Calculation of Dynamic Write Field for Perpendicular Recording Head Z. J. Liu1, H. H. Long2, J. T. Li1, E. P. Li3 , E. T. Ong3, and K. S. Chai1 1
Data Storage Institute, Mechatronics and Recording Channel Division, Singapore,
[email protected],
[email protected],
[email protected] 2 Hitachi Global Storage Technology Singapore, Pte. Ltd, Singapore, 417939,
[email protected] 3 Institute of High Performance Computing, Computational Electromagnetics & Electronics Division, Singapore,
[email protected],
[email protected]
Abstract-- This paper presents a dynamic magnetic field prediction for perpendicular writer heads in magnetic recording systems. The dynamic model considered the effect of time dependence and velocity of soft underlayer when compared with a static model. The effects of the spin speed of the disk platters, and rise time of the recording signals are investigated. The results showed that the write field performance is more sensitive to the spin speed than the rise time. The write field distribution in the soft underlayer is also studied with effect of various design parameters taken into consideration.
from analytical expression of the dynamic writer head model is compared with those obtained from numerical solutions. With the time dependence and the influence of the soft-magnetic underlayer taken into consideration, the model provides a promising approach to simulate the perpendicular recording write head field, which is crucial for optimal design of magnetic recording system and is helpful for the computational micromagnetic analysis of the perpendicular magnetic recording head and media combinations.
II. PREDICTION OF WRITE FIELDS I.
T
INTRODUCTION
ever increasing demand for higher capacity of data storage in modern personal computer, mobile computing devices and consumer electronics products, such as personal music players and media players continuously drives the research effort to push the boundaries of data storage technology. In this regard, the concept of perpendicular recording has received renewed attention in recent years with the hope that it is able to fulfill the market demands for ultra high density magnetic recording beyond what the longitudinal recording system can possibly achieve. [1]. However, there are new challenges related design of media, and head combinations for perpendicular recording systems. For example, one of the issues of major concern relates to high sensitivity of the signal-to-noise (SNR) to the switching field distribution (SFD) of media during the recording process [2,3]. An insight of the interdependence of recording performance on the design parameters cannot be established using an existing static model, e.g. [4]. In this paper, a dynamic magnetic write field for perpendicular recording is presented. The dynamic solution takes the effect of time dependence and velocity of recording media into consideration allowing the performance of the perpendicular recording head media combination in relation to the leading design parameters to be investigated. In addition, with the help of the dynamic model, the magnetic field and eddy current distribution in the soft underlayer are also studied. Computational results obtained HE
A dynamic solution of the write field distribution for perpendicular recording heads is developed using vector magnetic potential. This solution is an extension of a static writer head model, it is useful in the design phase for perpendicular recording systems to investigate the characteristics of the writing field versus design parameters as described in recent works[4][5].
Yoke
Coil
P1
G
P2
Air gap
g
Media SUL
Fig 1 Structure of 2-D magnetic head
The 2-D magnetic head model is schematically shown in Fig. 1 [6] and the dimensions of this model are listed in Table 1.
17th International Zurich Symposium on Electromagnetic Compatibility, 2006
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17th International Zurich Symposium on Electromagnetic Compatibility, 2006
Table I Dimension of 2-D head model
III.
Pole tip Width
0.1 µm
Return Yoke Width
2 µm
Total Head Width
4.1 µm
Pole Height
0.6 µm
Upper Yoke Height
0.4 µm
Fly Height
10 nm
Media Thickness
20 nm
SUL Thickness
50 nm
µr of Head Material
2000
µr of Media
2
µr of SUL
2000
σ of SUL
5 106 S/m
RESULTS AND DISCUSSIONS
A. Write-Field distribution The equal-potential lines under different velocity directions obtained by the analytical solution are plotted in Fig.3. These results are compared with numerical analysis with good agreement.
D$QDO\WLFDOPRGHO Airgap Media
SUL
Y y=h1 I
Magnet
y=h2 II
∂ A1 ∂ A 2 ∂M ( x) + 2 = I (t ) ∂x 2 ∂x ∂x 2
Airgap
∂ A2 ∂ A2 + 2 =0 ∂x 2 ∂y
Media
∂ A3 ∂ A3 + 2 =0 ∂x 2 ∂y
2
y=h3
2
2
III
y=h4
0
(a)
∂A 3 ∂A 4 1 ∂A 3 1 ∂A 4 , = = ∂x ∂x µ3 ∂y µ 4 ∂y
∂ A4 ∂ A4 ∂A ∂A + 2 = µσ ( 4 + V 4 ) ∂x 2 ∂x ∂x ∂x 2
SUL
∂A1 ∂A 2 ∂A1 ∂A 2 = , = ∂x ∂x ∂y ∂y
D)(0
∂A 2 ∂A 3 ∂A 2 1 ∂A 3 , = = µ 3 ∂y ∂x ∂x ∂y
2
y=0 IV
∂A1 =0 ∂y
2
2
A4 = 0
X
(b)
(c)
Fig. 3 Equal-potential line simulated by Analytical Solution (a) no velocity: a-1 analytical solution result, a-2 FEM result; (b) Left direction; (c) right direction
Fig 2 Problem Regions, governing equations and boundary conditions
Compared with the static writer head model [4], the governing equations in region one and four are treated differently. In Region 1, i.e. the region above ABS, the current carrying coil is modeled as an equivalent MMF source with the amplitude varying with time. In Region 2 for the air gap and Region 3 for the media, the field is governed by Laplace equations. In Region 4 for the soft under layer, the governing equation is expressed in its general form as:
& & & & ∂2 A4 ∂ 2 A4 ∂A 4 ∂A 4 + 2 = µσ ( +V ) ∂t ∂x ∂x 2 ∂y
Fig 4 Write field distribution versus distance/PW50 with different (a) rise time; (b) velocity
(1)
The general analytical solution in Region 4 is as follows, where the coefficients are determined by applying the boundary conditions:
A4 mn = eξn y (C4 mn cos[kn x + η n y ] + D4 mn sin[kn x + η n y ])e jζ m t + e −ξn y ( F4 mn cos[kn x − η n y ] + G4 mn sin[k n x − η n y ])e jζ m t (2) With reference to the static magnetic write field prediction, the vector potential in each region can be defined. The expression of the writer field can be determined by substituting the potential into the governing equations and boundary conditions. Fig 5 Write field distribution with position in down track direction and time
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17th International Zurich Symposium on Electromagnetic Compatibility, 2006
Figs 4 (a) and (b) illustrate the write field distribution at different rise time and various media velocity (i.e. velocity of the disk platters). It can be seen that the field distribution changes when the media velocity increases and the rise time reduces. The analytical solution provides a efficient tool to study the effects of the time dependence and soft underlayer properties on the distribution of perpendicular write head field, which is crucial for optimal design of magnetic recording system. Figure5 gives the write field distribution plotted as a function of time and positions in down track direction.
[2] J. P. Wang, Y. Y. Zou, C. H. Hee , T. C. Chong and Y. F. Zheng, "Approaches to tilted magnetic recording for extremely high areal density," IEEE Trans. Magn., vol. 39, pp. 1930-1935, July 2003. [3] J. J. Miles, R. Wood, T. Olson, H. Shute, D. Wilton, and B. K. Middleton, “Vector recording properties of perpendicular media,” IEEE Trans. Magn., vol. 38, pp. 2060-2062, Sept 2002. [4] Z. J. Liu, J. T. Li and H. H. Long, “Sensitivity analysis of write field with respect to design parameters for perpendicular recording heads,” J. Appl. Phys.., vol. 97, pp. 515-517, May 2005 [5] H. J. Ritchter, “An approach to recording on tilted media,” IEEE Trans. Magn., vol. 29, pp. 2258-2265, Sept 1993. [6] D. A. Thompson, “The role of Perpendicular Recording in the Future of Hard Disk Storage,” J. Magn. Soc. Jpn., vol. 21, pp. 915-741, August 1997.
B. Eddy Current The eddy current in the soft under layer is expressed as
Je = σ
∂A4 ∂A + σV 4 = Jt + Jv ∂t ∂x
(3)
The time dependent and velocity eddy current components of equation (3) are illustrated in figure 6. The value of eddy current subjected to time-dependence is much higher, as compared to the SUL velocity during the phase of time rise
Fig 6 The time dependent and velociy eddy current components versus distance/PW50
IV. CONCLUSION In this paper, a dynamic model of magnetic write field for perpendicular recording systems is presented. The purpose of this study was to ascertain the effect of time dependence and the velocity of soft underlayer on the write field distribution of perpendicular recording. The investigation on flux density and eddy current has revealed the important interdependence between write field profile and head dimensions, time and velocity of soft-magnetic underlayer. The presented dynamic model is a fast and useful tool for the design of the perpendicular recording heads. In addition, it also provides additional information for the micromagnetic modeling.
REFERENCES [1] M. Mallary, A. Torabi, and M. Benakli, “One terabit per square inch perpendicular recording conceptual design,” IEEE Trans. Magn., vol. 38, pp. 1719-1724, Sept 2002.
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