Read Back Signals in Magnetic Recording - Research Group Fidler

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Contents Contents KURZFASSUNG................................................................................................................................................... 2 ABSTRACT........................................................................................................................................................... 3 CONTENTS........................................................................................................................................................... 4 1 INTRODUCTION ....................................................................................................................................... 7 2 BASICS....................................................................................................................................................... 11 2.1 OHM’S LAW........................................................................................................................................ 11 2.2 MAXWELL’S EQUATIONS .................................................................................................................... 11 2.3 BASIC EQUATIONS OF MAGNETOSTATICS ........................................................................................... 12 2.4 INHOMOGENEOUS CONDUCTORS......................................................................................................... 14 2.5 GIBBS’ FREE ENERGY ......................................................................................................................... 15 2.5.1 Magnetostatic Energy.................................................................................................................... 16 2.5.2 Stray Field Energy......................................................................................................................... 16 2.5.3 Exchange Energy........................................................................................................................... 16 2.5.4 Magnetocrystalline Anisotropy Energy ......................................................................................... 17 2.6 EFFECTIVE FIELD ................................................................................................................................ 18 2.7 LANDAU-LIFSHITZ-GILBERT EQUATION ............................................................................................. 18 2.8 MAGNETORESISTANCE........................................................................................................................ 20 2.8.1 Magnetoresistance of Ferromagnets............................................................................................. 20 2.8.2 Anisotropic Magnetoresistance Effect........................................................................................... 21 2.8.3 Giant Magnetoresistance Effect .................................................................................................... 22 2.8.4 Tunneling Magnetoresistive Effect ................................................................................................ 26 2.9 RECORDING SCHEMES......................................................................................................................... 26 2.9.1 Longitudinal Recording................................................................................................................. 27 2.9.2 Perpendicular Recording .............................................................................................................. 27 3 ANALYTICAL CALCULATIONS ......................................................................................................... 29 3.1 RECIPROCITY PRINCIPLE..................................................................................................................... 29 3.2 LONGITUDINAL RECORDING ............................................................................................................... 29 3.2.1 Head Field..................................................................................................................................... 30 3.2.2 Signal Field ................................................................................................................................... 34 3.2.3 Signal of a Perfect Transition........................................................................................................ 34 4
Contents 3.2.4 Signal of Written Bits..................................................................................................................... 35 3.3 PERPENDICULAR RECORDING ............................................................................................................. 36 3.4 SIGNAL FIELD IN GAP ......................................................................................................................... 38 4 NUMERICAL METHODS....................................................................................................................... 41 4.1 FINITE ELEMENT METHOD.................................................................................................................. 42 4.1.1 Dirichlet Boundary Conditions ..................................................................................................... 44 4.1.2 Neumann Boundary Conditions..................................................................................................... 44 4.1.3 Linear equation solver................................................................................................................... 45 4.2 STRAY FIELD CALCULATION............................................................................................................... 46 4.3 ADAPTIVE CROSS-APPROXIMATION TECHNIQUE ................................................................................ 48 4.4 CONDUCTOR MODEL .......................................................................................................................... 49 4.4.1 Conductivity .................................................................................................................................. 49 4.4.2 Electric Potential........................................................................................................................... 50 4.4.3 Current Distribution...................................................................................................................... 50 4.4.4 Magnetic Field of Current............................................................................................................. 51 4.4.5 Hybrid FEM/BEM for Current Field............................................................................................. 52 4.4.6 Example: Long Wire...................................................................................................................... 54 4.4.7 Example: Coil................................................................................................................................ 55 4.5 TIME INTEGRATION ............................................................................................................................. 57 5 READ HEAD DESIGN ............................................................................................................................. 59 5.1 BIAS SCHEMES.................................................................................................................................... 59 5.1.1 Demagnetizing Factor................................................................................................................... 59 5.1.2 Hard Bias ...................................................................................................................................... 60 5.1.3 Exchange Bias ............................................................................................................................... 60 5.1.4 Synthetic Antiferromagnet............................................................................................................. 61 5.1.5 Sense Current ................................................................................................................................ 62 5.1.6 Crystalline Anisotropy................................................................................................................... 64 5.2 SHIELDING .......................................................................................................................................... 64 5.3 THERMAL STABILITY .......................................................................................................................... 64 6 FEM SIMULATIONS............................................................................................................................... 65 6.1 MODEL................................................................................................................................................ 65 6.1.1 Magnetic Model............................................................................................................................. 65 6.1.2 Conductor Model........................................................................................................................... 67 6.2 RESULTS ............................................................................................................................................. 69 6.2.1 Equilibrium State........................................................................................................................... 69 6.2.2 Transfer Curve .............................................................................................................................. 70 6.2.3 Influence of Shields ....................................................................................................................... 72 5
Page 1 and 2: DIPLOMARBEIT Read Back Signals in M
Page 3: Abstract This thesis concentrates o
Page 7 and 8: Introduction 1 IntroductionEquation
Page 9 and 10: Introduction In 1955, before the RA
Page 11 and 12: 2 BasicsEquation Section (Next) 2.1
Page 13 and 14: Basics curl H = 0 . (2.15) So H is
Page 15 and 16: Basics This is justified, because t
Page 17 and 18: Basics Here J ij represents the exc
Page 19 and 20: s Basics ∂J α ∂J =−γ J× He
Page 21 and 22: Basics for spin down electrons. An
Page 23 and 24: Basics Figure 2.4: Schematic model
Page 25 and 26: Basics channels in the parallel and
Page 27 and 28: Basics Nowadays there are again eff
Page 29 and 30: Analytical Calculations 3 Analytica
Page 31 and 32: Analytical Calculations developing
Page 33 and 34: Analytical Calculations t C 8 π =
Page 35 and 36: µ 0 Hsig [T] 0.030 0.025 0.020 0.0
Page 37 and 38: Analytical Calculations n n ⎛HH,
Page 39 and 40: z Analytical Calculations Figure 3.
Page 41 and 42: 4 Numerical MethodsEquation Numeric
Page 43 and 44: Numerical Methods ϕ ( x ) =δ . (4
Page 45 and 46: Numerical Methods current flowing o
Page 47 and 48: Numerical Methods ∫ ∫ ∫ si =
Page 49 and 50: Numerical Methods Figure 4.2: The l
Page 51 and 52: Numerical Methods j =−σgrad Φ.
Page 53 and 54: Numerical Methods within the volume
Page 55 and 56:
Numerical Methods Integration of Am
Page 57 and 58:
4.5 Time integration Numerical Meth
Page 59 and 60:
5 Read Head DesignEquation 5.1 Bias
Page 61 and 62:
Read Head Design The exchange bias
Page 63 and 64:
Read Head Design free layer (see Fi
Page 65 and 66:
FEM Simulations 6 FEM SimulationsEq
Page 67 and 68:
FEM Simulations Magnetic Material J
Page 69 and 70:
6.2 Results FEM Simulations In the
Page 71 and 72:
Output [V] 0.108 0.107 0.106 0.105
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FEM Simulations has a greater influ
Page 75 and 76:
Output Voltage [V] 0.1074 0.1072 0.
Page 77 and 78:
7 OutlookEquation Section (Next) Ou
Page 79 and 80:
Appendix A In case we have the func
Page 81 and 82:
Appendix B Moreover the second inte
Page 83 and 84:
List of Figures List of Figures Fig
Page 85 and 86:
List of Figures Figure 6.1: The mag
Page 87 and 88:
Bibliography [11] H. Katayama, M. H
Page 89 and 90:
Bibliography [38] W. F. Brown Jr.,
Page 91:
Lebenslauf Otmar Ertl Reinprechtsdo
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Read Back Signals in Magnetic Recording - Research Group Fidler

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