Read Back Signals in Magnetic Recording - Research Group Fidler

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H = H eff ABS sig sig λ cosh( h / λ) −1 h sinh( h/ λ) Analytical Calculations For large flux propagation lengths λ � h , which is normally the case, (3.30) simplifies to (3.30) h eff ABS λ ⎛ − ⎞ λ Hsig = Hsig⎜1−e ⎟. (3.31) h ⎝ ⎠ So the signal field roughly decreases exponentially between the shields from the ABS upwards. 40
4 Numerical MethodsEquation Numerical Methods Section (Next) Micromagnetic simulations require a discrete representation of the continuous magnetization distribution on a computer. Due to the strong ferromagnetic coupling the magnetization does not vary rapidly over short distances. So the discretization size can be much larger than the atomic lattice constant. Usual lengths of significant magnetization changes (widths of domain walls) are in the order of some nanometers for hard magnetic materials, for soft magnetic materials even one or two orders of magnitude larger. To keep numerical errors small, the discretization size should be smaller than the domain wall widths. Dynamic micromagnetic calculations require two major tasks. The first part is to calculate the stray field. For this purpose a partial differential equation (PDE) of the form Lu [ ( r)] = s( r ) (4.1) has to be solved. Here L denotes the differential operator, s is called source term and u is the unknown function, which fulfills this PDE. For stray field calculations u represents the magnetic potential. We also have to solve an equation of type (4.1) for the electric potential of an inhomogeneous conductor (see (2.31)). For this purpose the Finite Element Method is used. As second task we have solve an initial-value problem (IVP) of the form: y� = f(, t y), y( t ) = y . (4.2) 0 0 In case of the LLG equation y represents the magnetization. Therefore y 0 would be the initial magnetization. Here the time has to be discretized. We use a time integration routine, which automatically adapts the time steps. So for fast physical processes a smaller time step is chosen to increase accuracy. 41
Page 1 and 2: DIPLOMARBEIT Read Back Signals in M
Page 3 and 4: Abstract This thesis concentrates o
Page 5 and 6: Contents 3.2.4 Signal of Written Bi
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: z Analytical Calculations Figure 3.
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
Page 73 and 74: 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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