Read Back Signals in Magnetic Recording - Research Group Fidler

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Output Voltage [V] 0.1080 0.1075 0.1070 0.1065 0.1060 0.1055 0.1050 FEM Simulations Figure 6.11: The model of a perfect bit pattern. It consists of 30 perfectly written bits and is used for our read back signal calculations. The track width is 120 nm and the bit length 60 nm. The layer thickness is 12 nm and the spontaneous polarization is 0.44 T. The bits are alternately magnetized in positive and negative x-direction. 0.1045 0 100 200 300 400 x [nm] ΔR/R [%] 1.0 0.5 0.0 -0.5 -1.0 -1.5 0 100 200 300 400 without shields with shields x [nm] Figure 6.12: The read back signal for the periodic bit pattern calculated for the GMR sensor and for the whole read head (with shields). 76
7 OutlookEquation Section (Next) Outlook This work was a first step to take arbitrary current distributions into account in micromagnetic simulations. The program solves the LLG equation and simultaneously calculates the current distribution, which can be influenced by the magnetization. So it can be used for read back signal calculations. Of course it is also possible to calculate the read back signal of perpendicular recording layers. Here the additional SUL has to be taken into account. Spin valves with synthetic antiferromagnet can also be calculated, if the interlayer exchange coupling is introduced. Possible enhancements of this program are the consideration of eddy currents [41] [42] or finite temperatures. To take fluctuations at finite temperatures into account, a stochastic, thermal field H th is added to the effective field in the LLG equation [38] ∂J α ∂J =−γ J× ( Heff + Hth) + J × . (7.1) ∂t J ∂t s Future hard disks will make use of spin valves operating in CPP mode. Therefore simulations of CPP spin valves become more and more interesting. A current perpendicular to the layer structure leads to spin transfer, which has to be taken into account by an additional term, called spin torque term [39] ∂J α ∂J Cj =−γ J× H ′ eff + J× + J× J × J. (7.2) ∂t J ∂t J J′ 2 s s s Here J ′ is the magnetization of a reference layer, which polarizes the electrons. The polarized current transfers the spin to the actual magnetic polarization J and causes an additional motion of J. j is the local current density. For CPP spin valves the magnetization is transferred from the pinned layer to the free layer or vice versa. The application of this program is not restricted to read head simulations. It can also be applied, for example, on magnetic tunnel junctions (MTJs), which are used in MRAMs (Magnetic Random Access Memory). 77
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DIPLOMARBEIT Read Back Signals in M
Page 3 and 4:
Abstract This thesis concentrates o
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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
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2 BasicsEquation Section (Next) 2.1
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Basics curl H = 0 . (2.15) So H is
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Basics This is justified, because t
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Basics Here J ij represents the exc
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s Basics ∂J α ∂J =−γ J× He
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Basics for spin down electrons. An
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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: Output Voltage [V] 0.1074 0.1072 0.
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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