Read Back Signals in Magnetic Recording - Research Group Fidler

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a) Heff J −J x Jx Heff −J x Heff b) Basics Figure 2.1: a) Illustration of the damped precession of the magnetic polarization J around the effective field Heff, taken from [15]. b) Influence of the Gilbert damping constant on the field rise time in magnetic read heads. Head field strength as a function of time for different Gilbert damping constants within the head [43]. The dashed line depicts the current profile. The solid lines give the head field for α = 1, 0.5, 0.1, and 0.02. The fastest field rise time is achieved with intermediate damping (α = 0.5). 2.8 Magnetoresistance 2.8.1 Magnetoresistance of Ferromagnets A change in resistance of a material under an applied field is known as magnetoresistance. This effect was first discovered in 1856 by Lord Kelvin who was examining the resistance of an iron sample. He found a 0.2% increase of resistance when he applied a field in longitudinal direction, and a 0.4% decrease for the transversal direction. Thus, a positive and a negative change of resistance is possible, although intuitively one expects only positive magnetoresistance, because electrons are forced to take longer paths due to the magnetic field, which leads to more scattering. Nevertheless negative magnetoresistance occurs, which has to be explained in a different way. Mott [16] [17] could give a first explanation for this behavior. Figure 2.2 shows the typical band configuration of a transition metal. The bands are spontaneously split without external field. This phenomenon is also called band ferromagnetism. Scattering of electrons from the s- to the d-bands occurs only, if there are any unoccupied states available. Figure 2.2 shows the electron configuration at low temperatures. Here the spin up d-band is fully occupied. Thus scattering can only occur 20
Basics for spin down electrons. An applied magnetic field may increase the spin polarization and allows fewer s to d transitions, resulting in lower resistance. Figure 2.2: The spin-split bands of a ferromagnet [18]. 2.8.2 Anisotropic Magnetoresistance Effect The resistance of several ferromagnetic materials shows a dependence on the angle between magnetization and current. This effect is known as anisotropic magnetoresistance (AMR). Its origin is connected with the spin-orbit interaction and its influence on s-d scattering. This phenomenon can be described by assuming different resistivities for currents parallel and perpendicular to the magnetic field and leads to following relation: 0 2 ( 1 RAMR cos ) ρ=ρ + ⋅ θ . (2.50) Here θ is the angle between the current and the magnetization, and R AMR is the magnetoresistance ratio. Typical values of R AMR are about 2%. The concept of using the AMR effect for reading heads was first proposed by Hunt in 1971 [5]. AMR read heads were used from 1992 to 1998 in commercial hard disks. Their advantage was the much higher signal amplitude for smaller bits (higher data densities) compared to inductive read heads. Additionally magnetoresistive heads have reduced noise and inductance, and the output voltage is not dependent on the relative velocity of the head and the data layer. 21
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: s Basics ∂J α ∂J =−γ J× He
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
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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