Chapter 8. Conclusions and Further Work Overview of Findings

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1 8.1. Overview of Findings The aim of this thesis was to analyse, theoretically and experimentally, the signal and noise aspects of digital magnetic recording on longitudinal thin-film disk media. This involved the theoretical development of simplified models that: (i) explain the record, replay and noise processes and (ii) identify the parameters that limit the performance of a recording system. The performance of a recording system is measured here by the number of magnetisation reversals stored per unit length along the recorded track (linear or packing density). The investigations concentrated only on the head-tomedium interface parameters and on the bulk properties of the magnetic layer. Theory was also augmented by experimentation and the agreement between the two was tested Heads In Chapter 2, the assumption of infinite permeability of magnetic heads has allowed the derivation of closed form expressions for the fields from two dimensional head structures using the theory of magnetic potential. The closed form head field expressions given by Ruigrok (1990) for the semi-infinite gapped head geometry were found to be the best compromise between the simple, and less accurate, analytical field expressions of Karlqvist (1954), and the more accurate but computationally demanding field formulae of Fan (1960; 1961). A new technique for determining the exact values of the harmonic coefficients of Fan s equations was developed. This permitted the 290

2 exact field formulae of Fan to be more accessible (Wilton et al, 1998) and allowed the accuracy of other field expressions to be gauged. The surface field transform of the semi-infinite gapped head structure given by Lindholm (1975) predicts correctly the position of the head gap nulls and agrees with the exact surface field transform derived by Fan (1960; 1961). For infinite depth dimension, the magnetic potential in the gap region and beyond the pole edges was found to be insensitive to the pole lengths (Lindholm, 1975). As a result of this finding, the derived spatial field expressions for thin-film heads and their Fourier transforms were the superposition of the surface field (or surface potential) expressions in the gap region and beyond the pole corners. The closed form field expressions of Szczech et al (1986; 1987) and Bertero et al (1993) were found to give the closest agreement with signal and noise measurements when recording and replaying with thin-film heads. The difference between the two expressions was mainly in the magnitude of the oscillations in the head bumps. The two dimensional fields from one-sided sources (head and/or medium) are orthogonal and are therefore Hilbert transforms of each other (Mallinson, 1973; 1974). Real heads have zero DC response due to their finite dimensions (Mallinson, 1974). This has been proved by Lindholm (1976b) for a rectangular head geometry using superposition Readback Signal The replay process, described in Chapter 3, is linear due mainly to the linear magnetic characteristics of the replay transducer. Reciprocity predicts the replay signal due to an isolated transition as a correlation of the magnetisation divergence and the replay head sensitivity function. The exact expression for the replay pulse due to a recorded tanh transition was derived using contour integration. The Fourier transform of the isolated replay pulse exhibits bandlimited filters in the form of head and medium loss terms. For narrower pulse widths, the theory predicts the need for smaller gap lengths, lower flying heights and ultimately narrower recorded transitions. The replay signal 291

3 due to a sequence of recorded transitions is given by the linear superposition of individual responses. The slope of the roll-off curve at high packing densities is a strong function of the effective spacing (a+d). The tanh and error function transitions give rise to higher amplitudes at low to moderate packing densities and exhibit faster roll-offs at high packing densities. Linear InterSymbol Interference (ISI) occurring at high packing densities causes linear bit shift (pulse peaks move apart) and linear amplitude loss. The Fourier transform of the periodic replay signal from an all ones NRZI pattern consists of odd harmonics scaled by the magnitude of the Fourier transform of the isolated pulse Recording and Media Exact expressions for the medium fields for the tanh magnetisation transition, derived using contour integration (Appendix V), were illustrated in Chapter 4. Head image fields tend to reduce the medium fields. The image fields due to the semi-infinite gapped head structure were computed successfully. The net medium fields, after modification by the gapped head image fields, were found to be asymmetrical and exhibit local maxima at the gap corners. The extent of the written transition region was related to the head and medium parameters using the well-known slope theory. At the instant of writing, the theory predicts a reciprocal dependence on the square root of the head field gradient. With respect to the medium parameters, the theory was found to predict the following dependence: M rδ a (G, G`) H c where n varies between 0.5 and 1 depending on whether the write or the demagnetising processes has the sustainable influence. G and G` are constant factors added to account for the influence of the transition shape on the length of the written transition; G is for the write limit case and is less than 1 for the tanh and error function transitions, and G` is for the demagnetisation limit case and was proved to be greater than unity of the two former transitions. The above relation predicts that narrower 292 n

4 transitions can be written with reduced demagnetisation (by optimising the disk media or through head imaging). M δ / H in r c Non-linearities cause deviation from the signal behaviour as predicted by the principle of linear superposition. Non-linearities occur mainly due to the demagnetising fields of previously written transitions and their effect on neighbouring transitions and on the applied head field. Dibit recording was used to model the non-linear bit shift and nonlinear transition width change. Non-linear bit shift causes attraction between neighbouring transitions. The non-linear bit shift is a function of the demagnetising field of the previous written transition and can thus be decreased by reduced demagnetisation (enhanced imaging). Interaction fields also cause an increase in the length of written transitions leading to a non-linear amplitude loss. Head imaging was found to enhance the non-linear increase in transition length with increased packing density. The predicted magnitude of the increase in transition length was found to be small compared with the experimental observations. This was attributed to the limitation of the theory where the length of the previous written transition in a dibit was assumed fixed. Micromagnetic simulation has shown that the length of the previous written transition increases with packing density due to percolation (Moon and Zhu, 1991). The non-linear increase in transition length can be reduced with reduction in the length of the written transitions. The non-linearities of the recording process were found to be dependent on the functional form of the written transitions Transition Noise The two modes of medium transition noise were investigated theoretically in Chapter 5. The theory assumed a fixed transition shape and allowed the random variations in the centre positions and widths in the transition function. The magnetisation transition noise modes were found to be orthogonal (i.e. Hilbert transform pair). The noise voltage profiles were not orthogonal except for the case of an arctangent transition function where the noise voltages are identical (scaled by the noise variance of each noise mode). The Fourier transform of transition width noise voltage was found to be the wavenumber derivative of the Fourier transform of position jitter noise voltage. 293

5 The noise power spectral density (PSD) was written as the product of the signal power times the noise dependent terms. The jitter noise power increases at a second order with wavenumber and determines the long wavelength response of the noise PSD. Transition width noise power increases at a fourth order for the error function transition (approximately true for the tanh function) and dominates the short wavelength response of the noise PSD. The total noise power was shown to increase linearly for bit separations B πa. For small transition spacing ( B < πa ) positive correlations cause a supralinear increase in the total noise power. The theory explains and predicts positive correlations by the coupling of the magnetostatic fields between neighbouring fluctuating transitions. Positive jitter correlations cause an enhancement of the long wavelength component of the noise PSD. The integrated jitter noise power reaches a peak value at a packing density that is approximately equal to 2a. The tanh and error function transitions enhance the positive jitter correlations and increase the total noise power at high packing densities. Reducing the replay head flying height was found to reduce the total jitter noise power through the reduction of the spacing losses. Calculations indicated that the total jitter noise power increases with reduction in the record flying height (reduced transition lengths). Reduction of total jitter noise power can be achieved by reduction of the interaction fields (reduced demagnetisation through M rδ / H c and by enhanced imaging during replay). Theory predicted that the total noise power due to transition width variation was mainly dependent on the local variations in the transition length (due to local fluctuations in transition fields). The effect of noise correlations (interactions) in transition width noise becomes important only at very high packing densities. Replay head imaging increases the total transition width noise power. Calculations have indicated that the integrated transition width noise power can be reduced with reduced record flying height by writing shorter transitions. In general, the calculations indicate that position jitter noise will be dominant with reduced record flying heights. 294

6 The noise variance (and hence power) was found to be proportional to the track width and to the cross-track correlation length. The cross-track correlation length reflects the effect of the dimensions of the zig-zag on the noise variance. The increase in zig-zag dimensions was attributed to the short range intergranular exchange coupling forces. The increase in zig-zag dimensions leads to an increase the noise variance and hence in the noise power. Reduction of the transition noise can be achieved by reduction of the exchange forces through physical grain segregation (Johnson, 1992) Transition Shapes Inverse filtering was used in Chapter 6 to discover the shape of the recorded magnetisation transition as seen by the replay head. The Wiener optimal filter was used successfully to minimise the noise in the Fourier transform of captured waveforms. With high signal to noise ratios, the centre of energy alignment was found to reduce the jitter in captured replay pulses. The average noise voltage obtained from the captured replay pulses after alignment was found to agree with the theoretical noise voltage plots. Position jitter noise was observed to be dominant at small packing densities where transitions are isolated. The computed transitions were found to be non-symmetrical. For the high coercivity media, the calculated transitions may be approximated by the tanh or error function transitions. The corresponding transition lengths were found to be proportional to the theoretical values obtained from the slope theory. It was found that reduction of the corner wavenumber in a replay channel filter (head or electronics) increases the attenuation of the short wavelength components of a replay pulse causing a broadening and amplitude reduction in the filtered readback pulse. For a sequence of replay pulses, the limited filter bandwidth leads to a faster roll-off in the peak signal with increased packing density Measurements Measurements have been performed in Chapter 7 on four longitudinal thin-film disk media using two thin-film heads. Fittings to measured signal roll-off curves and 295

7 fundamental rms measurements indicated that linear superposition was valid for packing densities up to 150KFCI. Noise spectral measurements have exhibited an exponential spacing type loss dependence, which was attributed to non-linear effects at high packing densities; in particular, transition width broadening. The exponential dependence was common to all the media and heads. Good agreement between noise theory and spectral noise measurements was obtained in the linear and supralinear portions of the total power curves. The transition width parameters obtained from the fittings to the signal and spectral noise measurements all followed the same dependence on the demagnetisation ratio, i.e. decrease in transition length with reduced demagnetisation ratio. Reduction in the flying height and gap length during replay was found to improve the signal performance but increase the medium noise. Improved signal-to-medium noise performance can be achieved at high packing densities with reduced demagnetisation Limitations in Theory and in Experiment In Chapter 7, the theory was able to predict the signal and noise performance for a wide range of packing densities and deviation from measurements occurred around a packing density of 150KFCI. This was very clear in the fitting to the experimental integrated noise power curves. This is attributed to the assumption of linearity in the replay and record analyses. When modelling interactions, especially in dibits, linearity was assumed by which the longitudinal magnetostatic fields were superposed linearly as a function bit separation. Therefore, the agreement with the experimental data was limited to the portions where linear superposition in the measured signal (or noise) was known to be valid as indicated from comparison with the measured signal roll-off curves. By fitting theory to experiment, the transition width parameter was extracted. Although the measured transition lengths were consistent with their dependence on the demagnetisation ratio, there was slight spread in their values for different types of measurements. Two reasons may be attributed to that spread. The first aspect involves the incomplete knowledge of the exact parameters for the experimental heads 296

8 and media (flying height, medium thickness, overcoat thickness and remanant magnetisation) for implementation in the theoretical fittings. The second reason is related to the fact that the theory assumes a specific and fixed functional form for the recorded magnetisation transition. This introduces errors in the calculations since the actual recorded transitions are not fixed to a single transition function as demonstrated in Chapter 6. In the measurements, only two disks (with similar coercivities but with differing M r δ products) were used to test the influence of reduced head dimensions on the replay signal and noise. Although the results show that the recorded transition lengths are almost independent of the gap length and flying height, more tests are needed to be carried out on a range of heads and media to confirm this finding. If this is the case, then the recorded transitions are expected to be demagnetisation limited. However, the calculations indicated that the evaluated transition lengths from the write limit case were closer to the values obtained from measurements. Since the record theory considered in Chapter 4 only deals with the write and demagnetising limit cases, it is thought that the effects of relaxation after removal of the head field and head shunting during replay must be included. Although the work of Comstock and Williams (1971) and Maller and Middleton (1974) has dealt with such phenomena, their models are required to be recalculated for the parameters used in the experiments and the role of gapped head image fields needs to be taken into consideration Further Work The transition boundary between two magnetised states is known to exhibit the zig-zag microstructure (Yoshida et al, 1983; Arnoldussen and Tong, 1986). Despite the existence of the zig-zag structures, the simplified cross track average transition functions (like the arctangent and tanh transitions) were successful in predicting the recording, replay and noise aspects of magnetic recording. Recent findings have explained this by pointing out the vector nature of the recorded magnetisation transitions in the cross track dimension. Simplified (Middleton, Aziz, Wdowin and Miles, 1998) and micromagnetic (Wdowin et al, 1998; Beardsley, 1989) modelling 297

9 have shown that the sawteeth structure can be constructed as the vector sum of a divergence free magnetisation component (flux-closure pattern) that produces no fields, and a curl free magnetisation component (can be represented by an arctangent like function) that produces the stray fields and induces the replay signal. This work is in need of further development to relate the sawteeth parameters to the medium parameters and to validate the present theories that rely on the one dimensional transition functions. Furthermore, the effect of superposition of these zig-zag structures needs to be studied as that would be useful in predicting the percolation phenomenon that occur at high packing densities. In Chapter 7, the noise power was measured using a spectrum analyser. The spectrum analyser gives the average power of noise but does not provide any phase information. That is, the spatial distribution of noise relative to the measured signal is not known. To identify the spatial distribution of noise, the time series noise autocorrelation calculations on captured data are performed (Tang, 1985). The noise voltage autocorrelation has been shown for one of the experimental disks in Chapter 6. However, the replay pulses were captured on a single location on the recorded track. In order to include most of the transition noise statistics, the capturing process must be repeated for a number of locations on the recorded track. Once this is achieved, fitting can then be made using the theory developed in Chapter 5 to obtain the transition length parameter and the cross track correlation length. It has been shown that similar mechanisms give rise to transition width noise and reverse DC erase noise (Aoi et al, 1986). To obtain more insight into the mechanism of transition noise in thin-film media, the noise power spectra of reverse DC erase noise are required to be measured. This will also allow the integrated reverse DC erase noise to be found as a function of write current where information about the cross track correlation length and dm/dh can be extracted (Zhu, 1992). Further investigation is needed to understand and quantify theoretically the loss factor α obtained by fittings to measured noise PSDs in Chapter 7. If it is mainly related to the non-linear increase in transition length, then analyses are required to relate this loss 298

10 factor (or the exponential dependence) to the interaction fields and to the statistical nature of the percolation process as a function of packing density. Finally, since limitations were found with the inductive thin-film replay heads (improvement of signal with reduced head dimensions is matched by the increase in medium noise), the theoretical and experimental studies are required to be extended for the use of magneto-resistive replay transducers. This will improve the signal performance and eliminate the ripple (head bumps) in the measured signal and noise waveforms. 299