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The effect of track width on transition noise in longitudinal thin-film media
Journal of Magnetism and Magnetic Materials 120 (1993) 375-378 North-Holland
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The effect of track width on transition noise in longitudinal thin-film media J.J. Miles and B.K. Middleton Information Storage Research Group, Department of Electrical Engineering, University of Manchester, Dover Street, Manchester M13 9PL, UK A hierarchical micromagnetic model has been used to investigate the effect of reducing track width upon recorded transition noise in longitudinal thin films. This has demonstrated that although effects due to magnetization transition profile variations can be accounted for by simple statistics, timing jitter is a more complex phenomenon. 1. Introduction Earlier work by the authors [1] demonstrated that the transition width parameter ' a ' calculated from micromagnetic simulations matches that calculated from analytical arctangent theory [2] for all variations of medium thickness, exchange coupling and texture investigated. The recording (or signal) performance of longitudinal media at moderate densities can therefore be described to a first approximation by simple analytical theory. This paper investigates the further problem of noise and considers the validity of analytical/ statistical techniques for noise prediction. There are continuing attempts to reduce track width in recording systems. It is well known that as track width is reduced, the signal-to-noise ratio deteriorates, and it is important to be able to predict the effects of noise in system design. This paper employs a micromagnetic model to investigate the increase in noise as track width is reduced, and seeks verification that simple statistical models can be used in system design. It has been shown that the transition noise power spectrum can be accurately determined from the variances of transition position and width [3], or equivalently replay pulse amplitude, width and position. These parameters have been used as a measure of noise in this paper. 2. Description of the model A hierarchical micromagnetic model Of a granular or segregated cobalt film was employed for the simulations [4]. In this model the film sample is assumed to consist of N discrete grains of material which are uniformly magnetized, and which interact via dipoleCorrespondence to: Dr. J.J. Miles, Information Storage Research Group, Department of Electrical Engineering, University of Manchester, Dover Street, Manchester M13 9PL, UK. Tel.: +44-61-275-4554; telefax: +44-61-275-4512.
dipole and weak exchange coupling. Each grain has uniaxial anisotropy, with the easy axes randomly distributed in plane with a uniform distribution. The film is 500 ,A thick, with 400 .& diameter grains of pure cobalt, with M s = 1.5 × 106 A / m and H k = 2.24 × 105 A / m . With a packing fraction of approximately' 75%, the overall value of M s for the film is 1.125 × 106 A / m . Hysteresis loops are calculated by initially saturating the film and applying an external field of 1.5 H k to maintain saturation. The external field is then reversed in steps of 0.005 H k until a reverse field of 1.5 H k is achieved. At each step in the external field a set of N Landau-Lifshitz equations: dM/ dt
To l +ct 2 ( M i X H T ) aCTG Mi × ( M i × HT)
l+a~
IMil
(1)
are integrated until a stable equilibrium is achieved. Magnetization transitions are calculated by initialising the magnetization in the form of an ideal step function transition (or transitions), maintained by an equivalent step function external field of magnitude 1.5 H k. This external field is then reduced to zero magnitude in steps of 0.005 H k in the same manner as the hysteresis loop calculations. This procedure results in 'demagnetization limit' transitions; i.e. the narrowest transitions which could be written in the media with an ideal write head. By this method the behaviour of the media can be distinguished from write effects, and media performance can be properly assessed. 3. Results The behaviour of the films was investigated for three values of the exchange coupling parameter C* [5]. Values of C * = 0.025, 0.075 and 0.125 were cho-
0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
376
ZJ. Miles, B.BA Middleton / Transition noise in thin-film media
•
!i:~
~ .....
.
.
.
.
.
?;i i Fig. 1. A pair of transitions spaced 1.29 I~m apart. The magnetizations are shaded to indicate the sign of the magnetization in the track direction.
sen, giving weak, moderate and strong exchange coupling between the grains, respectively. For the hysteresis calculations a sample of 2.5 × 2.0 p.m (3132 grains) was used. The films had squareness ( M r / M s) of 0.87, 0.88 and 0.9, with coercivities of 0.5, 0.38 and 0.34 x 105 A / m , respectively. Fox the transition calculations a sample of length 2.58 p~m (along the track) and width 7.15 p.m (across the track) with 11 520 grains was used. In all cases pairs of transitions spaced 1.29 p.m apart were generated so that there was no asymmetry at the boundaries. Eight transition pairs were simulated for each value of the exchange coupling strength, each of the eight simu-
CROSS tn
lations employing a different random sample of easy axes, giving 16 different transitions for each value of C*. An example transition pair for C* = 0.075 is shown in fig. 1, which shows typical variations in the nature of the transitions across the track. In this particular case the upper transition tends to have rather larger zig-zag structures than the lower one, and the transitions are closer towards the left-hand side, with a corresponding increased tendency for breakthrough between transitions. These variations arise from the random anisotropy of the grains of material and are the origins of noise. For tracks of reasonable width the effects are averaged out, so that the effects are small. This is
TRACK
AVERAGE
1.0
X X
"~"
0.5
0.0
'tI0 . . . .
115" x (um)
-0.5'
-i .0
Fig. 2. The transition profile along the track direction for the transition pair of fig. 1, with the fitted arctangent function.
J.J. Miles, B.K. Middleton / Transition noise in thin-film media demonstrated by the cross track average magnetization, which is plotted in fig. 2, showing a regular pair of transitions with surprisingly little noise. Also shown is a best fit arctangent series, which follows the actual transition shape extremely well. Using the cross track average magnetization profile, the output voltage waveform was then calculated using the reciprocity theorem [2], assuming a conventional Karlqvist-type head of gap = flying height a 0.25 I~m. For each pulse the peak height and position was accurately found using a quadratic fit to interpolate between a few computed voltage points (either five or six) in the near vicinity of the peak. For these samples the output voltage was computed at 2 nm intervals, so that the total distance over which fitting was performed was 10 nm, or approximately 4% of the replay gap. Thus fitting has no filtering effect on the output signal over this range because of the spatial filtering performed by the head over a much larger length scale, and the fit acts soley to interpolate and to reduce the number of voltage calculations required for accurate identification of peak position. The width at half height (PWs0) was then calculated directly from the computed replay waveform. The standard deviations of peak height, width and position were tlaen evaluated as measures of the transition noise using the 16 transitions for each value of C*. As expected, all the above noise parameters increase with increased exchange coupling between the grains. The noise was then evaluated in the same manner for narrower tracks, by computing the average magnetization across a central region of the sample with the appropriate width. For track widths (w) below 3.5 i~m it is possible to examine more than one independent track within each sample, and so the maximum possible number of independent transitions were considered in all cases to obtain the best estimates of the noise. The output voltages were normalised to unit track width to compensate for signal reduction as w is reduced, so that the calculated noise is a proper measure of signal to noise ratio. Track widths down to w = 0.25 Ixm were evaluated. The calculated noise values are summarised in figs. 3, 4 and 5, showing as log-log plots the effect of reducing w upon the standard deviation of replay pulse amplitude, width and position respectively. All noise parameters increase as w is reduced, as expected. Pulse amplitude and width variations arise from variations in the transition profile, and the transition profile is a cross track average of a random structure, with the amount of material contributing being proportional to w. Thus a simple statistical approach would predict a standard deviation dependence upon w -°'5.
377
E f f e c t of Track Width
g .~. ~
rn
1.0. 0.75
o ~ m
0.5 C* = 0.075 Ce = 0.025
*
0.25
®
' '-0'.5'''
gradient gradient
"01~
"
-0.555i -0.5889
'010'
' ' '0.~5 ....
015'
' ' '0.~5'
'
log ( Track Width (urn})
Fig. 3. The effect of tracl~ width upon amplitude modulation, showing least-squares fits to the data.
E f f e c t of Track Width
121
ffl
m Ca = 0,. 125 gradient'
--0.5228.
025
~
"
~
-
:o:o,7. . . . . . . . . . . . . -0.5
-0.25
0.0
0.25
%
0.5
0.75
log ( Track Width (urn))
Fig. 4. The effect of track width upon pulse width modulation, showing least-squares fits to the data.
Effect of Track Width ~ .~
1.0.
®
o
0.75
~
0.25'
mE) m
e, C* = 0 . 0 ~ i
i
I
-0.5
i
i
i
i
gradient: I
i
-0.~5
i
i
i
-0.8~3 l
0.0
i
i
® ~ i
i
#
0.25
i
i
i
i
I
0.5
i
i
i
i
i-i
i
0.75
log ( Track Width (um))
Fig. 5. The effect of track width upon timing jitter, showing least-squares fits to the data.
378
J.Z Miles, B.K~ Middleton / Transition noise in thin-film media
The calculated gradients are in good agreement, confirming that the simple statistical approach is a useful model for pulse amplitude/width modulation noise. The situation for timing jitter is less clear, with jitter varying as w -°'8. This gradient appears to be similar for all values of C*, and indicates that jitter noise increases more rapidly than expected as track width is reduced. For the moderately and strongly exchange-coupled films the overall gradients of the log-log plots are close to those for the weakly coupled films. However the gradients appear to decrease for very narrow tracks, with the change of behaviour occurring between track widths of 2.5 and 4 p.m for C* = 1.25 and between 1.5 and 1.8 t~m for C* = 0.075. The domain or vortex sizes in each case are approximately 0.5-1.5 I~m for C * = 0.125 and 0.2-0.6 ttm for C* = 0.075. This observation appears to indicate that where there is moderate or strong exchange coupling the domains or vortices are coupled strongly enough to act as distinct magnetic entities, and have a significant effect upon the gradient at track widths of approximately three times the feature size. However, since the limit values of the jitter are approximately 10 ns or 150 nm (comparable to the domain size), further work will be required to determine whether it is the track width that acts to limit jitter or whether there is an upper limit to the magnitude of the jitter determined by the displacement along the track; i.e. if in fact position jitter is simply limited to approximately the domain size regardless of track width effects. 4. Conclusions
Transition noise arising from variation in magnetization profile varies as w -°'5 as would be expected
from simple statistical considerations. Timing jitter appears to increase more rapidly than expected as track width is reduced, and this result requires further study. In extremely narrow tracks noise may not be as high as expected from a simple statistical approach, but in modem high-coercivity media with decoupled grains this is not likely to occur at practicable widths. These results relate to low or moderate densities with little interaction/correlation between adjacent transitions. It is known that noise increases as transitions interact, and it is not clear what effect track width would have on this process. In this study track edge noise has been neglected, and only on track noise is considered. This situation corresponds to the case where a narrow M - R read head is used with a wider inductive write head. For most other cases edge noise might be considered to be an additional component which is independent of track width.
This work was performed with the assistance of the University of Manchester, SERC and the EC CAMST initiative.
References
[1] J.J. Miles and B.K. Middleton, IEEE Trans. Magn. MAG27 (1991) 4954. [2] B.K. Middleton, in: Magnetic Recording Volume 1 - Technology, eds. C.D. Mee and E.D. Daniel (McGraw Hill, 1987) chap. 2. [3] J.J. Moon, L.R. Carley and R.R. Katti, 3. Appl. Phys. 63 (1988) 3254. [4] J.J. Miles and B.K. Middleton, J. Magn. Magn. Mater. 95 (1991) 99. [5] J.G. Zhu and H.N. Bertram, J. Appl. Phys. 63 (1988) 3248.
Ad"
The effect of track width on transition noise in longitudinal thin-film media J.J. Miles and B.K. Middleton Information Storage Research Group, Department of Electrical Engineering, University of Manchester, Dover Street, Manchester M13 9PL, UK A hierarchical micromagnetic model has been used to investigate the effect of reducing track width upon recorded transition noise in longitudinal thin films. This has demonstrated that although effects due to magnetization transition profile variations can be accounted for by simple statistics, timing jitter is a more complex phenomenon. 1. Introduction Earlier work by the authors [1] demonstrated that the transition width parameter ' a ' calculated from micromagnetic simulations matches that calculated from analytical arctangent theory [2] for all variations of medium thickness, exchange coupling and texture investigated. The recording (or signal) performance of longitudinal media at moderate densities can therefore be described to a first approximation by simple analytical theory. This paper investigates the further problem of noise and considers the validity of analytical/ statistical techniques for noise prediction. There are continuing attempts to reduce track width in recording systems. It is well known that as track width is reduced, the signal-to-noise ratio deteriorates, and it is important to be able to predict the effects of noise in system design. This paper employs a micromagnetic model to investigate the increase in noise as track width is reduced, and seeks verification that simple statistical models can be used in system design. It has been shown that the transition noise power spectrum can be accurately determined from the variances of transition position and width [3], or equivalently replay pulse amplitude, width and position. These parameters have been used as a measure of noise in this paper. 2. Description of the model A hierarchical micromagnetic model Of a granular or segregated cobalt film was employed for the simulations [4]. In this model the film sample is assumed to consist of N discrete grains of material which are uniformly magnetized, and which interact via dipoleCorrespondence to: Dr. J.J. Miles, Information Storage Research Group, Department of Electrical Engineering, University of Manchester, Dover Street, Manchester M13 9PL, UK. Tel.: +44-61-275-4554; telefax: +44-61-275-4512.
dipole and weak exchange coupling. Each grain has uniaxial anisotropy, with the easy axes randomly distributed in plane with a uniform distribution. The film is 500 ,A thick, with 400 .& diameter grains of pure cobalt, with M s = 1.5 × 106 A / m and H k = 2.24 × 105 A / m . With a packing fraction of approximately' 75%, the overall value of M s for the film is 1.125 × 106 A / m . Hysteresis loops are calculated by initially saturating the film and applying an external field of 1.5 H k to maintain saturation. The external field is then reversed in steps of 0.005 H k until a reverse field of 1.5 H k is achieved. At each step in the external field a set of N Landau-Lifshitz equations: dM/ dt
To l +ct 2 ( M i X H T ) aCTG Mi × ( M i × HT)
l+a~
IMil
(1)
are integrated until a stable equilibrium is achieved. Magnetization transitions are calculated by initialising the magnetization in the form of an ideal step function transition (or transitions), maintained by an equivalent step function external field of magnitude 1.5 H k. This external field is then reduced to zero magnitude in steps of 0.005 H k in the same manner as the hysteresis loop calculations. This procedure results in 'demagnetization limit' transitions; i.e. the narrowest transitions which could be written in the media with an ideal write head. By this method the behaviour of the media can be distinguished from write effects, and media performance can be properly assessed. 3. Results The behaviour of the films was investigated for three values of the exchange coupling parameter C* [5]. Values of C * = 0.025, 0.075 and 0.125 were cho-
0304-8853/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
376
ZJ. Miles, B.BA Middleton / Transition noise in thin-film media
•
!i:~
~ .....
.
.
.
.
.
?;i i Fig. 1. A pair of transitions spaced 1.29 I~m apart. The magnetizations are shaded to indicate the sign of the magnetization in the track direction.
sen, giving weak, moderate and strong exchange coupling between the grains, respectively. For the hysteresis calculations a sample of 2.5 × 2.0 p.m (3132 grains) was used. The films had squareness ( M r / M s) of 0.87, 0.88 and 0.9, with coercivities of 0.5, 0.38 and 0.34 x 105 A / m , respectively. Fox the transition calculations a sample of length 2.58 p~m (along the track) and width 7.15 p.m (across the track) with 11 520 grains was used. In all cases pairs of transitions spaced 1.29 p.m apart were generated so that there was no asymmetry at the boundaries. Eight transition pairs were simulated for each value of the exchange coupling strength, each of the eight simu-
CROSS tn
lations employing a different random sample of easy axes, giving 16 different transitions for each value of C*. An example transition pair for C* = 0.075 is shown in fig. 1, which shows typical variations in the nature of the transitions across the track. In this particular case the upper transition tends to have rather larger zig-zag structures than the lower one, and the transitions are closer towards the left-hand side, with a corresponding increased tendency for breakthrough between transitions. These variations arise from the random anisotropy of the grains of material and are the origins of noise. For tracks of reasonable width the effects are averaged out, so that the effects are small. This is
TRACK
AVERAGE
1.0
X X
"~"
0.5
0.0
'tI0 . . . .
115" x (um)
-0.5'
-i .0
Fig. 2. The transition profile along the track direction for the transition pair of fig. 1, with the fitted arctangent function.
J.J. Miles, B.K. Middleton / Transition noise in thin-film media demonstrated by the cross track average magnetization, which is plotted in fig. 2, showing a regular pair of transitions with surprisingly little noise. Also shown is a best fit arctangent series, which follows the actual transition shape extremely well. Using the cross track average magnetization profile, the output voltage waveform was then calculated using the reciprocity theorem [2], assuming a conventional Karlqvist-type head of gap = flying height a 0.25 I~m. For each pulse the peak height and position was accurately found using a quadratic fit to interpolate between a few computed voltage points (either five or six) in the near vicinity of the peak. For these samples the output voltage was computed at 2 nm intervals, so that the total distance over which fitting was performed was 10 nm, or approximately 4% of the replay gap. Thus fitting has no filtering effect on the output signal over this range because of the spatial filtering performed by the head over a much larger length scale, and the fit acts soley to interpolate and to reduce the number of voltage calculations required for accurate identification of peak position. The width at half height (PWs0) was then calculated directly from the computed replay waveform. The standard deviations of peak height, width and position were tlaen evaluated as measures of the transition noise using the 16 transitions for each value of C*. As expected, all the above noise parameters increase with increased exchange coupling between the grains. The noise was then evaluated in the same manner for narrower tracks, by computing the average magnetization across a central region of the sample with the appropriate width. For track widths (w) below 3.5 i~m it is possible to examine more than one independent track within each sample, and so the maximum possible number of independent transitions were considered in all cases to obtain the best estimates of the noise. The output voltages were normalised to unit track width to compensate for signal reduction as w is reduced, so that the calculated noise is a proper measure of signal to noise ratio. Track widths down to w = 0.25 Ixm were evaluated. The calculated noise values are summarised in figs. 3, 4 and 5, showing as log-log plots the effect of reducing w upon the standard deviation of replay pulse amplitude, width and position respectively. All noise parameters increase as w is reduced, as expected. Pulse amplitude and width variations arise from variations in the transition profile, and the transition profile is a cross track average of a random structure, with the amount of material contributing being proportional to w. Thus a simple statistical approach would predict a standard deviation dependence upon w -°'5.
377
E f f e c t of Track Width
g .~. ~
rn
1.0. 0.75
o ~ m
0.5 C* = 0.075 Ce = 0.025
*
0.25
®
' '-0'.5'''
gradient gradient
"01~
"
-0.555i -0.5889
'010'
' ' '0.~5 ....
015'
' ' '0.~5'
'
log ( Track Width (urn})
Fig. 3. The effect of tracl~ width upon amplitude modulation, showing least-squares fits to the data.
E f f e c t of Track Width
121
ffl
m Ca = 0,. 125 gradient'
--0.5228.
025
~
"
~
-
:o:o,7. . . . . . . . . . . . . -0.5
-0.25
0.0
0.25
%
0.5
0.75
log ( Track Width (urn))
Fig. 4. The effect of track width upon pulse width modulation, showing least-squares fits to the data.
Effect of Track Width ~ .~
1.0.
®
o
0.75
~
0.25'
mE) m
e, C* = 0 . 0 ~ i
i
I
-0.5
i
i
i
i
gradient: I
i
-0.~5
i
i
i
-0.8~3 l
0.0
i
i
® ~ i
i
#
0.25
i
i
i
i
I
0.5
i
i
i
i
i-i
i
0.75
log ( Track Width (um))
Fig. 5. The effect of track width upon timing jitter, showing least-squares fits to the data.
378
J.Z Miles, B.K~ Middleton / Transition noise in thin-film media
The calculated gradients are in good agreement, confirming that the simple statistical approach is a useful model for pulse amplitude/width modulation noise. The situation for timing jitter is less clear, with jitter varying as w -°'8. This gradient appears to be similar for all values of C*, and indicates that jitter noise increases more rapidly than expected as track width is reduced. For the moderately and strongly exchange-coupled films the overall gradients of the log-log plots are close to those for the weakly coupled films. However the gradients appear to decrease for very narrow tracks, with the change of behaviour occurring between track widths of 2.5 and 4 p.m for C* = 1.25 and between 1.5 and 1.8 t~m for C* = 0.075. The domain or vortex sizes in each case are approximately 0.5-1.5 I~m for C * = 0.125 and 0.2-0.6 ttm for C* = 0.075. This observation appears to indicate that where there is moderate or strong exchange coupling the domains or vortices are coupled strongly enough to act as distinct magnetic entities, and have a significant effect upon the gradient at track widths of approximately three times the feature size. However, since the limit values of the jitter are approximately 10 ns or 150 nm (comparable to the domain size), further work will be required to determine whether it is the track width that acts to limit jitter or whether there is an upper limit to the magnitude of the jitter determined by the displacement along the track; i.e. if in fact position jitter is simply limited to approximately the domain size regardless of track width effects. 4. Conclusions
Transition noise arising from variation in magnetization profile varies as w -°'5 as would be expected
from simple statistical considerations. Timing jitter appears to increase more rapidly than expected as track width is reduced, and this result requires further study. In extremely narrow tracks noise may not be as high as expected from a simple statistical approach, but in modem high-coercivity media with decoupled grains this is not likely to occur at practicable widths. These results relate to low or moderate densities with little interaction/correlation between adjacent transitions. It is known that noise increases as transitions interact, and it is not clear what effect track width would have on this process. In this study track edge noise has been neglected, and only on track noise is considered. This situation corresponds to the case where a narrow M - R read head is used with a wider inductive write head. For most other cases edge noise might be considered to be an additional component which is independent of track width.
This work was performed with the assistance of the University of Manchester, SERC and the EC CAMST initiative.
References
[1] J.J. Miles and B.K. Middleton, IEEE Trans. Magn. MAG27 (1991) 4954. [2] B.K. Middleton, in: Magnetic Recording Volume 1 - Technology, eds. C.D. Mee and E.D. Daniel (McGraw Hill, 1987) chap. 2. [3] J.J. Moon, L.R. Carley and R.R. Katti, 3. Appl. Phys. 63 (1988) 3254. [4] J.J. Miles and B.K. Middleton, J. Magn. Magn. Mater. 95 (1991) 99. [5] J.G. Zhu and H.N. Bertram, J. Appl. Phys. 63 (1988) 3248.