Read Back Signals in Magnetic Recording - Research Group Fidler

Analytical Calculations
3 Analytical CalculationsEquation Section (Next)
3.1 Reciprocity Principle
For any two volumina V 1 and V 2 with given magnetization the following equation is valid.
∫ ∫
Mr ( ) ⋅ H( r) dV = Mr ( ) ⋅H(
r ) dV
(3.1)
1 2 1 1 2 1 2 2
V V
1 2
Here 1 H and 2
H denote the magnetic fields caused by the magnetizations in volumes 1 and 2
respectively. This fact is called reciprocity principle, and its proof is illustrated below.
Partial integration of (3.1) and taking equations (2.16) and (2.19) into consideration lead to
�∫
∫
σ ( r) ⋅Ψ ( r) dA − ρ ( r) ⋅Ψ ( r)
dV =
m 1 2 1 1 m 1 2 1 1
∂V1
V1
�∫
∫
σ ( r ) ⋅Ψ ( r ) dA − ρ ( r ) ⋅Ψ ( r ) dV .
m 2 1 2 2 m 2 1 2 2
∂V2
V2
The final substitution of both magnetic potentials using (2.22) shows equality.
3.2 Longitudinal Recording
Longitudinal recording means that the magnetization of written bits shows in track direction.
To read information it is necessary to detect the stray field of the stored bits. For longitudinal
recording the stray field reaches its maximum at the transitions, where opposite oriented
magnetizations come together.
(3.2)
Figure 3.1 shows a schematic model of a read head. In the middle of two shields there is the
sensing layer. In case of a GMR sensor this layer is equal to the free layer. The shields are
assumed to have infinite permeability and infinite extension. The plane, which contains the
bottom sides of the two shields and the sensing layer, is called air bearing surface (ABS).
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