of modern permanent magnets is emphasized, and so initially the development of the relationships that are required to model today's materials for a variety of common applications is considered. To the extent that a historical review is provided in this chapter, it is of those fundamental equations of electromagnetism that are needed to understand the performance of magnets in circuits and devices.

There are many properties of a permanent magnet that are considered in its design for a magnetic device, but most often it is the demagnetization curve that initially determines its suitability for the task. Its shape contains information on how the magnet will behave under static and dynamic operating conditions, and in this sense the material characteristic will constrain what can be achieved in the device design.

The B versus H loop of any permanent magnet has some portions which are almost linear, and others that are highly non-linear. The shapes of these B versus H loops, or at least the demagnetization portions of them, tell the designer a lot about the suitability of the material for a given application. A brief derivation of the B versus H loop is presented, to illustrate the microscopic mechanisms that determine the macroscopic performance of a magnet.

Introduction

Analytical techniques, such as finite element analysis, provide accurate solutions for two- or three-dimensional field distributions in complex geometries, which in turn may be used to predict device performance with similar precision. However, these techniques require a detailed definition of the geometry and boundary conditions to be solved, which assumes that an initial design already exists. While providing an accurate field solution for a defined geometry, they will not optimize it - suggestions for changes to dimensions, materials, excitations, etc. must come from the designer, to be analyzed via a field solution. Consequently, while computer-based field analysis is an effective tool for simulating a known device, it is too cumbersome for design optimization.

Preliminary designs are usually performed using a magnetic circuit model of the device in which each component or magnetic flux path is represented by a discrete element. Equations representing the magnetic circuit components are derived in this Chapter, and the elements they define are used in an equivalent circuit (similar in many respects to an electrical analog circuit). This is a simple model, which can be easily optimized for any performance requirements. Thereafter, field analysis may be employed to verify the operation of the device, and to fine-tune the design.

Introduction

Using simplifications for the actual paths followed by flux in a magnetic device provides an approximate model as described in Chapter 4, which is useful both for preliminary selection of component materials and dimensions and for performing sensitivity analyses. Before building a prototype device, however, it is often desirable to perform a more detailed analysis of the flux distribution, to investigate the validity of the prior assumptions, and perhaps also to account for effects such as saturation and eddy currents. Depending upon the complexity of the design and the nature of the effects to be studied, a more accurate analytical solution of the field distribution may be attempted directly, or with the aid of commercially available computer software. The objective in this chapter is to provide the basis for the representation of magnetic fields in complex geometries, and an understanding of the most common techniques that are presently available.

The nature of the fields that occur in electromechanical devices may be categorized into three levels of complexity. The most straightforward are magnetostatic fields, which result from excitation at zero frequency. Nevertheless, materials may still be represented by non-linear characteristics in magneto static field solutions, as in the case of saturation. The next level of complexity involves alternating current excitation, which adds the effects of eddy currents to the field solution.

Introduction

Chapter 2 provides a review of basic electromagnetic theory as applied to static magnetic fields. Neither wave motion nor eddy current effects caused by conductive media are considered: it is presumed that all time scales are long compared to these phenomena. Time enters only through the constant head-to-medium relative speed, v, so that all temporal information is transformed immediately into the fundamental spatial recording process by x = vt or dx/dt. The purpose of this chapter is to provide useful relations for the determination of fields, both from integrals over field sources and solutions of differential equations for field potentials. Thus, the framework will be provided for the determination of magnetic fields from magnetized heads (Chapter 3) and media (Chapter 4), and in addition, expressions for Fourier and Hilbert transforms will be presented for utilization in spectral analysis of recording signals and noise. These transforms involve operations on the spatial variable, x, which represent the head-to-medium motion direction. In particular, the Fourier transform will be expressed in terms of the spatial transform variable, k: the wavenumber or inverse wavelength (2π/λ). For direct correspondence with measured frequency the simple transformation f = vκ/2π can be utilized.

In magnetic recording the track width is generally large with respect to dimensions in the nominal recording plane, which includes the head-to-tape motion direction and the direction perpendicular to the medium surface (thickness direction). Therefore, two-dimensional field expressions are useful and will be given explicitly in this chapter. In two dimensions the Fourier transforms acquire a particularly simple form yielding the familiar exponential spacing loss.

Introduction

The fundamental noise in magnetic recording is due to the granularity of the medium. If amplitude as well as phase modulation noise sources are not present, particulate noise remains. This noise can exhibit a different character in tapes than in thin films, because thin films have strong magnetic interactions and are densely packed. Nonetheless, particulate noise is basic to all recording media. The structure of this chapter will be to discuss first granularity noise neglecting particle correlations. The total noise power is simply a sum of the independent noise power from each particle or grain. Next, correlation effects are discussed that can involve spatial as well as magnetic correlations. A general formalism will be given, but only simple examples will be examined. The difficulty is that particulate noise modeling is based on Poisson statistics, which are valid only for point or infinitesimally small particles. The effects of finite particle size for moderately dilute systems, which leads to non-overlap effects, can only be included approximately. Granularity noise in thin films, where the grains are tightly packed, must be analyzed differently. A simple approach will be discussed in Chapter 12. In this chapter signal-tonoise ratios are estimated, and wherever appropriate, comparison will be made with the results for continuum fluctuations calculated in Chapter 10. The chapter begins with a calculation of the replay voltage pulse and spectrum of a single particle following previous analyses (Thurlings, 1980, 1983; Arratia & Bertram, 1984). A simplified model of particle clustering is presented at the end of this chapter. Only stationary correlations are discussed in this chapter. Non-stationary effects are the focus of Chapter 12.

Introduction

This chapter presents the formalism associated with the calculation of playback voltages. Expressions for both real time waveforms, such as isolated pulses, as well as spectra will be derived. The playback process involves low flux levels in the playback head; thus, linear system theory may be utilized to relate a recorded magnetization pattern to the reproduce voltage at the head terminals. The chapter begins with a simple example of the waveform obtained by direct calculation of the playback flux. However, it is generally much more convenient to utilize the formalism of reciprocity. The principle of reciprocity states that the playback flux at any instant is equal to a correlation of the recorded magnetization and the field per unit current of an energized playback head. This principle will be derived and the conditions for its usage discussed in detail. Following that, general playback formulas will be given and specific examples will be discussed for both longitudinal and vertical recording. In this chapter the playback of isolated pulses will be treated. The effects of pulse superposition, ‘linear superposition’, for both the ‘roll-off curve’ as well as linear bit shift will be analyzed in Chapter 6. The discussion will focus on playback by an inductive head. However, since reciprocity may be adapted to magnetoresistive (MR) playback heads, the results presented here apply only with slight modification. Reciprocity as applied to MR heads is discussed in Chapter 7.

In analysis of the recording process the head can be placed either above (e.g. Fig. 5.1) or below (e.g. Fig. 5.3) the medium.

Introduction

In this chapter analysis of the playback process is extended to consider the effects of multiple transitions. First the concept of linear superposition in magnetic recording is introduced. Two examples are discussed in detail: (1) square wave recording of alternating transitions with a fixed bit spacing and (2) dibit recording of a pair of transitions. In the former both the ‘roll-off’ curve of the peak voltage versus density will be derived as well as the spectrum or Fourier transform. The utility of spectral measurements for analysis of the recording process will be emphasized as in Chapter 5. The relation of the square wave spectrum to an ‘effective’ channel transfer function will be given. In this chapter, as in the previous one, a comparison will be made between longitudinal and perpendicular recording. The effects that relate solely to differences in a change in magnetization orientation will be emphasized. In this way the playback effects and record phenomena discussed in Chapter 8 can be distinguished.

Linear superposition

The magnetic recording process is not strictly linear. A linear integral relation does not occur where a change in input amplitude yields a proportional change in output voltage. In fact an impulse does not exist because the ‘input’ to the recording channel consists of step functions of voltage or current that produce transitions of magnetization. However, a restricted linearity applies as long as transitions are not written too closely. A transfer function can be defined whose product with the input spectrum yields the output spectrum.

Introduction

Noise in magnetic recording arises from three predominant sources: the playback amplifier, the playback head, and the recording medium. Amplifier noise depends on current or voltage noise sources. Head noise arises from the loss impedance of the head due to the complex part of the permeability (Figs. 3.2, 3.3). Since the head impedance is matched to the amplifier, inductive head noise results as Johnson noise with the loss impedance as the effective noise resistor (Davenport & Root, 1958). Playback head loss impedance and head noise limited system signal-tonoise ratios have been discussed in detail (Smaller, 1965). In Chapters 10, 11 and 12, analysis of the predominant medium noise mechanisms will be presented. The discussion will focus on calculations of the power spectral density. Measurements of noise spectra can be utilized readily to identify and analyze medium noise sources.

Medium noise arises from fluctuations in the medium magnetization. This noise can be separated into three somewhat distinct sources: amplitude modulation, particulate or granularity noise, and phase or transition noise. An illustration of modulation and transition noise is shown in Figs. 10.1 (a), (b), respectively. In conventional amplitude modulation noise, the fluctuations are proportional to the recorded medium magnetization or flux levels. As the recording density is increased, the noise regions decrease relative to the bit length or transition separation and the noise decreases, as measurements in Fig. 10.2(a) show. Transition noise refers, in general, to fluctuations that are concentrated near the recorded transition centers (Fig. 10.1(b)).

Introduction

This chapter will address noise arising from fluctuations localized at the transition. Transition noise is dominant in metallic thin films where the average magnetization lies in the longitudinal or recording direction (Bertram, et al., 1992). Transition noise can also occur in perpendicular film media. These media are prepared either by sputtering or by plating processes and are extremely uniform so that conventional sources of amplitude modulation noise, as discussed in Chapter 10, are not present. The fundamental feature of thin films that gives rise to transition noise is the almost completely dense packing of these polycrystalline media (Fig. 1.2). With dense packing the medium noise depends strongly on the state of magnetization.

In Figs. 12.1 (a), (b) illustrations of the magnetization configurations for grains with solely longitudinal orientation are shown for a saturated medium (a) and an erased medium (b). For the saturated case the ‘poles’ at the ends on one grain cancel those of each adjacent grain. In this case no noise voltage will occur. In the erased case the average magnetization vanishes. To achieve this state, adjacent grains with opposite magnetization will occur, giving rise to localized ‘poles’ at the grain interface of twice the magnitude of that of individual grains. Even with magnetization correlation, a random distribution of these ‘double’ poles will occur, of both polarities, leading to a replay noise voltage. In general, noise voltage sources will occur for all configurations where the medium is not saturated. The greatest number of noise sources will occur for states where the average magnetization vanishes. Media uniformly magnetized at various states along the major loop will exhibit fluctuations that maximize at the remanent coercive state.

Introduction

In this section fields and Fourier transforms of a variety of inductive head configurations will be presented. The field patterns are of interest for both the recording process and, via reciprocity, the playback waveforms. First, the concept of head efficiency will be introduced. Following that, approximate and exact expressions for the fields in the gap vicinity of a very wide head will be derived and compared. The effect of finite head length as well as finite track width will be discussed in terms of approximate expressions. The results of studies of head field saturation will be included. The chapter will conclude with a discussion of the effect of keepered media on head fields.

The function of a recording head is to transfer efficiently the mmf that results from a current applied to the windings into field at the gap region where the recording medium passes. Two state-of-the-art structures are shown in Figs. 1.4 and 3.1. Figure 3.1 shows a head designed for highdata- rate recording in high-density helical scan tape recorders (Ash, et al., 1990). This structure exhibits the extreme dimensional scaling typical of most head structures: the gap length is sub micron (g ∼ 0.25μm), the gap depth and gap width are between one and two orders of magnitude larger (∼ 10–30μm), and the head major dimensions are in the mm range. The example in Fig. 3.1 is of a structure completely laminated to allow for operation at frequencies ∼150MHz. An inductive head, commonly of this geometry, is either completely ferrite for medium coercivity applications or ‘metal-in-gap’ for use on high coercivity media for video (8mm or DAT) or data recording (Jeffers, 1986; Iizuka, et al., 1988).

Introduction

In this chapter, models will be discussed that give insight into the recording process. In contrast to the playback process, the recording of magnetization patterns is a non-linear phenomenon. Thus, except for special cases, analysis must be by computer simulation. It is the long-range magnetostatic fields that cause computer simulations to be iterative and extremely time consuming. There are two philosophical approaches to computations of the record process. One is to neglect the fine details and develop reasonably approximate models that capture the main physical features of the process. Such simplified models allow for analytic solutions of magnetization patterns or solutions that require a minimum of computer simulation. This simplified approach is useful for developing guidelines in media development (e.g. the effect of coercivity or remanence changes) or in head–media interface geometry development (effect of head–medium spacing, record gap, medium thickness). Parameters can be easily changed in simplified models.

The other approach is to develop full numerical micromagnetic models. These are required in order to compute detailed, or second order effects, of the recording process, such as noise, edge-track writing, and non-linear amplitude loss and thus, for example, give fundamental input to error-rate calculations. Simulations can give detailed information about pulse asymmetry in tape recording (Bertram, et al., 1992) or the fluctuations of the transition center across the track that leads to position jitter or transition noise in thin film media (Zhu, 1992). For example, in Fig. 8.1 the vector magnetization distribution from micromagnetic simulation of a recorded transition in thin film media is shown.

Magnetic recording is a technology that has continually undergone steady and substantial advancement throughout its history. Typically, in the last two decades areal densities in computer disk recording have increased by over two orders of magnitude. This development has occurred via the simultaneous growth in new materials for heads and media, advanced signal processing schemes, and mechanical engineering of the head–medium interface. In addition, there has been substantial growth in the theoretical understanding of the magnetic behavior of heads, media and, in general, the magnetic recording process. Fundamental understanding of the physics of magnetic recording is necessary not only for system design, but so that the specific behaviour of magnetic components can be analyzed, either analytically or numerically, saving time-consuming and expensive experimentation. For example, it is difficult to produce all the media variations required to perform a thorough comparison of different modes of recording, such as longitudinal and perpendicular recording.

In recent years there have been many publications that cover the fundamentals and applications of the magnetic recording process. These books or papers have been either technically oriented discussions of specific topics or have provided an introduction at an elementary level to the basics of magnetic recording. The philosophy of this book is to provide a pedagogical introduction to the physics of magnetic recording. The level is advanced and all basic aspects of magnetic recording are included: magnetic fields of heads and media, the linear replay process, the non-linear recording process including interferences, and medium noise.

Introduction

Magnetized recording media produce fields by virtue of divergences in the magnetization pattern. Thus, (2.8) can be utilized to obtain the magnetic fields for any specified magnetization pattern. For two-dimensional geometry it is often convenient to utilize the simple form given by (2.22), or under certain conditions (2.26). Magnetized media are particularly simple to analyze since, in general, they extend infinitely far along the x axis and possess a finite thickness or magnetization depth which does not vary along the x axis. In this section expressions are given for the fields for single magnetization transitions that are either longitudinally or vertically oriented. That discussion will be followed by a general relation for the Fourier transform of the fields. This section is concluded by a discussion of the fields from sinusoidally magnetized media. Only two-dimensional geometries will be considered.

Single transitions

We begin by deriving the fields produced by a single, perfectly sharp transition as sketched in Figs. 4.1(a) and 4.2(a) for a longitudinally and vertically directed magnetization, respectively. The coordinate system (x, y) is centered at the center of the medium at the transition center. Equation (2.26) may be utilized for both cases, since the volume charge for the case of a sharp transition of longitudinal magnetization is equivalent to a surface charge of σ = 2M at the transition center (x = x0) extending from − δ/2 < y < δ/2. The fields for a longitudinal magnetization utilizing (2.26) (r1, r2, θ are noted in Fig. 4.1 (a)) yield:

These fields are plotted versus x for fixed y in Fig. 4.1(b) along the medium centerline (y = 0) and in Fig. 4.2(c) at the medium surface y = δ/2.

Magnetic recording is the central technology of information storage. Utilization of hard disk drives as well as flexible tape and disk systems provides, inexpensively and reliably, all features essential to this technology. A data record can be easily written and read with exceedingly fast transfer rates and access times. Information can be permanent or readily overwritten to store new data. Digital recording is the predominant form of magnetic storage, although frequency modulation for video recording and ac bias for analog recording may persist in consumer applications. Data storage is universally digital. Superb areal densities for disk drives and volumetric densities for tape systems are achievable with extremely low error rates. In the last decade there have been extraordinary advances in magnetic recording technology. Current densities and transfer rates for disk systems are typically 60Mbits/in2 and 10Mhz, respectively, but systems with densities of 1–2Gbits/in2 are realizable (Wood, 1990; Howell et al., 1990; Takano, et al., 1991). The ability to coat tape with extremely smooth surfaces has permitted the development of very high density helical scan products (SVHS, 8mm video) (Mallinson, 1990). The digital audio helical scan recorder (DAT) is representative of very high density tape recording with linear densities of greater than 60kbits/in, track densities of 250 tpi, and volumetric densities on the order of 50Gbits/in3 (Ohtake, et al., 1986). High data rate tape recording systems near 150MHz have been developed (Ash, et al., 1990; Coleman, et al., 1984). In general, densities and data rates of magnetic recording systems have been increasing at a rate exceeding a doubling every three years.