Read Back Signals in Magnetic Recording - Research Group Fidler

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
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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).
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