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Submitted on 1 Jan 1988
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THE STUDY OF RECORDING SIMULATION USING
EXACT FIELDS
Jyh Yang, Huei Huang
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Suppl6ment au no 12, Tome 49, dhcembre 1988
THE STUDY O F RECORDING SIMULATION USING EXACT FIELDS1
Jyh Shinn Yang and Huei Li Huang
Department of Physics, National Taiwan University, Taipei, Taiwan, ROC
Abstract. - The exact head field and image field are used to study the recording behaviors of ring and thin film head. We find that: (1) for ring head, the readback voltage is smaller than that from using Karlqvist's head approximation.
(2) For thin film head, the image field in writing process cannot be neglected.
Introduction
Conformal mapping was used by many to get head field for the two-dimensional recording head, but fre- quently in an implicit form. For examples, Curland and Judy [I] used Karlqvist's potential values as its initial value for Newton iteration to obtain the head field values. In order t o investigate the image effect of the head gap and pole as fast as possible, Lindholm [2] replaced ring head with a slotted plane and, thin film head with a superposition of component heads to avoid the troublesome root-finding problem.
In this paper we derive the mapping function that maps the entire upper edge of the recording head in the z plane onto the real axis of complex't plane. Using the slotted-plane mapping function as the initial value for Newton iteration, we obtain the inverse mapping function t (z)
.
The latter can be used t o calculate the head field and the image field to simulate the behaviors of the recording system. Hysteresis loop, both major and minor, were generated by extending Nishimoto's interpolation methods [3]. The details are described as follows.Exact head field, image field and hysteresis loop
Schwarz-Christoffel transformation is used to map the upper edge of ideal ring and thin film heads in the z plane onto the real <-axis of the t plane [4]. In the z plane the potential is Vo and -Vo a t the left and right head pole, resp
...
The potential along the <-axis is Vo forE
<
0 and -VO for<
>
0. Therefore, the head field in the uppert
plane iswhere g is the gap length, Ho is the deep gap field and z (t) is the corresponding mapping function [4].
The demagnetization field from magnetization in the recording media in the presence of head is
where K, is the kernel function of the head-media sys- tem and implicit in z and z'. Thus, once t (z) is found,
'supported in part by the National Science Council.
the total field is readily obtainable. The method t o solve for t (z) has been reported elsewhere 141 in which good convergence was achieved within 3-5 iterations using the slotted-plane mapping function as an initial value for t (z) in Newton iteration.
As for all orders of minor loops, Nishimoto's interpo- lation method [3] was extended, given the major loop value. In the method the major loop may be repre- sented by either experimental data or Preisach's model or an analytic formula. The analytic formula for major loop may be hyperbolic tangent, i.e.
M (H, sn) =
M,
tanh tanh-IS) (3) where S, H,, M, and sn (= & l ) is the squareness, the coercive force, the saturation magnetization and thesign of field variation, resp ... For the first-order minor loop, we define the interpolation formula as
M (H, f 2) - M (H, ~ 1 ) - M I - M (H, 7 1 ) M (H,
f
1) - M (H, ~ 1 )-
M (HI,f
1) - M (H, TI)( A ) \^I
where the integers 1 and 2 represent the major loop and first-order minor loop, resp. and ( H I , MI) is the turning point on the major loop. For the second- and higher-order minor loops, we resort t o the formula de- veloped in [3]. It is interesting that the loops become identical t o that developed by Potter [5] when we re- place M (H, ~ 1 ) in (4) with snM,.
Recording simulation and results
Assume that the track width W (media thickness 6) is much larger (smaller) than the gap length g and the magnetization in media is confined in the downtrack direction (2). The governing equations are
M (z) = F (H: (z)
,
history) ( 6 ) where z = z+
iy, y is the distance from the media center t o head pole. The difficulty in computing the integral in (5) is that K, is implicit in z and z' and the divergence occurs whenx' -+
x
or z' -+ z. To solve the problem we rewrite Ke as K, = KO+
(K, - KO) whereC8 - 2020 JOURNAL DE PHYSIQUE
KO is the kernel function of the simple plane and its order of pole a t
z'
= z is the same as that of K,. So, we see easily that K, - KO is a smooth function of z and z'. To solve (5) and (6) simultaneously, we use sell- consistently iterative method 161. The time-dependent deep-gap field depends on the input current waveform and properties of head pole. We assume that Ho (x) is in exponential form,Ho (3) = (Hi
-
snH,) exp[-
(3 - 5%)+
snHm,Ii
5
Z5 3i+1 (7)
where hi is the deep-gap field a t head positionI;
a t which the current switches, s n (=f
1) is the sign of the current variation, H, is the corresponding maximum deep-gap field, andP
is the response parameter of the head pole. Now t o calculate the readback voltage, the well-known reciprocity theorem is used. We find that the magnetization pattern after the writing head is far removed and the remagnetization pattern at the instant when the playback head approaches seem to differ very little and give nearly the same readback voltages.The thin film media having H, = 7 000 Oe, M, =
800 emu/cc, S = 0.85,
S
= 0; 05 pm and the tribit cur- rent waveform with H,,, = 4 000 Oe and /3 = 0.5 pm which switches a t Zi = -2, 0,2 pm are used to simu- late the performance. Figure 1 shows the simulation results for ring head with g = 0.9 and d = 0.1 pm in which the solid line stands for using the exact field and the dotted line using the conventional Kralqvist's head (Karlqvist head field+
ungapped image). The magne- tization patterns due to both methods differ very little from each other even a t such low spacing. However, the readback voltage due to the exact field is smaller than that due t o the Karlqvist's head (also shown in Tab. I). Comparison of the dibit and tribit magnetiza- tion patterns obtained by using exact(solid), simple- plane (dashed) and free-space image(dotted), resp. for thin film heads with g = 0.9, p = 2.0 and d = 2.0 pm is shown in figure 2. The image field due t o head pole plays different role in writing process. For ditbit and tribit it is close t o that obtained for the simple-plane and free-space, resp. This can be resulted from the total magnetic image charges induced on the outside face of the left pole. As t o the characteristic bump be- fore the first transition, this is explained as due to the negative stray field of the thin film head beyond theTable I. - Comparison of ring head readout peak volt- ages from arctangent transition ( a = 0.2 g ) at several spacings (d). d l 9 0.4 0.3 0.2 0.1 0.05 0.01 exact 0.847 0.951 1.07 1.21 1.29 1.34 karlqvist 0.877 0.994 1.14 1.31 1.41 1.49 error (%) 3.5 4.5 6.5 8.3 9.3 11
+\\-;lfl
E+5
0 L -== Z 0.-..
r- -i LI D x ? A m 0 t-- &.r" m 'I-
o X O R X - : NFig. 1. - Ring head tribit magnetization pattern and read- back voltage. Solid: exact field, dotted: Karlqvist's head.
Fig. 2. - Thin film head dibit and tribit magnetization pat- terns. Solid: exact, dotted: free-space, and dashed: simple- plane image.
pole piece, since the bump is reduced with increasing spacing or pole-length.
Conclusion
A numerical method to solve the implicit tranforms for ring and symmetric thin film head is presented. Simulation study suggests that: (1) for ring head, the Karlqvist's head is a reasonable approximation in writ- ing process. However, it yields larger readback signals than the present method. (2) For thin film head, the neglect of the image field due t o head pole in writing process may result in appreciable error.
[I] Curland, N. and Judy, J., I E E E Trans. Magn.
MAG-22 (1986) 1901.
[2] Lindholm, D. A., IEEE Trans. Magn. MAG-13 (1977) 1463.
[3] Nishimoto, K., et a/., IEEE Trans. Magn. MAG-
10 (1974) 769.
[4] Yang, J. S. and Huang, H. L., Submitted to I E E E Trans. Magn.
[5] Potter, R. I., I E E E Trans. Magn. MAG-7 (1971) 873.
[6] Iwasaki, S. and Suzuki, T., I E E E Trans. Magn.
