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Read Back Signals in Magnetic Recording - Research Group Fidler

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Analytical Calculations<br />

t<br />

C<br />

8<br />

π<br />

= . (3.15)<br />

Insert<strong>in</strong>g <strong>in</strong> (3.11) leads to the f<strong>in</strong>al result for the head field<br />

⎛γ x( x + gz , ) −γx( xz , ) −γx( − x+ gz , ) +γx( −xz<br />

, ) ⎞<br />

MSL t ⎜ ⎟<br />

H H ( xz , ) = ⋅ 0<br />

8 g ⎜ ⎟<br />

. (3.16)<br />

⎜γ z( x + gz , ) −γ z( xz , ) +γz( − x+ gz , ) −γz( −xz<br />

, ) ⎟<br />

⎝ ⎠<br />

Now a normalized head field H H can be <strong>in</strong>troduced, which is <strong>in</strong>dependent from the sensor<br />

magnetization<br />

H<br />

n<br />

H<br />

⎛γ x( x + gz , ) −γ x( xz , ) −γ x( − x+ gz , ) + γ x(<br />

−xz<br />

, ) ⎞<br />

t ⎜ ⎟<br />

( xz , ) = ⋅ 0<br />

8 g ⎜ ⎟<br />

. (3.17)<br />

⎜<br />

z( x + gz , ) − z( xz , ) + z( − x+ gz , ) − z(<br />

−xz<br />

, ) ⎟<br />

⎝γ γ γ γ ⎠<br />

Figure 3.3 shows the normalized head field at z = − 10 nm and for t = 5 nm and g = 27.5 nm ,<br />

so that the total gap is 60 nm. For longitud<strong>in</strong>al record<strong>in</strong>g only the x-component contributes,<br />

because the magnetization po<strong>in</strong>ts ma<strong>in</strong>ly <strong>in</strong> this direction.<br />

H x<br />

0.06<br />

0.04<br />

0.02<br />

0.00<br />

-0.02<br />

-0.04<br />

-0.06<br />

-100 -50 0 50 100<br />

x [nm]<br />

H z<br />

-0.02<br />

-100 -50 0 50 100<br />

x [nm]<br />

Figure 3.3: The x- and the z-component of the normalized head field of a read head with<br />

60 nm gap, and sens<strong>in</strong>g layer thickness 5 nm, 10 nm below the ABS.<br />

0.06<br />

0.05<br />

0.04<br />

0.03<br />

0.02<br />

0.01<br />

0.00<br />

-0.01<br />

33

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