Transcript Head

Heads II
Inductive and AMR Head
T. Stobiecki
6 wykład 8.11.2004
Write head field
Ferrite heads the core is usually made of NiZn or MnZn.
Insulators can be operated at frequency > 10MHz
Thin film heads yoke (core): permalloy (81Ni19Fe) or aluminium - iron - silicon alloy (AlFeSi) typically 2- to 4 µm thicknesses.
Write head field
H0 
0.4NI
gw
(2.1)
In high-density recording, the deep gap
field required is:
H 0  3H C
(2.2)
where HC is the coercivity of the recording
medium
where BS is the saturation flux density
of the pole of yoke material
H0  0.6BS
(2.3)
Plots of the horizontal
component Hx vs. distance x




H0
yg w
1 
 (2.4)
HX 
tan
2
gw 
 2

2
x y 

4 

Note that the trajectory closer to the head (A-B)
has both a higher maximum field and higher field
gradient dHx/dx.
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.
x
M ( x)  M Rtan   (2.5)

f
2
1
where f is so called transition slope
parameter. As f is reduced, the transition
becomes steeper. The binary ideal step
function is for f=0.
Bit size
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 Hx=Hc, 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: x  (d   / 2)
3
The maximum head field gradient:
HC
3
 dHx 
(2.6)

 
2 (d   / 2)
 dx  max
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:
 4M R
 dHd 

 
f2
 dx  max
(2.7)
The maximum gradient occurs at the center (M=0) of the transition. The smaller the value of the slope
parameter f , the higher the magnitude of the demagnetizing field and its gradient.
dM dM d H head  H demag 
(2.8)

For digital write process, the slope equation is used:
dx dH
dx
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
1
 2 HC
2
f  2
 d   / 2
 3 MR

(2.9)
Plots of magnetization, „charge”density and demagnetizing field
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:
M ( x) 
x
M Rtan1  

f
2
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.
 2 HC

f  2
 d   / 2
 3 MR


1
2
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:
M X ( x)  M R sin kx
(3.1)
Where MR is the maximum amplitude of recording medium magnetization and k is the
wavenumber (k=2/), where  is the sinusoidal wavelnegth. The horizontal and
vertical components of fringing field at point (x,y) below the medium are:
H y ( x, y)  2M R (1  e kd )e ky sin kx
H x ( x, y)  2M R (1  ekd )eky coskx
(3.2a)
(3.2b)
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:
(1  e  k )e  kd sin kg / 2
 ( x)  4M RW
sin kx (3.3)
k
kg / 2
where d is the head-to-medium spacing, g is the gap length, and W is the track
width.
Output voltage
The time rate of change of the flux, N, in a head coil with N turns is proportional to the
read-head’s output voltage, E.
E  10 8
d ( N )
d
d
 10 8 N
 10 8 NV
dt
dt
dx
(3.4)
whereV is the head-to-medium relative velocity. On putting Eq.(3.3) into Eq. (3.4), the result
is:
sin kg / 2
E ( x)  108 NVW 4M R (1  e k )e kd
cos kx (3.5)
kg / 2
Note that the output voltage is proportional to the number of coil turns N, the head-tomedium 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.
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 f=V/ 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.
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.
R  R0  R cos2  (4.1)
Magnetoresistive sensor
  sin 1 (H y / H k ) (4.2)
R  R0  R[1  (H y / H k ) 2 ] (4.3)
The value of demagnetizing field, avereged over the element depth, is
proportionat to ratio width to length (T/D).
Magnetoresistance vs. disk field
The vertical field is not sufficient to saturate MR-element, that is, My<Msat at the
middepth y=D/2, an exact analytical solution for the magnetization angle  as a
function of element depth is:

 H
( y )  tan1  bias
 2M S T

For MR-element HK<<yHD.

 D 


2
   y  
 2 
 

2
1
2
(4.4)
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.
AMR - head
U out
M x 2x /  1  e2 /  1  e2w / 
 IR

e
  y HD
2 /  2w / 
 
Areal data storage density vs. time for inductive and
MR read heads
Write/read head of HDD

