Read Back Signals in Magnetic Recording - Research Group Fidler

Basics
This is justified, because the sense current through MR sensors is normally held constant and
the current density is quite large for the small dimensions of a MR reading head. (The current
density is only limited due to the heat dissipation. Typical values for the critical current
density are 10 7 -10 8 A/cm 2 .) So local charge concentrations are immediately compensated.
Applying the divergence operator on both sides of equation (2.29) gives
div j = 0 . (2.30)
Thus the source term of the continuum equation (2.14) vanishes. Combining (2.2), (2.28), and
(2.30) leads to a generalized form of Laplace equation
div( σgrad Φ ) = 0.
(2.31)
If the electric potential is known, it is possible to evaluate the current density using
j =−σgrad Φ.
(2.32)
2.5 Gibbs’ Free Energy
The equilibrium state of an isothermal and isobaric thermodynamic system is characterized by
the minimum of its Gibbs’ free energy E.
∫
E = F − J⋅H dV
(2.33)
ext
F = U −T⋅ S+ p⋅ V is the free energy, where U is the inner energy, T the absolute
temperature, S the entropy, and V the volume of the magnetic system. For constant
temperatures and neglected magnetostrictive effects, which means keeping the volume and
the temperature constant, the free energy is reduced to U. The inner energy U can be
calculated as the sum of the stray field energy E S , the exchange energy E exch , and the
magnetocrystalline anisotropy energy E ani , so the total Gibbs’ free energy can be written as
E = ES+ Eexch + Eani+ EH.
(2.34)
Here E H is the magnetostatic energy and arises from the external field H ext . The equilibrium
state of such a magnetic system is determined by
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