Read Back Signals in Magnetic Recording - Research Group Fidler

More documents

Recommendations

Info

Time Integration CVODE ∂J ∂t i = f ( t, J , J ,..., J ) i 1 2 N Numerical Methods START Read geometry (FE mesh) and material parameters Calculate the B matrix for the hybrid FE/BE method Set the initial magnetization t, J1, J2,..., J N f1, f2,..., f N Increase time (t) t < tfinal END Hexch + Hani + HS+ Hcurr + Hext �� H Figure 4.5: Schematic diagram of the simulation cycle. Adapted from [31]. eff LLG f1, f2,..., f N σ ( J ) Φ, j H ext () t 58
5 Read Head DesignEquation 5.1 Bias Schemes Read Head Design Section (Next) For AMR and GMR reading heads, magnetic layers with a uniform predefined magnetization direction are necessary. Besides a single domain state is desirable, to avoid Barkhausen noise due to moving domain walls. Therefore the magnetizations of these layers have to be forced into a certain direction by biasing. The most important bias schemes used in MR read heads are explained below. 5.1.1 Demagnetizing Factor The field of a magnetized body, the stray field, or also called demagnetizing field H S , acts on the magnetization itself. This field is proportional to the magnetization M and opposite directed within the body. So the demagnetizing field can be written as N =− H M (5.1) S d Here N d is the demagnetizing factor, which is generally a tensor and only depends on the shape of the body. Principal axis transformation leads to three demagnetizing factors a N , N b , N c for each axis one respectively. For their sum Na + Nb + Nc = 1 (5.2) always holds. The longest axis corresponds to the smallest demagnetizing factor. It is also the preferred direction for the magnetization, because then the stray field energy has its minimum (see (2.37)). A GMR element basically exists of two ferromagnetic layers, which should be magnetized perpendicular in respect to each other in ground state. Moreover the free layer should be able to rotate freely. Therefore the shape of these layers has to be almost quadratic (with an aspect ratio close to 1) in order not to discriminate a magnetization direction. 59
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 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: 4.5 Time integration Numerical Meth
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
show all

Read Back Signals in Magnetic Recording - Research Group Fidler

Create successful ePaper yourself

Delete template?

Save as template?