TDK Corporation
`
`Exhibit 1007
`
`Page 1
`
`TDK Corporation Exhibit 1007 Page 1
`
`

`
`Magnetic Information Storage
`Technology
`
`TDK Corporation Exhibit 1007 Page 2
`
`

`
`ACADEMIC PRESS SERIES IN ELECTROMAGNETISM
`.....................................................................................................
`
`Electromagnetisrn is a classical area of physics and engineering which still plays
`a very important role in the development of new technology. Electrornagnetism
`often serves as a link between electrical engineers, material scientists, and applied
`physicists. This series presents volumes on those aspects of applied and theoretical
`electromagnetism that are becoming increasingly important in modem and rapidly
`developing technology. Its objective is to meet the needs of researchers, students,
`and practicing engineers.
`
`This is a volume in
`ELECTROMAGNETISM
`
`ISAAK Mmaaxcoyz, Ssmss EDITOR
`Umvensmr or MARYLAND, COLLEGE PARK, MARYLAND
`
`TDK Corporation Exhibit 1007 Page 3
`
`

`
`Magnetic Information Storage
`Technology
`
`Shan X. Wang
`Department of Materials Science and Engineering
`(and of Electrical Engineering)
`Stanford University
`Stanford, California
`
`Alexander M. Taratorin
`IBM
`Almaden Research Center
`
`San lose, California
`
`ACADEMIC PRESS
`
`San Diego London Boston
`New York Sydney Tokyo Toronto
`
`TDK Corporation Exhibit 1007 Page 4
`
`

`
`The cover page illustrates a hard disk drive used in modern computers. Hard
`disk drives are the most widely used information storage devices. The block
`diagram shows the principle of the state~of~the-art disk drives. Any information
`such as text files or images are first translated into binary user data, which are
`then encoded into binary channel data. The binary data are recorded in magnetic
`disks by a write head. For example, the magnetization pointing to the right (or
`left) represents "l” (or ”O”). The magnetization pattern generates a voltage
`waveform when passing underneath a read head, which could be integrated with
`the write head and located near the tip of the stainless suspension. The voltage
`waveform is then equalized, i.e., reshaped into a proper form. This equalization
`step, along with a so-called maximum likelihood detection algorithm, allows us
`to detect the binary channel data with a high reliability. The trellis diagram shown
`with 16 circles and I6 arrows is the foundation of maximum likelihood detection.
`The detected binary channel data are then decoded back to the binary user data,
`which are finally translated back to the original information.
`
`Transferred to Digital Printing 2004
`
`This book is printed on acid~free paper. ®
`
`Copyright © 1999 by Academic Press
`
`All rights "reserved.
`No part of this publication may be reproduced or transmitted in any form or by
`any means, electronic or mechanical, including photocopy, recording, or any
`information retrieval system, without permission in writing from the publisher
`ACADEMIC PRESS
`
`a division of Harcourt Brace <9’ Company
`525 B Street, Suite 1900, San Diego, California 92101-4495, USA
`http: //www.apnet.con1
`Academic Press
`24-28 Oval Road, London NW1 7DX, UK
`http: / /www.hbuk.co.ul</ap /
`
`Library of Congress Cataloging-in-Publication Data
`Wang, Shan X.
`Magnetic information storage technology / Shan
`X. Wang, Alex Taratorin.
`‘
`p. cm. —-— (Electrornagnetism)
`Includes index.
`ISBN 0-12~734570-1
`
`I. Wang, Shan X.
`1. Magnetic recorders and recording.
`II. Taratorin, A. M.
`III. Title.
`IV. Series.
`TK7881.6.W26
`1998
`62l.39’7~~dc21
`
`98-24797
`CIP
`
`Printed in the United States of America
`9900010203
`MB
`987654321
`
`TDK Corporation Exhibit 1007 Page 5
`
`

`
`Academic Press Series in
`
`Electromagnetism
`
`Edited by: Isaak Mayergoyz, University of Maryland! College Park, Maryland
`
`BOOKS PUBLISHED IN THE SERIES:
`
`John Mallinsonz Magneto~Resistioe Heads: Fundamentals and Applications
`Alain Bossavit, Computational Electroniagnciism: Variational Formulations,
`Complementarity, Edge Elements
`Georgia Bertotti, Hysteresis in Magnetism: For Physicists, Material Scientists,
`and Engineers
`Isaak Mayergoyz, Nonlinear Diffusion of Electromagnetic Fields
`
`RELATED BOOKS
`
`John Mallinson: The Foundations of Magnetic Recording, Second Edition
`Reinaldo Perez: Handbook of Electromagnetic Compatibility
`
`TDK Corporation Exhibit 1007 Page 6
`
`

`
` or Inductive
`
`
`
`tReC0rdinsHead and
`Magnetic Medium
`
`7
`
`In this chapter we will discuss the magnetic fields generated by an ideal-
`ized magnetic recording head and magnetic medium to pave the way for
`the presentation of read and write processes in the next two chapters.
`Magnetic recording is mostly concerned with very.-high~frequency signals,
`and the high—frequency components of a magnetic field are of vital impor-
`tance. Therefore, Fourier transforms are employed extensively to analyze
`magnetic fields and readback signal waveforms, and a brief review of
`Fourier transform and notations used in this book will be given first.
`
`2.1 FOURIER TRANSFORMS OF MAGNETIC FIELDS
`IN FREE SPACE
`
`Fourier transform is widely used in science and engineering, but its defini-
`tion is not unique. Waveforms are most often expressed in time (t) or
`displacement (x) domain, f(t) or f(x), respectively, where x = lit and v is
`the velocity. The temporal Fourier transform of waveform f(t) is defined
`as
`
`I-‘(f) =
`
`dtf<t>e~i2m
`
`(2.1)
`
`where the variable f is the frequency. The corresponding inverse Fourier
`transform is
`
`f(t) = f°° df F(f)e‘2"7’.
`
`(2.2)
`
`The spatial Fourier transform of f(x) is defined as
`
`F(k) =
`
`dx f(x)e‘”"‘,
`
`..,er,.vx.W.;.<;iar»¢ss;s;1ait:;2.“»)2.“e7z*':§é‘e>,‘:sz‘I::
`
`TDK Corporation Exhibit 1007 Page 7
`
`

`
`32
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`where variable k is the wavevector. The corresponding inverse Fourier
`transform is
`
`(2.4)
`f(x) = 51;]: dic F(k)e No;
`Note that there are other forms of definition for Fourier transforms, and
`one should be careful when using a mathematics handbook to look up
`the Fourier transforms ofa given function. In magnetic recording it usually
`holds that x = zit, k = 277//I = 2777‘/U, where x is the displacement along the
`head-medium relative motion direction, 7) is the relative Velocity between
`recording head and medium, t is the time, and A is the wavelength.
`Magnetic information is recorded along a linear track spatially, but it is
`often captured on an oscilloscope in time domain. It is important to
`remember that the spatial and temporal waveforms have the following
`relations:
`
`ax) 2 at),
`F(k) = o - F(f).
`Hereafter we often use spatial Fourier transform in analyzing magnetic
`recording, The results must be translated into experiments in time domain
`(oscilloscope) or frequency domain (spectrum analyzer) by the above equations.
`The Fourier transform is a linear operation. When it is combined with
`some other operations, there are useful relations as listed in Table 2.1. In
`particular, the Fourier transform of the convolution of two functions, de-
`fined as
`
`(2.5,
`
`f(x) *g<x) 5 six’ f(x’)g(x — x’),
`
`(2.6)
`
`is the product of their Fourier transforms.
`There is an important relation between a function and its Fourier
`transform called Parseval’s theorem, indicating that the total energy of 21
`
`TABLE 2.1. Fourier Transforms‘
`
`Differentiation
`Translation
`Modulation
`Convolution
`
`Multiplication
`
`Function
`gig}
`ax
`f(x - II)
`e*"°"f(x)
`f(x) * g(x)
`f(x)g(x)
`
`Fourier transform
`ikF(k)
`.
`e"""'F(k)
`I-‘(k — ko)
`I-‘(k)G(k)
`P(k> * G(k)
`
`TDK Corporation Exhibit 1007 Page 8
`
`

`
`2.1 FOURIER TRANSFORMS OF MAGNETIC FIELDS IN ‘FREE SPACE
`
`33
`
`function is the same whether it is expressed in the real space (at) or in the
`Fourier space (k):
`
`l:dx|f(x)|2 : dkll-“(k)l2.
`
`(2.7)
`
`Now let us consider the free space magnetostatic potential, which
`obeys Lap1ace’s equation:
`
`V2(/7 = 0.
`
`The magnetic field is, of course,
`
`H = ~V¢2.
`
`(1.17)
`
`(1.15)
`
`In a two-dimensional (2D) problem (x—y plane) Laplace’s equation is
`simply
`
`‘.3.2£5_(_’£:_fl + fli‘./.32 : 0.
`6x2
`ayz
`
`(23)
`
`Performing Fourier transform to Equation (2.8) with respect to x, we
`obtain
`
`—k2¢(k, y) = 0.
`=
`(z'k)2¢(k, y) +
`where ¢(k, y) E [W dxr/2(x,y)e"”"‘. A general solution of ¢(k, y) is
`
`(2.9)
`
`qS(k, y) = A+(k)e’<r + A_(k)e”"V.
`
`(2.10)
`
`_
`
`The potential must approach zero when it is infinitely distant from the
`field sources. If the free space in question is completely at one side of
`the field sources such as magnetic charges or permeable materials, i.e.,
`the field sources are below a certain plane (3; < 0), then the potential will
`vanish at y = +00, and the potential in the free space is
`
`¢(k, y) = ¢>(k,0)e""'V (y > 0).
`
`(2.11)
`
`This means that the Fourier transform (FT) of a magnetostatic potential
`with respect to x would decay exponentially in y direction if the free space
`is at one side of field sources! It follows that the Fourier transform of the
`magnetostatic field with respect to x will decay exponentially in the y direction
`as well:
`
`Hx(lc, y) 2 FT (-3?) =—ik¢(k, y) = H,,(k,O)e""‘lV(y > 0),
`Hy(k/ y> E PT (-99) = —§9'9g‘~'-Q = IkI¢(k, y) = Hy(k,o>e~1'<'r
`
`ay
`
`ay
`
`(2.12)
`
`TDK Corporation Exhibit 1007 Page 9
`
`

`
`“‘“.”W€l:9~§§W"
`
`34
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`where Hx(lc,O) = —ik¢>(k,O), Hy(k,0) = lkI¢(k,O). It can be shown that
`
`Hy(k, y) = isgn(k)Hx(k, y),
`
`sgn(k) E
`
`1fork>O,
`0 for k = 0,
`-—1 for k < O.
`
`(2.13)
`
`This states that in 213 free space, the Fourier transforms of the two field compo-
`nents are identical in magnitude and only difier in phase by i 90°. Taking a
`logarithmic of the field components, we obtain that
`
`20logH,,(k, y) = 20logH,,(k,0)*54.6% (as),
`20logHy(k, y) = 20logHy(k,0)"54.6% (as),
`
`where A = 277/k is the wavelength. This means that the Fourier transform
`of a magnetic field component with respect to x will drop ’’linearly’' in the y
`direction at a rate of 54.6 dB per wavelength. This is an equivalent way of
`describing the exponential decay. The exponential decay is often called.
`the Wallace spacing loss in magnetic recording, and is only valid for the
`Fourier transforms rather than a magnetic field itself! Spacing loss is one
`4 of the most important factors to be considered in magnetic recording, and
`will be discussed more in Chapter 3.
`Now let us derive another important relation for a free space potential,
`¢(x,y), based on the Fourier transform of convolution. It is the inverse
`spatial Fourier transform of </>(k, y):
`
`ax, y) = FT”‘l¢(k, y)] = PT“1I<;5(k,0)e“"“Vl
`= ¢(x,0) *FT"'1[e“‘”"V]
`
`M
`"' ¢s(-X)
`
`i___l__,_
`77(x2 + 3/2)
`
`where ¢>S(x) E ¢(x,0) is the surface magnetic potential at y = 0. Thus
`
`«
`
`:: .2 0°
`
`’_.....___.__....__.¢(xl)
`</>(x, y) Wfwax (X _ 5,), + yz.
`
`(2.15)
`
`This means that the magnetic‘ potential (anal thus magnetic field) can be ex-
`pressed by the surface magnetic potential at y = 0 alone without any other
`information. With the above relations in hand, we now turn to the funcla~
`mentals of inductive recording heads.
`
`TDK Corporation Exhibit 1007 Page 10
`
`

`
`2.2 INDUCTIVE RECORDING HEADS
`
`2.2 INDUCTIVE RECORDING HEADS
`
`As introduced in Chapter 1, an inductive recording head is essentiallyva
`h0rsesh0e~shaped soft magnet with an air gap and electric coils. Of course,
`the real structure of inductive recording heads is actually more compli-
`cated. Most audio and video recorders, and low—end. hard disk drives
`employ so-called ferrite ring heads that consist of magnetically soft bulk
`ferrites machined into head structures. A more advanced version of the
`ring head is metal-in-gap (MIG) ring head, in which a metal layer with a
`higher saturation such as Sendust (FeSiAl alloy) is deposited in the head
`gap such that a larger Write field can be achieved. The ring heads are not
`the focus of this book, and their details can be found in the reference books?
`Nowadays most hard disk drives being shipped employ thin film
`heads that evolve from IBM 3370 thin-film heads, first introduced in the
`l970s. The cross section of an inductive thin-film head is shown in Fig.
`2.1a. The bottom and top magnetic poles are electroplated permalloy
`(Ni80Fe2o) layers, typically 2~4 pm thick. The four—layer, 54—turn coils are
`made from electroplated copper. The insulation layers separating coils
`and magnetic poles are formed by hard~cured photoresists. The head gap
`region is enlarged and shown in Fig. 2.lb. The gap layer is a sputtered
`alumina (A1203) layer in submicron thickness (~0.9 pm in original IBM
`3370, now commonly <O.3 ,u.m). The pole tip width of two magnetic poles
`(P1 and P2), along the direction perpendicular to the cross section, is
`approximately the data trackwidth written to and read from the magnetic
`disk. Therefore, they are made very narrow, ranging from >10 ,um in the
`old days to submicron width in the state-of-the-art heads. Thin~film heads
`are batch fabricated in a fashion similar to that in VLSI technology, and
`will be discussed in detail in Chapter 5.
`
`2.2.1 Karlqvist head equation
`
`The magnetic field of an inductive head is complex because the head
`geometry is very complicated. Head fields can be solved numerically by
`finite element modeling or boundary element modeling, and sometimes
`analytically by conformal mapping, Green functions, or transmission line
`model, some of which will be described in Chapter 5. Here We describe the
`simplest yet most useful head model. In a Classical paper published in 1954,
`Karlqvist idealized an inductive head with the following assumptions3:
`
`1. The permeability of magnetic core or film is infinite.
`2. The region of interest is small compared with the size of the mag-
`netic core that the head can be approximated geometrically as
`
`.>L~‘«s,,
`
`TDK Corporation Exhibit 1007 Page 11
`
`

`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`(a)
`
`(b)
`
`Inductive thin-film head. (a) A cross section showing the alu1nina~
`FIGURE 2.1.
`TiC substrate, magnetic layers (P1 and P2), coils, insulation layers, alumina under-
`coat, and overcoat. (b) Enlarged head gap region.
`
`shown in Fig. 2.251. This is traditionally called a Karlqvist head.
`The magnetic core is much wider than the head gap, and the whole
`head is infinite in the z direction. Therefore, the problem becomes
`two—dimensional in the x—y plane, i.e., the paper plane.
`. The magnetic potential across the head gap varies linearly with x,
`as shown in Fig. 2.2b. This means that the magnetic field in head
`gap, Hg, is constant down to y = O, and the magnetic potential in
`the magnetic core is zero because of its infinite permeability. The
`surface magnetic potential of a Karlqvist head at y = 0 is the same
`as the magnetic potential deep across the head gap:
`
`lxl S g/2,
`for
`~Hgx
`¢s(x) = -gI-I8/2 for xzg/2,
`gHg/2
`for
`x 5 —g/2.
`
`(2.16)
`
`TDK Corporation Exhibit 1007 Page 12
`
`

`
`2.2 INDUCTIVE RECORDING HEADS
`
`(a)
`
`FIGURE 2.2. Schematic of Karlqvist head and magnetic potential.
`
`Consequently, the magnetic potential of the Karlqvist head at y > 0
`is
`‘
`
`I
`
`d>5(x’)
`(x __ x/)2 _l_ :1/2
`
`_ Z °°
`¢(x, y) — Trwdx
`= —I—ff[(x + g/2)ti-m"1<
`_.z1,,9c.:.5L_2_>::y3]
`
`x+g/2
`
`)—-(x — g/2)tan"1<
`
`x*8/2)
`y
`
`2 (x~g/2)2+y2'
`
`TDK Corporation Exhibit 1007 Page 13
`
`

`
`38
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`Then the x and 3/ components of .the Karlqvist field are given by
`
`Hx(x, y) = ~29? = -I—{3[tan'1<-x—-tézg)-tan’1(x H 8/2)]
`7r
`__ Hi
`-1
`SH
`in
`__ jrgtan [x2 + yz __(g/D2] ,
`
`y
`
`y
`
`6x
`
`(2.17)
`
`(x+g/2)2+f
`_ __:3_g_{3__ __H
`Hy(x' y) *
`ay ~
`5:-1n(x —~ g/2)2 + yz‘
`
`It can be readily shown that, for a Karlqvist head, the contours of constant
`H, are circles going through the head gap comers.
`At the small gap limit, g —-> 0, then
`
`y
`H,,(x, y) = E35
`vr xi + r?’
`
`Hylxw H) 2
`
`-5135"
`7 x2 + y2'
`
`(2.13)
`
`This is the magnetic field produced by a line current located at the head
`gap edge.
`The Karlqvist field components as a function of x (displacement along
`data track) at a constant y (spacing between magnetic medium and head
`air-bearing surface) are plotted in Fig. 2.3. The field amplitudes drop and
`the pulses widen with increasing y. Both the amplitude and shape of
`the head field are important in magnetic write process, while the shape
`determines the sensitivity of an inductive read head. These concepts will
`become clear in Chapters 3 and 4.
`In this text we will mostly be concerned with longitudinal magnetic
`recording in which magnetic medium is magnetized along the data track
`direction, so the x component of head field is very relevant. The Fourier
`transform of the x component of the Karlqvist field is
`
`Hxgcl y 2 0) = ggg e-Ihy
`kg/ 2
`
`=gH
`3
`
`sin(kg/ 2)
`kg/2
`
`e"kV for k>0.
`
`‘ (2.19)
`
`We often concentrate on k > 0 in Fourier transforms, particularly in
`experiments. The constant coefficient above is the Fourier transform of
`the surface magnetic field, which is in the form of a single square pulse:
`
`”
`
`H"(x’3/*0) — l0g for
`
`_ H for
`
`lxlsg/2,
`
`|x|>g/2.
`
`TDK Corporation Exhibit 1007 Page 14
`
`

`
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`TDK Corporation Exhibit 1007 Page 15
`
`

`
`40
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`This square wave nature leads to the vanishing of the field transform
`when the wavevector satisfies k = 211 mg, or when the wavelengths are A
`= 277"/k = g/n, where 11. = 1, 2, 3.
`.
`.
`. These vanishing points are called
`the gap nulls.
`The assumptions made by Karlqvist about the surface potential is not
`very accurate near the gap corners (or air-bearing surface), a conformal
`mapping technique is used by Westmijze to solve the head field accu—
`rately/1 The accurate solution of the Karlqvist head without using assump-
`tion #3 (on p. 36) is very close to the Karlqvist expression far away
`from the gap corners, but drastically different near the gap corners. One
`consequence is that the gap nulls are slightly modified‘ For example, the
`first gap null actually occurs at a wavelength of ~1.136g instead of g!
`
`2.2.2 Head magnetic circuit
`
`In the Karlqvist model, the deep gap field Hg must be known to calculate
`the head field in magnetic medium, but only write current is directly
`controlled. Therefore, we need to understand the relation between the
`write current and the deep gap field. As a simplest example, an inductive
`recording head is modeled as a soft magnet core of constant cross section
`area AC with an air gap of constant area Ag, as shown in Fig. 2.4a. If the
`magnetic flux due to the fringe field near the head gap is neglected, then
`the magnetic flux Q5 is constant throughout the inductive head because
`of flux conservation:
`
`45 = BCAC = B3/lg,
`
`(1.7)
`
`where B, and Bg are the magnetic flux densities in core and gap, respec-
`tively. From Ampere’s law, we have
`
`NI = Hg, + H33,
`
`(1.12)
`
`where N is the number of coil turns, I is the write current, H6 is magnetic
`field in the magnetic core (not to be confused with coercivity), and la
`and g are the length of the magnetic core and head gap, respectively.
`Substituting magnetic field by magnetic flux density using the constitutive
`relations [Equation (l.10)], Ampere’s law becomes
`
`2,
`
`Q§(l»5c/1voAc + /-to/la) '
`
`g
`
`where pc is the permeability of magnetic core, while the air permeability
`is 1.
`
`TDK Corporation Exhibit 1007 Page 16
`
`

`
`2.2 INDUCTIVE RECORDING HEADS
`
`(a) Simplest inductive recording head model, and (b) its equivalent
`FIGURE 2.4.
`magnetic circuit.
`
`Similar to the concept of electrical resistance, we define the magnetic
`reluctance of a section of soft magnet of length l, cross section area A, and
`absolute permeability ,u. as
`
`R
`
`_l_
`“A.
`
`(2.20)
`
`Then, Arnpere’s law can be rewritten as
`
`H.
`=
`1
`2 _g_
`NI — cI>(R, + .128), R, _ IWCOAC, Rg _ /Mg.
`
`(2.21)
`
`In other words, the recording head model in Fig. 2.4a can be represented
`by a magnetic circuit as shown in Fig. 2.4b. The magnetomotive force is
`NI, the magnetic flux is <13, and the core and gap reluctances are in series,
`corresponding to voltage, current, and two resistors in series in an electric
`circuit. This type of magnetic circuit model is Very useful in analyzing
`magnetic recording heads and other magnetic devices.
`
`TDK Corporation Exhibit 1007 Page 17
`
`

`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`The head efficiency E is defined as the percentage of magnetomotive
`force across the head gap out of the total magnetomotive force of the
`head coils: (We used the same symbol for efficiency, electric field, energy,
`etc.; the meaning is distinguishable from the context.)
`
`H 8
`
`R5
`
`The head efficiency is determined by the head geometry and core material
`property. If E = 1, the inductive head transfers all the coil magnetomotive
`force NI to the gap region. If the head efficiency is known, the head deep
`gap field Hg can be easily calculated from write current.
`
`2.3 MAGNETIC RECORDING MEDIUM
`
`Magnetic recording media in hard disk drives contain either magnetic
`particles in organic binders (particulate disks) or continuous magnetic
`thin films (thin—film disks), which must have coercivities large enough to
`support the magnetic transitions to be written. Thin-film disks, presently
`the dominant magnetic disks, are actually complex multilayer structures
`as shown schematically in Fig. 2.5. The aluminum substrate is plated with
`an amorphous NiP undercoat to make the disk rigid, smooth, and properly
`textured. A chromium underlayer is often used to control magnetic prop-
`
`Lubricant ~30 A
`Overcoat
`100-~200 A
`Magnetic Film 2o<»5o0 A
`
`hromium Underlayer 1000-2000 A
`
`Al Substrate ~O.8 mm
`
`FIGURE 2.5. A schematic cross section of thin film hard disk.
`
`TDK Corporation Exhibit 1007 Page 18
`
`

`
`23 MAGNETIC RECORDING MEDIUM
`
`43
`
`erties and microstructures of the magnetic recording layer. The magnetic
`bye: (typically Co—based alloy) is covered by a carbon overcoat layer and
`lubricant. The last two layers are necessary for the tribological perform-
`ance of the head-disk interface and for the protection of magnetic layer.
`The disk must rotate underneath a flying head at a very high speed (>5000
`RPM), with a fly height as small as ~1.5 pin. (~38 nm). The fly height is
`the distance between the head air bearing surface to the disk top surface,
`while the magnetic spacing is the distance between head pole tips and the
`magnetic layer. The fly height is only a fraction of the magnetic spacing,
`and the latter is most relevant in the write and read processes. The non-
`magnetic layers in thin film disks are treated just like air when calculating
`magnetic fields.
`
`2.3.1 Magnetic fields of step transition
`
`Magnetic field of magnetized recording medium is produced by bound
`currents (in current picture), or equivalently by magnetic charges (in
`charge picture) within the magnetic medium. The latter picture is often
`more convenient and is thus widely used. In this case, the magnetic field
`can be computed from the volume charges inside the medium and the
`surface charges at the interfaces (Chapter 1):
`
`—>
`
`fie’) = ~f7—rm<v -zT4<'r">> il3¥d87'
`
`7? __ 7Il3
`‘*2!
`
`'1’
`
`(1.19)
`
`+ Z1;[j<a -z2<r'>>W _ W
`
`’ " ’ —d2?'.
`
`A magnetic medium typically extends infinitely along the x~axis and
`has a finite thickness. Similar to the case of recording heads, the z direction
`(across track) can often be assumed to be uniform, and the problem can
`be simplified into a 2D geometry in the x—y plane.
`Consider a single, perfectly sharp step transition written on a magnetic
`medium:
`
`M(x) = {
`
`“M,
`M,
`
`for
`for
`
`x < O,
`x > 0.
`
`(223)
`
`Then there i.s a surface charge density of am == ~2M,, at the transition
`center at = 0 extending from -— 6/2 < y < 6/2, where 6 is the magnetic
`
`M,.new
`
`TDK Corporation Exhibit 1007 Page 19
`
`

`
`44
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`medium thickness, M, is the remanence magnetization of the magnetic
`medium, and the center plane of the magnetic medium is y = 0. (Note
`that the y-origin is different from that in Section 2.2.) Using the second
`term of Equation (1.19), we can easily show that the horizontal and vertical
`magnetic fields produced by the transition are
`
`77
`
`x
`
`x
`
`Hx(x, y) 2 — M—’[tan‘"‘1<y—:-Q/-2)~tan‘”'1<-3-:-élgfl ,
`
`I-Iy(x,_1/) = —-2-;_ I1[————~—-————————(Z_6/2)2 +
`
`M,
`
`( + 6/2)2 + 2
`
`(2.24)
`
`These equations should be valid both inside and outside the magnetic
`layer. The magnetic field of a unit charge step transition at x = 0 is
`
`277'
`
`JC
`
`___ _L[tan—1(y + 5/2)_ tan—1<y ~
`H;;step(xl
`__1_
`(3/+6/2)2+x2]
`use
`
`Hy t P(x, y) — 47rln[—-—————————-—~(y_ 5/2? + X2
`.
`
`x
`
`,
`
`2.3.2 Magnetic fields of finite transition
`
`If a magnetic transition is not sharp, then the field patterns produced are
`broadened compared with the sing1e—step transition. Assuming that the
`finite transition does not change shape in the y and z direction, then the
`magnetic charge at each location x’ is equivalent to a step transition with
`a surface charge density of -6M(x')/ax’. The magnetic field at x produced
`by such a step transition (located at x = x’) is
`
`Hitemx _ xny) = —6My(3QI)/33Cr[tan/1<y + 542) _tan_ (
`Hgtepoc _ xgy) : —aM,(aC,)/a:¢.m[(y + 5/2)2 + (x ~ xr)2] .
`
`27r
`
`477'
`
`x — x
`
`(y — 6/2)2 + (x — x’)2
`
`Based on the principle of superposition, the net magnetic field produced
`by a finite transition is the integration of the fields due to all the step
`transition distributed from ~00 to +00:
`
`Hx ory(x’
`
`; foo dxlliitggi/(x ‘xi’
`
`: H
`
`aM(x)
`ax
`
`*H;;sg;g(x, y).
`
`(2.27)
`
`TDK Corporation Exhibit 1007 Page 20
`
`

`
`2.3 MAGNETIC RECORDING MEDIUM
`
`45
`
`That is to say, the magnetic field of a finite transition is the convolution of the
`longitudinal gradient of the magnetization and the magnetic field ofa unit charge
`step transition. We must know the shape of the magnetization transition
`to calculate its magnetic field.
`A real magnetization transition in magnetic media can be modeled
`by an analytical function such as arctangent function, hyperbolic tangent
`function, and error function, of which the arctangent function is the most
`convenient.5 In this case, a magnetic transition centered at x = 0 can be
`modeled as
`
`M(x) = —2M;rtan~1<§>,
`
`(2.28)
`
`where a is the transition parameter. The bigger it is, the Wider the transi-
`tion. If a = 0, the transition is an ideal sharp step transition. Both the step
`transition and arctangent transition are shown in Fig. 2.6.
`The longitudinal gradient of the arctangent transition is
`
`a
`6M(x) ___ _2£VI_t
`6x
`7r x2 + a2’
`
`M(x)
`IIIIIIIIIIIIIIIIII
`
`--u------nu-nu--n
`
`FIGURE 2.6. Step (dashed) and arctangent (solid) transitions of magnetization.
`
`TDK Corporation Exhibit 1007 Page 21
`
`

`
`46
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`so the magnetic fields of a finite transition can now be expressed by the
`following convolution [Equation (2.27)]:
`
`2M,a
`Hxory(xIl/) : “ 77, x2 + '12 *H:%s*;<x, y>.
`
`Now the magnetic fields can be solved analytical1y.6 Inside the medium
`(M S 6/2),
`
`Hx(x,y) = —%[tan"1< )+ tan“1<a—————-——y + 6/2)-2tan“1<
`
`77’
`
`X
`
`X
`
`
`M,1n[(a — y + a/2)2 + x2
`
`27r
`
`(a+y+8/2)2+x2'
`
`Outside the medium (M 2 6/2),
`
`H (x y) 2 MA/&[.an~—1<a_:lrl~:<1/2>_tan—1<e_tl3zl:i/2)]
`Hy(x,y) = :5;ln[
`(Q +|}/1+ 6/2)2 + X2] (+ fory>a/2, ~fory< —6/2).
`
`DC
`
`)6
`
`(2.31)
`
`(a + ]y| -8/2)2 + x2
`
`W"
`M
`
`Note that Equations (2.30) and (2.31) become the same as those of the
`step transition [Equation (2.24)] if a = 0. Furthermore, all the fields exterior
`to the medium are identical to those from the step transition when y is replaced
`by y i a (plus for y > 0, minus for y < 0), as if the field were produced by a
`step transition displaced further by a distance of the transition parameter.
`The x—component of magnetic field along the medium centerline, with
`an arctangent magnetization transition and the medium thickness 6 = a
`or 2a, are shown in Fig. 2.7a. The magnetic fields inside the medium are
`always opposite in direction to the magnetization as they should. The
`demagnetizing field diminishes at the center of the transition (x = 0) or
`far away. (The perpendicular demagnetizing field at y = 0 is zero because
`of symmetry.) The x— and y—component of magnetic field above the mag-
`netic medium is shown in Fig. 2.7b. This field is the field detected by the
`magnetic read head.
`
`TDK Corporation Exhibit 1007 Page 22
`
`

`
`2.3 MAGNETIC RECORDING MEDIUM
`
`PN
`
`.0EV-‘U1
`
`
`
`
`
`LongitudinalDemagnetizingFieldH,flVI,
`
`E ‘
`
`5 gE
`
`‘
`E0)
`‘LE01)
`
`_J.
`
`402
`
`Downtrack Position x/a
`
`a‘
`
`E:1
`2%“
`§Cl
`
`FIGURE 2.7. Longitudinal demagnetizing field (a) eilong the centerline in the
`medium (y = 0), (b) above the medium (y = 5/2 + d, 111 ~ 6 ~ a).
`
`TDK Corporation Exhibit 1007 Page 23
`
`

`
`48
`
`CHAPTER 2
`
`Inductive Recording Head and Magnetic Medium
`
`References
`1. R. A. Witte, Spectrum and Network Measurements, (Engelwood Cliffs, NJ: Prentice
`Hall, 1991). H. N. Bertram, Theory of Magnetic Recording, (Cambridge, UK:
`Cambridge University Press, 1994, pp. 3846).
`. R. M. White, Introduction to Magnetic Recording, (New York, NY: IEEE Press,
`1985, Chapter 3).
`
`. O. Karlqvist, ‘Calculation of the magnetic field in the ferromagnetic layer of
`a magnetic drum,” Trans. Roy. Inst. Technol. Stockholm, vol. 86, p. 3, 1954.
`. W. K. Westmijze, ”Studies on magnetic recording,” Philips Res. Rep, Part II,
`8(3), 161, 1953.
`
`. H. N. Bertram, Theory of Magnetic Recording, (Cambridge, UK: Cambridge Uni~
`versity Press, 1994, Chapter 4).
`
`. R. I. Potter, ”Analysis of saturation magnetic recording based on arctangent
`magnetization transitions,” I. Appl. Phys, 4(4), 1647, 1970.
`
`TDK Corporation Exhibit 1007 Page 24
`
`

`
`CHAPTER 3
`
`Read Process in Magnetic
`Recording
`
`Important aspects of the readback process in magnetic recording will be
`studied in this chapter. We will first discuss the reciprocity principle for
`calculating readback signal, then derive the readback voltage pulses of
`various types of magnetic transitions. The chapter ends with the discus-
`sion of linear superposition of multiple transitions and spectrum analysis
`of readback signals.
`When a magnetic recording medium with written magnetic transitions
`passes underneath an inductive recording head, the magnetic flux pro-
`duced by each transition is picked up by the head. The variation of the
`magnetic flux produces an ”induced” voltage in the head coil, i.e., a
`readback signal. Therefore, the readback signal can be calculated from
`Faraday’s law. However, the magnetic flux actually going through the
`head coil is very difficult to calculate directly. Instead of using the cumber-
`some direct method, a powerful theorem called reciprocity principle, com~
`monly used to calculate the magnetic flux through the head coil, will be
`introduced first.
`
`3.1 RECIPROCITY PRINCIPLE
`
`The reciprocity principle is based on the fact that the mutual inductance
`between any two objects #1 and #2 is one quantity and the same: Mn =-
`M21. Consider the two objects to be a recording head and a magnetic
`element of recording medium located at (x, y, Z) with a volume of dxdydz,
`as shown in Fig. 3.1, where d is the magnetic spacing between the head
`pole tips and the top of magnetic recording layer. Assume that the magne-
`tization in the medium is horizontal along the x-axis, then we only need
`to consider the longitudinal component of the magnetic field. This is often
`called longitudinal recording as opposed to perpendicular recording in which
`
`49
`
`TDK Corporation Exhibit 1007 Page 25
`
`

`
`CHAPTER 3 Read Process in Magnetic Recording
`
`FIGURE 3.1. Reciprocity between recording head and magnetic medium.
`
`the magnetization is vertical (along the y-axis). If the coil (object #1) has
`an imaginary write current 1'1, which produces a head field Hx, then the
`magnetic flux through the medium element dxdydz at location (x,y, 2)
`(object #2) due to current 1'1 is
`
`défizl = ,u,(,Hx(x, y, z)dydz.
`
`Because the equivalent surface current density is M,,(x — 7, y, z), in the
`unit of A/m, the equivalent current at the four surfaces (parallel to the
`x-axis) of the magnetic element dxdydz is
`
`1'2 = M,,(x — E, y, z)dx,
`
`where Y = vt is the moving distance of the medium relative to the head.
`Then, the magnetic flux through the head coil due to the magnetic element
`dxdydz (or equivalent current 1'2), d 4312, is related to d (D21 by the following
`relation:
`
`d4512 = 61¢;
`i2
`i1
`
`TDK Corporation Exhibit 1007 Page 26
`
`

`
`34 RECIPROCITY PRINCIPLE
`
`51
`
`The magnetic flux through the head coil due to the magnetic element
`dxdydz is then
`,
`-
`
`1
`
`MM _
`_.. .m‘°-P1x’(1_"' 3/’ Z») Mx(x 2
`
`
`
`. 1
`
`3'5, y, z)dxdydz.
`
`Therefore, the total magnetic flux through the head coil is expressed by
`head field per unit head current and the medium magnetization:
`00
`d 6
`no
`(15 = ,u0Lm dxj 14L_dy.Lwd2f Mx(x -‘Airy, 2),
`
`(3:1)
`