Read Back Signals in Magnetic Recording - Research Group Fidler

More documents

Recommendations

Info

Basics 2 2 2 2 2 2 2 2 2 ( ) ( ) f ( α , α , α ) = K + K α α +α α +α α + K α α α + ... . (2.44) ani 1 2 3 0 1 1 2 2 3 3 1 2 1 2 3 α 1 , 2 α , and α 3 denote the direction cosines of the cubic lattice vectors to the direction of the magnetic polarization J. In both cases the first term K 0 can be neglected, because it does not depend on angle and is therefore a constant term. 2.6 Effective Field The effective magnetic field H eff which acts on the magnetization can be calculated by the variation of Gibbs’ Free Energy. δE 2A δfani ( J) H =− = ΔJ− + H + H + H eff 2 S ext curr δJ J s δJ (2.45) Here the first term corresponds to the exchange field H exch , and the second one to the anisotropy field H ani . The additional contribution H curr is the field due to currents. In fact this field is a contribution to the external field H ext , but here it is written separately, because from now on ext H is used to describe homogeneous fields, whereas H curr are fields due to currents, and can be calculated using the Biot-Savart Law 1 r−r′ Hcurr () r = × 4π ∫ j r−r′ V 3 dV ′ , (2.46) which was empirically found by Jean Baptiste Biot and Félix Savart in 1820. 2.7 Landau-Lifshitz-Gilbert Equation To find out the equilibrium state of a magnetic system equation (2.35) can be used. To get information about the magnetization dynamics, i.e. about the dynamic behavior of the magnetic polarization J, it is necessary to apply a full 3-dimensional treatment of the time evolution of the magnetic polarization, which is described by the Gilbert equation of motion 18
s Basics ∂J α ∂J =−γ J× Heff + J × . (2.47) ∂t J ∂t This equation is mathematically equivalent to the Landau-Lifshitz-Gilbert equation (LLG) ∂Jγ γ α =− J× Heff − J× ( J× H eff ) . (2.48) ∂ t +α J +α 2 2 ( 1 ) s ( 1 ) Here J s is the spontaneous polarization and γ is the gyromagnetic ratio 5 γ= 2.210175× 10 m/As . The first term in this equation describes the precessional movement of the magnetic polarization vector J around the effective field H eff . The second phenomenological term stands for the energy dissipation during the movement and causes a movement towards the direction of the effective field. The motion of the magnetization is visualized in Figure 2.1a. The strength of the damping is characterized by the dimensionless Gilbert damping constant α . Large α means strong damping. There are many processes which contribute to the damping in magnetic solids, for example magnon-magnon, magnon- phonon interactions, or eddy currents. So the damping constant is an intrinsic property of matter and can also be varied in practice, for instance by doping [14]. In general, except for thin layers (see Section 6.2.4), high damping constants lead to coherent motion of the magnetization and therefore to faster reversal processes. Figure 2.1b shows the field of a simulated write head as function of time for different Gilbert damping constants. It can be seen that for damping constants of about 0.5 the fastest switching time is achieved [43]. ∂ J In equilibrium, thus if = 0 , equation (2.47) simplifies to ∂t J× H eff = 0, (2.49) which means that in equilibrium the magnetic polarization J is aligned either parallel or antiparallel to the effective field H eff . The unrealistic case of antiparallel alignment is irrelevant, because this solution is not stable, and in this case small deviations lead to a movement in direction of the effective field due to the damping term in (2.48) (see also Figure 2.1a). 19
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: Basics Here J ij represents the exc
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
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?