Heads II Inductive and AMR Head

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Heads IIInductive and AMR Head

• T. Stobiecki

6 wyklad 8.11.2004
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Write head field
Ferrite heads the core is usually made of NiZn or
MnZn. Insulators can be operated at frequency gt
10MHz Thin film heads yoke (core) permalloy
(81Ni19Fe) or aluminium - iron - silicon - alloy
(AlFeSi) typically 2- to 4 µm thicknesses.
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Write head field
(2.1)
In high-density recording, the deep gap field
required is
(2.2)
where HC is the coercivity of the recording medium
where BS is the saturation flux density of the
pole of yoke material
(2.3)
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Plots of the horizontal component Hx vs. distance
x
(2.4)
Note that the trajectory closer to the head (A-B)
has both a higher maximum field and higher field
gradient dHx/dx.
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Written magnetization transition

• When the written current is held constant, the
  magnetization written in the recording medium is
  at one of the remanent levels MR. When the write
  current is suddenly changed from one polarity to
  the other, the written magnetization undergoes a
  transition from one polarity of remanent
  magnetization to the other.

(2.5)
where f is so called transition slope parameter.
As f is reduced, the transition becomes steeper.
The binary ideal step function is for f0.
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Bit size
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Written magnetization transition
The write current is adjusted so that horizontal
component of Hx on the midplane of the recording
meets a specific criterion. This criterion, is
that the horizontal position, where the field
HxHc, must coincidence with the position where
the head field gradient, dHx/dx, is greatest.
Meeting this criterion sets both the magnitude of
the write current Iw and the x position of the
center of the magnetization transition The
maximum head field gradient
(2.6)
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Written magnetization transition
Note that because the magnetization increases
through transition, the pole density is negative
(south polarity). The maximum (slope) gradient of
the demagnetizing field is
(2.7)
The maximum gradient occurs at the center (M0)
of the transition. The smaller the value of the
slope parameter f , the higher the magnitude of
the demagnetizing field and its gradient. For
digital write process, the slope equation is
used For a square loop recording medium, dM/dH
is very high, and a convinient approximation is
to set the maximum head field gradient equal to
the maximum demagnetizing field gradient. Upon
setting Eqs.(2.6) and (2.7) equal, the results is
(2.8)
(2.9)
Plots of magnetization, chargedensity and
demagnetizing field
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Written magnetization transition
The writting problem is now completly solved
because f is but the single parameter required to
define fully the magnetization transition of
equation
Possible ways to reduce the transition width, by
reducing f, are to use higher coercivities, lower
remanences, smaller flying heights, and thinner
media. With the exception of lowering the
remanence, all have been exploited in the past.
When inductive reading heads are used, reducing
the remanent magnetization is not an acceptable
strategy, however, because it always reduces the
signal and signal-noise ratio of the
recorder. Equation for transition slope parameter
f is also used in the simplified design of the
shielded magnetoresistive head.
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Recording medium, fringing fields
The written magnetization waveform is indicated
as dashed line . The magnetic field and flux
fringes equally above and below the medium,
flowing from the north to the south poles.
Suppose the written magnetization
waveform Where MR is the maximum amplitude of
recording medium magnetization and k is the
wavenumber (k2?/??), where ? is the sinusoidal
wavelnegth. The horizontal and vertical
components of fringing field at point (x,y) below
the medium are
(3.1)
(3.2a)
(3.2b)
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Read-head flux
The reading head has the same structure as that
writing head and the poles have high magnetic
permability (?dB/dH), most of the fringing flux
flows deep in the head passing through coil. Very
little flux flows through the air gap. The ratio
of the flux passing through the coil to the flux
entring the top surface of the head is called the
read-head efficiency. In inductive heads the
effciency ?80. The reading flux where d is the
head-to-medium spacing, g is the gap length, and
W is the track width.
(3.3)
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Output voltage
The time rate of change of the flux, N?, in a
head coil with N turns is proportional to the
read-heads output voltage, E. whereV is the
head-to-medium relative velocity. On putting
Eq.(3.3) into Eq. (3.4), the result is Note
that the output voltage is proportional to the
number of coil turns N, the head-to-medium
velocity V, and the written remanency MR.. The
term in parentheses in Eq. (3.5) is called the
thickness loss and it shows that the read head is
unable to sense the magnetization patterns
written deep int the medium. The exponential term
e-kd is called the spacing loss an it is often
quoted as 55d/? dB. The factor sinkg/2/(kg/2) is
called the gap loss. At the first gap null, at
wavelength ?g, the gap loss term is equal zero.
The fact that the output voltage waveform is a
cosine when a sine wave is written shows that the
phase of the output signal is lagging 90o behind
the written magnetization.
(3.4)
(3.5)
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Output spectrum
When the reading head passes over a written
magnetization transition, the coil flux,?(x), and
output voltage E(x).
The peak amplitude of the output voltage as a
function of frequency is called the spectrum. The
temporal frequency fV/? and the angular
frequency ?2?f . The spatial frequency or wave
number k 2?/ ? ?/V, so that ?Vk. The spatial
frequency spectrum corresponding to Eq.(3.5) is
just A(k)E(x)/coskx. Note that it has zeros at
both dc and the first gap null ? g.
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AMR- Anisotropic magnetoreistance effect
AMR effect can be described as a change of
resistance in respect to the angle ? between
sensing current and magnetization M.
(4.1)
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Magnetoresistive sensor
(4.2)
(4.3)
The value of demagnetizing field, avereged over
the element depth, is proportionat to ratio width
to length (T/D).
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Magnetoresistance vs. disk field
The vertical field is not sufficient to saturate
MR-element, that is, MyltMsat at the middepth
yD/2, an exact analytical solution for the
magnetization angle ? as a function of element
depth is
(4.4)
For MR-element HKltltyHD.
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The work point of MR output signal
The slope of this approximated characteristic is
equal to ?R/2yHbias and it represents the
sensitivity of the MR-element when vertical bias
field is used.
When the proper vertical bias field is used, the
output voltage, I?R, is large and linear.
Typically, deviations from linearity cause about
20dB of even harmonic distortion, which is
stisfactory for a binary or digital channel, is
not sufficiently linear for an analog signal
channel. If vertical biasing is not used, the
response is of low sensitivity and is highly
nonlinear.
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AMR - head
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Areal data storage density vs. time for inductive
and MR read heads
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Write/read head of HDD
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