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The Limits of the Wallace Approximation for PMR Recording at High Areal Density B. Marchon, K. Saito, B. Wilson, and R. Wood Hitachi GST, San Jose Research Center, San Jose, CA 95135 USA
This paper discusses the validity of the Triple Harmonic method and the Wallace readback model for the determination of head500 Gb in2 areal density. For the recording system disk spacing variations in today’s perpendicular recording (PMR) systems at investigated here, and in the limit of high frequency, approximately beyond the frequency corresponding to the 2 T (0011) pattern, this method fails, as head and electronic noise start to interfere. In the low-frequency range of PMR systems, the Wallace equation does not apply any longer. Accurate magnetic spacing variations can be obtained by using the FFT of the intensity ratio of the readback signals, and fitting with the appropriate algebraic expression. Using this method, a repeatability of less than 0.1 nm was obtained, by using a random data pattern of only four 512 bytes data sector long. Index Terms—Flying height control, head-disk interface, magnetic recording, readback signal, Wallace spacing loss.
I. INTRODUCTION
II. EXPERIMENTAL
S the head media spacing (HMS) in today’s disk drive has now crossed the 10 nm mark [1], it is becoming increasingly important to control head disk clearance precisely, down to the Angstrom level. If clearance drifts higher, signal integrity is deteriorated, and if clearance is too low, mechanical interactions start to increase, possibly leading to wear of the thermal actuator (TFC) ‘bulge’, and subsequent reader or writer degradation. Today, TFC power setting is set during drive manufacturing, and schemes have been proposed to dynamically adjust it during drive operation in order to keep the head-disk clearance constant [2]. A typical technique for measuring HMS fluctuations uses the Wallace spacing equation [3], [4] and the triple harmonic method, where a specific pattern of 0’s and 1’s is written on the dedicated track of the disk, and signal amplitude is measured at two different frequencies, one being three times the other [5]–[8]. If 1 T corresponds to the (01) pattern, schemes that have been proposed involve the 1 T,3 T or 2 T,6 T pairs for instance. Even though this method can be very accurate (to the needed Angstrom level), it is found to usually require a large data set, and one or more dedicated tracks of data is often used, impacting drive capacity. In addition, it necessitates seeking to that reference area of the drive every time TFC calibration is needed, which has a performance impact if one wants to control TFC in real time (e.g. at least once every second). In addition to the performance and real estate impact, the Wallace readback signal equation does not strictly apply to perpendicular recording (PMR) systems, at least in the limit of low frequency [9]–[11].
A
Manuscript received February 22, 2011; accepted May 15, 2011. Date of current version September 23, 2011. Corresponding author: B. Marchon (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2011.2157672
Experimental signal waveforms from random recorded data were extracted from an experimental 65 mm drive spinning at 10,000 rpm, under various clearance values. The recording linear density was 1970 kbpi (kilobits per inch), corresponding to a bit length of 12.9 nm, and a 1 T pattern (01) spatial fre. Disk velocity at a radius of 30.6 quency of mm was 32.1 m/s. The slider form factor was of femto size, and its mothership flying height was 9.5 nm. A TFC heater was used to actuate the reader at various clearances over the recorded data track. The largest TFC power used was 67 mW, corresponding to the TFC bulge in near contact with the disk surface. Waveforms were further analyzed using the Matlab computing environment. A Gaussian convolution window was used to smooth out the power spectrum data. Waveforms from four consecutive 512 bytes data sectors, corresponding to approximately one full servo sector, were averaged in the frequency domain. For the fitting of the readback signal ratio at various TFC powers, the head to soft-underlayer spacing is needed. For the disk and slider used in this study, this value was 54.2 nm at zero TFC power. III. THEORETICAL BACKGROUND Wallace spacing strictly applies only to 2D magnetic configurations. It also requires that all the magnetization be on one side of the line or plane at which the field is measured. If either the field source (written track) or the measurement-width (reader-width) is much wider than wavelength divided by , then the 2D approximation becomes very accurate. This is especially true if there is a difference between the reader and [12], [13]. wider greater than The read head is assumed to measure the vertical field component at the head air-bearing surface (ABS). In that sense, the read head, which is a strongly magnetic soft structure, is entirely on the wrong side of the measurement plane from the medium. However, to the extent that the read-head structure is magnetically very soft and a forms a perfect image of the magnetization in the medium, the net result is simply to double the field at the ABS surface and Wallace spacing still holds. There is,
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MARCHON et al.: LIMITS OF THE WALLACE APPROXIMATION FOR PMR RECORDING AT HIGH AREAL DENSITY
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Fig. 1. Schematics of the amplitude ratio method. The LMR curve describes the Wallace equation (1), whereas the PMR curve follows equation (2).
however, an underlying assumption that the media magnetization is perfectly hard and is not altered at all by the presence of the soft head structure. While this is may be a reasonable assumption for longitudinal recording or for a single-layer perpendicular medium, it becomes very untrue when the medium includes a soft magnetic underlayer. In terms of images, there is now formed an infinite series of images between the soft underlayer and the soft head structure. Under these conditions of multiple images, the response to wavelength and to spacing becomes quite complex. Fortunately, with the assumption that both the medium and the soft head structure can be represented by continuous films, it is possible to derive analytic expressions [13] for the spacing dependence. These come into play primarily at long wavelengths where the separation between the head and soft-underlayer become . At the very longest wavelengths, on comparable with wide tracks, the response asymptotes simply to the media filling factor (media thickness/head-underlayer spacing). At very long wavelengths (low-frequency), uncorrected Wallace spacing can erroneously give huge apparent spacing changes. An illustration of the above considerations is reproduced on Fig. 1. According to the Wallace equation, the readback signal intensity from a random data pattern should scale exponentially with head-media spacing (HMS) , according to (1) is the frequency content of the signal at a spatial where vs. , where frequency . As a result, plotting is the reference HMS at zero TFC, should yield a slope equal , or change in clearance. to the change in HMS As pointed out earlier, the Wallace readback equation in the case of PMR is a little more complex. According to [14], one can express the readback signal as (2) where is the thickness of the magnetic recording layer, the is the thickness of the exchange break layer (EBL), and total head-to-soft underlayer spacing. Equation (2)’s clearance . The sensitivity is implicitly associated with the value of now becomes amplitude ratio for a clearance change (3)
Fig. 2. Power spectrum (Log scale, after Gaussian filtering) of the readback signal obtained for increasing TFC power of 0, 15, 28, 41, 55, and 67 mW.
in the high-frequency regime asymptotes to The limit of the Wallace equation, whereas in the limit of zero frequency, it , as levels off to a finite, non-zero value of seen on the schematics illustrated on Fig. 1.
IV. RESULTS AND DISCUSSIONS A. Power Spectrum vs. Clearance On Fig. 2 are reproduced the power spectra (logarithmic scale) of the readback signal obtained at various values of the TFC power. The high-frequency components roll off sooner for variahigher clearance, as expected. The corresponding tions are reproduced on Fig. 3, where the reference amplitude is taken at zero TFC power. It is immediately apparent that the linear high-frequency region outlined on Fig. 1 does not , frequency corresponding hold much beyond to the 2 T pattern (0011). This behavior likely arises from the fact that the noise starts dominating when the signal weakens. In the limits of zero signal, and in the presence of a noise that is independent of spacing, the amplitude ratio becomes unity, or zero in a logarithmic scale. It should be pointed out, however, that media noise should follow the same spacing behavior as the recorded data readback signal, and therefore, only the head and electronic noise are responsible for this effect. , the In the low-frequency range below ca. logarithmic ratio does deviate from the linear regime as well, as predicted. As discussed earlier, the intercept of the amplitude ratio at zero frequency is dependent upon both the clearance as well as the head-soft underlayer spacing . change This, in principle, provides a method to estimate HMS, if the disk magnetic structure is known [10]. This will be discussed further in the paper. It should be pointed out that the exact range of linearity is expected to be very system-dependent, and that the precise frequency threshold for deviations from linearity might be substantially different for systems of various areal densities, SNR (media, head and electronics) etc.
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Fig. 5. Readback signal ratio (log scale) in the low-frequency range. The symbols represent experimental data, and the solid lines are the theoretical values, using Equation (3). Fig. 3. Power spectrum (Log scale, after Gaussian filtering) of the readback signal obtained for increasing TFC power of 15, 28, 41, 55, and 67 mW, ratio-ed to the spectrum obtained with no TFC.
a broad spectrum content, and fitting the entire frequency range, as opposed to recording and processing two discrete frequencies only, such as in the 2 T–6 T method. C. Fitting the Low-Frequency Region
Fig. 4. Clearance change as a function of TFC power, calculated from a linear regression of the linear region of the curves shown on Fig. 3.
B. Clearance Change Estimation The data shown earlier exemplifies the shortcomings of using the Wallace approximation for the evaluation of spacing variations, since deviations were identified both in the low-frequency and high-frequency limits. in In terms of the (01) or 1 T pattern of the present study, it can be concluded that measuring spacing changes using the 2 T,6 T methodology is inadequate for today’s recording systems, since the range of Wallace linearity, based on to 2 our data, spans a region only 5 T T wide. It can even be surmised that the 2 T signal is already on the edge of the linear zone, which might produce erroneous results in some cases. Using this 2 T–5 T “Wallace” zone, we performed a linear regression and extracted the clearance change for each TFC power setting. This was done on four different servo sectors around the track. Results are reproduced on Fig. 4. The reproducibility of the data, using this method, is very good, with a standard deviation of less than 0.1 nm for each power step. This result highlights the importance of choosing the appropriate frequency range in the linear region. It also demonstrates the value of using a random data pattern with
As pointed out earlier, the readback signal of a PMR system does not follow the simple Wallace equation in the low-frequency regime (wavelength greater than 5 T or so). A more complex algebraic derivation needs to be used, as described on (3). This equation, in principal, allows the determination of the [10]. We attempted to fit the head-soft underlayer spacing experimental data using this expression, and with the spacing values obtained from the linear regression of the 2 T–5 T region value of 54.2 nm for our as discussed above. Using the slider-disk combination, we were able to obtain a very reasonable agreement with the data, as shown on Fig. 5. The question then arises whether this technique would allow the determination of the absolute head-media, or magnetic spacing, for any head-disk system of known magnetic layer thickness. Considering the remarkable agreement between data and model shown on Fig. 5, it is not too far fetched to think that it might be possible with a reasonably good accuracy. The precise experimental measurement of HMS has been the subject of several papers [6], [7], but to our knowledge, no unequivocal method has fully emerged. The methodology outlined here might provide impetus for further studies on the topic. V. CONCLUSION The results discussed here demonstrate the limits of the triple harmonic method for today’s recording systems, as it appears that the frequency range where the Wallace method holds does not fully span a wide enough range. By restricting oneself to the linear region in the 5 T to 2 T range, a linear fit of the readback signal of a random data pattern can be performed, and HMS changes can be calculated with greater accuracy than by using only two discrete frequencies. The precision of this method could also be further improved by fitting the data with the more accurate PMR spacing model, also allowing, in principal, the determination of the absolute head-media separation, as long as the media layer thicknesses are known.
MARCHON et al.: LIMITS OF THE WALLACE APPROXIMATION FOR PMR RECORDING AT HIGH AREAL DENSITY
ACKNOWLEDGMENT The authors would like to thank R. Pit and F. Crimi for their interest in this work, and for providing details of the disk and slider characteristics. REFERENCES [1] B. Marchon and T. Olson, “Magnetic spacing trends: From LMR to PMR and beyond,” IEEE Trans. Magn., vol. 45, no. 10, pp. 3608–3611, Oct. 2009. [2] Y. S. Tang, S. Y. Hong, N. Y. Kim, and X. D. Che, “Overview of fly height control applications in perpendicular magnetic recording,” IEEE Trans. Magn., vol. 43, no. 2, pp. 709–714, Feb. 2007. [3] R. L. Wallace, “The reproduction of magnetically recorded signals,” Bell Syst. Tech. J., vol. 30, pp. 1145–1173, 1951. [4] W. K. Shi, L. Y. Zhu, and D. B. Bogy, “Use of readback signal modulation to measure head disk spacing variations in magnetic disk files,” IEEE Trans. Magn., vol. 23, no. 1, pp. 233–240, Jan. 1987. [5] B. Liu, Z. M. Yuan, and Y. J. Man, “Tribe-magnetics and nanometer spaced head-disk systems,” IEEE Trans. Magn., vol. 37, pp. 918–923, 2001. [6] Z. M. Yuan and B. Liu, “Absolute head media spacing measurement in situ,” IEEE Trans. Magn., vol. 42, no. 2, pp. 341–343, Feb. 2006.
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[7] J. F. Xu, J. D. Kiely, Y. T. Hsia, and F. E. Talke, “Head-medium spacing measurement using the read-back signal,” IEEE Trans. Magn., vol. 42, no. 10, pp. 2486–2488, Oct. 2006. [8] Y. Shimizu and J. G. Xu, “Two-dimensional flying-height modulation mapping at HDD drive level,” IEEE Trans. Magn., vol. 42, no. 10, pp. 2516–2518, Oct. 2006. [9] S. Gebredingle, S. Gider, and R. Wood, “The magnetic spacing sensitivity of perpendicular recording,” IEEE Trans. Magn., vol. 42, no. 10, pp. 2273–2275, Oct. 2006. [10] Z. Jin, C. J. Fu, X. B. Wang, Y. N. Zhou, and J. Fernandez-de-Castro, “Spinstand measurement of head keeper spacing in perpendicular recording,” IEEE Trans. Magn., vol. 42, no. 10, pp. 2270–2272, Oct. 2006. [11] D. Guarisco, Z. H. Li, B. E. Higgins, K. Saito, Y. Wu, and A. LeFebvre, “Drive integration in perpendicular recording (invited),” J. Appl. Phys., vol. 99, 2006. [12] D. T. Wilton and R. W. Wood, “Transmission of magnetic fields in three-dimensional multilayered structures,” IEEE Trans. Magn., vol. 44, no. 7, pp. 1861–1873, Jul. 2008. [13] R. W. Wood and D. T. Wilton, “Readback responses in three dimensions tor multilayered recording media configurations,” IEEE Trans. Magn., vol. 44, no. 7, pp. 1874–1890, Jul. 2008. [14] D. T. Wilton and R. Wood, “Readback responses for complex recording media configurations,” IEEE Trans. Magn., vol. 40, no. 1, pp. 112–128, Jan. 2004.
