The potential of bit patterned media in shingled recording

Journal of Magnetism and Magnetic Materials 324 (2012) 314–320

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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm

Invited Paper

The potential of bit patterned media in shingled recording S.J. Greaves a,, H. Muraoka a, Y. Kanai b a b

RIEC, Tohoku University, Katahira 2-1-1, Aoba ku, Sendai 980-8577, Japan IEE, Niigata Institute of Technology, Kashiwazaki 945-1195, Japan

a r t i c l e i n f o

a b s t r a c t

Available online 21 December 2010

Shingled recording on continuous and bit patterned media (BPM) is compared. From a recording viewpoint, continuous media have the advantage due to the lack of a need to synchronise writing with dot position. For BPM the write windows at 4 Tbit/in2 are only a couple of nm across, requiring extremely tight manufacturing tolerances. In readback, BPM have the higher SNR over a wide range of areal densities due to the absence of transition noise and erase bands. Significant increases in areal density could be achieved using BPM, provided dot uniformity could be maintained. & 2010 Elsevier B.V. All rights reserved.

Keywords: Shingled recording Composite media Bit patterned media

1. Introduction The concept of shingled recording envisages writing overlapping tracks, leaving the track edge as a record of the written data [1]. Shingled recording can be applied to both continuous media and bit patterned media, each with its own advantages and disadvantages [2,3]. This paper will discuss the results of shingled recording simulations and will compare the performance of continuous media and BPM at areal densities of 2–4 Tbit/in2. The comparison can be split into two parts: writing and reading. When writing on a continuous medium it is not necessary to worry about the medium microstructure and a sequence of bits can be written anywhere on the disk and later recovered, provided the location of the bits is known. Each written bit extends over a number of grains in the medium and if one or two grains within the bit have the wrong polarity it is still possible to recover the original data. With BPM the location of the bits (dots) is pre-defined and cannot be changed. When writing on BPM it is essential that the correct information is written in the correct location. The switching of the head field must be tightly synchronised with the dot position, otherwise write errors will occur. From the point of view of readback it is BPM that have the advantage. In theory, BPM consist of arrays of regular, identical dots and the readback signal is free of noise, aside from contributions from adjacent tracks and neighbouring dots. In practice, BPM have distributions of size and position which increase noise. Continuous media suffer from transition noise and fluctuations in output signal due to irregular bit shapes and sizes. Such noise can be reduced by using media with smaller grains, but the need for thermal stability

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places a lower limit on the grain size. Therefore, as a rule, continuous media will have higher noise than BPM.

2. The models 2.1. The recording media The recording layers of the media were formed from exchangecoupled composite (ECC), dual layer materials consisting of magnetically hard and soft layers exchange-coupled together [4,5]. ECC grains can have improved thermal stability compared with a single phase grain with the same switching field. ECC grains can also exhibit a reduced dependence of the switching field on applied field angle. This is important in magnetic recording where the field from a write head is usually inclined at the track edges and trailing edges. The hard layer of the ECC grains had a thickness of 6 nm, saturation magnetisation, Ms, of 500 emu/cm3 and uniaxial anisotropy, Ku, of 22  106 erg/ cm3. The soft layer was 10 nm thick with Ms of 900 emu/cm3 and Ku of 1  106 erg/cm3. The media were modelled using 16 layers, each 1 nm thick. The exchange coupling between adjacent layers in the hard and soft phases, and at the interface between the hard and soft layers, was 10 erg/cm2. This implies that the hard and soft phases are strongly coupled, i.e. there is no exchange break layer between them. The layer thicknesses, Ms and Ku were the same for both the continuous media and the BPM. The continuous media were formed from weakly exchange-coupled discrete grains with an average size of 4.6 nm and an average pitch of 5.5 nm. Here, the grain area is the square of the grain size. The exchange coupling strength between neighbouring grains depended on the grain boundary thickness [6], but was 0.275 erg/cm2 for the average grain boundary thickness of 0.9 nm. The grain size distribution was 9%, Ms and Ku distributions were both 5% and the easy axis dispersion was 31.

S.J. Greaves et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 314–320

The BPM consisted of cylindrical dots arranged on the vertices of a square lattice with a fixed dot pitch and a dot diameter half of the dot pitch. Randomness was introduced into the BPM via distributions of dot size and position, characterised by standard deviations ss and sp, respectively. Images of portions of the continuous and BP media are shown in Fig. 1. The continuous medium in Fig. 1(a) has a preprogrammed pattern with a 17 nm bit length extending across the width of the medium and this was used as the initial state prior to writing tracks. The pre-programmed pattern represents an ideal magnetisation configuration that might be written by a head with an infinite head field gradient. Even if it were possible to realise such a state, transition noise would still be present in the readback waveform due to the irregularity of the transitions. The BPM shown in Fig. 1(b) has no dot size or position distribution and the only noise in the readback waveform will come from side reading of adjacent tracks.

2.2. The write head

design was essentially the same as that described in [2] and the air bearing surface (ABS) of the main pole had a base width of 70 nm and a length of 130 nm. The spacing between the ABS of the main pole and the surface of the recording layer (mag. spacing) was 5 nm, the recording layer thickness was 16 nm and there was a 1 nm nonmagnetic interlayer between the bottom of the recording layer and the soft magnetic underlayer (SUL). The head was shielded on the right and trailing edges and the gap between the shield and the main pole was 10 nm. Profiles of the field from the write head in the centre of the recording layer are shown in Fig. 2. The cross-track fields were evaluated along the trailing edge of the main pole and the downtrack fields were taken 20 nm to the right of the central axis of the main pole as it is the fields in this region that will write the track edges. Both the vertical component of the head field, Hz, and the effective head field, Heff, calculated using the angular variation of the switching field of a single grain, Hs ðyÞ, are shown. Heff was calculated using Heff ¼ jHhead j  Hs ð0Þ=Hs ðyÞ, where y is the angle of the resultant head field from the perpendicular axis. The grain switching field showed little dependence on applied field angle for angles from 0 to 201, hence Heff and Hz are similar in Fig. 2. The

200

200

190

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170

Down track (nm)

Down track (nm)

A write head with a triangular main pole was used for recording. The same head was used for continuous and BP media. The head

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110

100 100

315

100 120

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160

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Cross track (nm)

140

160

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Cross track (nm)

Fig. 1. Images of portions of the recording media. Left: a continuous medium with an average grain pitch of 5.5 nm. Right: A bit patterned medium with a dot pitch of 13 nm. (a) Continuous medium and (b) patterned medium.

18

18 Hz Heff

16

14

12

Hz, Heff (kOe)

Hz , Heff (kOe)

14

16

10 8 6

12 10 8 6

4

4

2

2

0 100

200

300

400

Cross-track position, x (nm)

500

Hz Heff

0 100

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500

Down-track position, y (nm)

Fig. 2. Cross-track and down-track profiles of the field from the write head in the centre of the recording layer. The schematic diagrams of the main pole ABS show where the profiles were taken. (a) Cross track and (b) down track.

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maximum gradients of Hz were 340 and 368 Oe/nm in the crosstrack and down-track directions. The maximum gradients of Heff were 361 and 392 Oe/nm. 2.3. The read head For the reading of recorded tracks, sensitivity functions of magneto-resistive (MR) heads were used. The head-medium spacing was the same as the write head (5 nm) and the width of the free layer was 14 nm, with a shield-to-shield spacing of 25 nm. In such narrow read heads, thermally induced fluctuations of the free layer magnetisation can make a large contribution to the total noise. Considering the amplitude of the readback signals, only around 20% of the surface area of the BPM used in these simulations consisted of magnetic material, compared with 70% for the continuous medium, and the output from the head was proportionately smaller as a result. It is possible to increase the size of the dots in the BPM to obtain larger readback signals, but doing this also increases magnetostatic interactions between dots. This results in an undesirable increase in the switching field distribution, further complicating the writing process. Thus, in general, the signals from BPM will be lower than those from a continuous medium. Thermal noise in the MR sensor was calculated by modelling the free layer as a 14 nm  6 nm  14 nm film discretised into 2 nm cubes. A cross-track bias field of 1 kOe was applied and the noise spectrum was calculated at 300 K in the absence of any stray fields from media. The frequency distribution of the thermal noise is shown in Fig. 3. The peak in the noise spectrum was at 6.85 GHz, with only about 20% of the total noise occurring at frequencies below 5 GHz. For a 4 Tbit/in2 patterned medium with a dot pitch of 12.7 nm and a read head velocity of 25 m/s, the maximum signal frequency would be slightly less than 1 GHz. A low-pass filter should, therefore, be able to remove the majority of the thermal noise. The inset to Fig. 3 shows the total amount of thermal noise present in the readback signal for various cut-off frequencies, fcut. For each point, all noise below fcut was included and all noise above fcut was excluded. The noise is expressed as the RMS value of the vertical component of the free layer magnetisation. To estimate the response of the free layer of the MR head to a medium, a micromagnetic simulation was performed in which the read head was passed over a section of continuous medium. In this simulation the magnetisation of the read head was calculated using micromagnetics, as described above, and the medium magnetisation was assumed to be constant. One half of the medium was magnetised up, the other half magnetised down. For this calculation

the medium had no grain boundaries and the transition between the regions magnetised up and down was perfectly straight. The output signal of the read head at each down-track position, Vm (y), was assumed to be equal to the vertical magnetisation of the free layer. Output signals were also calculated from the sensitivity function of the MR head using reciprocity and the same magnetisation pattern to obtain Vr (y). The influence of thermal noise in the MR sensor was added to the reciprocity calculation by comparing the amplitudes of the output signals calculated by the two methods. For the comparison, the output signals when the read head was over the centre of a saturated section of the medium were used. The thermal noise in the reciprocity calculation was then given as Nr ¼ Nm  Vr / Vm, where Nm is the integrated noise from the micromagnetic calculation.

3. Recording on continuous and BP media 3.1. Continuous media Shingled tracks were written on the continuous media with various track pitches from 13 to 25 nm. The signal to noise ratio (SNR) of the written tracks was evaluated with a 14 nm wide MR read head and some results are shown in Fig. 4 for the case when the read head was on-track. The SNR for a written track of frequency f was calculated using Sf/Nf; if SNR is calculated using Siso, the signal from an isolated transition, the resulting SNR values can be much larger, particularly at high density [7]. The ‘‘As-written’’ data in Fig. 4 were taken from unshingled tracks immediately after writing and a track pitch equal to the width of the ABS (70 nm) has been assumed, although the actual written track width was somewhat wider than this. As might be expected, the narrower the tracks become, the smaller the SNR at any given linear density. The data points shown in Fig. 4 are the average of at least ten trials and the error bars represent one standard deviation of the SNR. The data were fitted with linear curves weighted to the standard deviation at each point. Using the fitted curves the maximum linear density for each shingled track pitch was calculated for a range of SNR values. From this, the maximum areal density can be obtained and these data are shown in Fig. 5. If the minimum usable SNR were 0 dB, the areal density is predicted to increase from around 1 Tbit/in2 in a non-shingled system to 3 Tbit/in2 in a shingled drive with a 13 nm track pitch. The amount of gain depends on the minimum SNR that can be tolerated. If 6 dB of SNR is required, the maximum areal density drops to 2 Tbit/in2. Figs. 4 and 5 assume that the read head is able to follow the written tracks without deviation. If the read head is offset from the

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30 14 nm × 6 nm × 14 nm free layer

α = 0.02

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SNR (Sf / Nf ) (dB)

Hx = 1 kOe

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TP = 13 nm TP = 15 nm TP = 18 nm TP = 25 nm As-written

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T = 300 K

Integrated noise (〈Mz〉 / Ms)

Noise (〈Mz〉 / Ms)

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0

-10

〈P〉 = 5.47 nm 14 nm wide MR read head

0.00 0

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20

Frequency (GHz) Fig. 3. Noise spectrum from free layer of MR sensor in the absence of a medium. Cross-track bias field ¼1 kOe, T¼ 300 K, a ¼ 0:02. Inset: integrated noise versus lowpass filter cut-off frequency, fcut.

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1600 1200 Linear density (kfci)

2000

2400

Fig. 4. SNR vs. linear density for continuous recording media with various shingled track pitches. /PS ¼ average grain pitch.

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3.2. Write windows for BPM When recording on BPM there must be close synchronisation between the switching of the head field and the position of the dots 3.5 SNR = 0 dB SNR = 2 dB SNR = 4 dB SNR = 6 dB SNR = 8 dB SNR = 10 dB

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+2.2 Tbit/in2

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〈P〉 = 5.47 nm 14 nm wide MR read head

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80

Track pitch (nm) Fig. 5. Estimated maximum areal density vs. shingled track pitch for a range of minimum SNR values.

Table 1 Areal densities (in Tbit/in2) for read head track misregistration from zero to 6 nm. Target SNR ¼0 dB. Track pitch

13 nm

15 nm

18 nm

25 nm

0 nm 2 nm 4 nm 6 nm

3.10 3.05 2.86 2.60

2.96 2.87 2.71 2.48

2.63 2.53 2.40 2.21

2.24 2.19 2.11 1.98

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−30

0 −40 −35 −30 −25 −20 Cross track offset, x (nm)

0.9

5 Switching probability

Down track offset, y (nm)

5

1

10

Down track offset, y (nm)

Areal density (Tbit/in2)

3

being written. The write window is defined as the range of initial write head positions for which a dot could be successfully written without also overwriting dots in the adjacent track or previously written dots. Large write windows permit broader distributions of magnetic parameters and dot positions to be tolerated. To calculate the write windows for BPM, recording simulations were carried out by writing single bits. The head velocity was 25 m/s and the distance the head moved along the down-track axis during the writing of a bit was equal to the dot pitch. The write windows were calculated from switching footprints such as the one shown in Fig. 6(a). The figure shows the probability of a target dot being switched for a range of initial write head positions. The centre of the target dot is at (0,0) and the position of the head is defined as the centre of the trailing edge of the main pole at the start of the simulation. For recording, the boundaries of the regions where the switching probability, P, is equal to unity and P¼0 are of the most interest. A program was developed to search for these boundary regions and therefore the number of trials at each point varied. The switching footprint in Fig. 6(a) shows the situation after a maximum of 200 trials at some points. In Fig. 6(a) the target dot was not switched when the initial position of the write head was more than 37 nm to the left of the dot, or more than 7 nm in front of the dot as the write field was too small to switch the dot. When the dot was underneath the main pole the probability of switching was unity after 200 trials. To calculate the write window the switching footprint is replotted in Fig. 6(b) showing two contours drawn along the boundaries of the regions where the switching probability, P, was zero and unity. A line is then drawn along the down-track axis at a tangent to the P¼0 contour and a second line is drawn TP to the right of this line. In this example TP is the track pitch, which is 13 nm and the second line is at x ¼  24 nm. If the write head is initially to the right of the x¼  24 nm line, adjacent track erasure (ATE) may occur since the adjacent track dots will fall inside the P¼0 contour. Therefore, to avoid ATE the write head must initially be to the left of the x ¼ 24 nm line. Next, the P¼0 contour is replotted after the transform y¼y  TP. To avoid overwriting previously written dots the initial position of the write head must be above the replotted P¼0 contour. The write window is, therefore, the region bounded by the P ¼1 contour, the replotted P¼0 contour and the line at x ¼ 24 nm. If the initial position of the write head lies in this region there will be no ATE and no erasure of previously written dots.

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0.3

Switching probability

track centre (track misregistration), or the centre of the written track fluctuates due to cross-track motion of the write head during recording, the SNR will be reduced. Table 1 shows the predicted maximum areal densities for read head offsets from the track centre from zero to 6 nm. In the case that the write head position fluctuates during recording the areal densities should be lower than those shown in Table 1 as tracks may be squeezed and partially erased, lowering the SNR.

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Fig. 6. Footprint showing dot switching probabilities for a range of initial write head positions (left) and write window derived from the footprint (right). Dot pitch¼ 13 nm, Ku ¼ 22  106 erg/cm3. (a) Footprint. (b) Write window.

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3.3. Effect of skew, density and Ku dispersion

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Down-track position (nm)

Skew = 0° Skew = 15° 0

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σp = 1 nm2

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Cross-track position (nm) Fig. 7. Write windows for a 15 nm dot pitch with Ku ¼22  106 erg/cm3.

-5

Ku = 19.8×106 erg/cm3 Down-track position (nm)

Write windows for a 15 nm dot pitch, an areal density of 2.87 Tbit/ in2, are shown in Fig. 7. The two values of skew refer to the angle of the write head during recording. For zero skew the trailing edge of the main pole lay along the cross-track axis. For 151 skew the right edge of the main pole lay along the down-track axis. When the skew was zero the width of the write window was about 9 nm, the length was 10 nm and the area was 88 nm2. The effect of skew was mainly to reduce the width of the write window to around 5.5 nm whilst the length was almost unchanged, except near the left edge of the write window. The area was reduced by 30% to 61 nm2. For the continuous media with a track pitch of 15 nm, increasing the skew from zero to 151 reduced the maximum areal density from 2.96 to 2.39 Tbit/in2 as increased skew resulted in wider erase bands between shingled tracks. The points inside the write window for zero skew in Fig. 7 represent the possible distributions of dot centres for a dot position distribution with sp ¼ 1 nm. There are 10 000 points in total, all of which lie within the write window. However, the outer edge of the position distribution is less than 1 nm from the edge of the write window in some places. This means that the switching of the head field must be controlled to better that 1/15th of the dot pitch, or with an accuracy of better than 0.04 ns (the time to write one bit is 0.6 ns). If sp were reduced, the constraints on the switching of the head field could be relaxed and vice-versa. Note that this calculation uses a single value of Ku and only considers head and dot position variations: if there is a distribution of Ku values the tolerances become tighter, as discussed below. Write windows for BPM with a dot pitch of 13 nm are shown in Fig. 8. Suppose the BPM has dots with an average value of Ku of 22  106 erg/cm3 and a Ku dispersion of 710%. The position of the write window depends on the dot Ku: variations in Ku shift the write window up or down the track where the head field is larger/ smaller. The amount of displacement of the write window is thus explicitly related to the head field gradient, with higher gradients resulting in less displacement. The write window for Ku ¼22  106 erg/cm3 was about 7 nm long and 5 nm wide with an area of 44 nm2, less than half the area of the write window for a BPM medium with a 15 nm dot pitch. The write windows for Ku 710% are also shown in Fig. 8. The area of the write windows did not change appreciably over the Ku range studied here, but if Ku becomes too large the head will be unable to write on the medium and the write window will shrink. For a medium with a Ku dispersion it is the intersection of the write windows for all Ku values that determines the write window for the system as a whole. As can be seen in Fig. 8, the common area of the three write windows was 1.7 nm2 in a region about 1 nm long and 1.5 nm wide.

Ku = 22.0×106 erg/cm3 0

Ku = 24.2×106 erg/cm3

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Fig. 8. Write windows for a 13 nm dot pitch with various Ku. Skew ¼01.

In this example, even a dot position distribution of sp ¼ 0:33 nm would be insufficient to ensure that 10000 dots remain within the write window and many dots fall outside the write window for a 10% dispersion of Ku. The write windows shown in Fig. 8 were calculated with a maximum of 200 trials at each point: as the number of trials increases the area of the windows shrinks and it is likely that the common area of the three windows would disappear if the number of trials were increased to e.g. 1000, although time constraints mean that this cannot be confirmed.

4. Readback 4.1. Comparison of continuous and BPM media To compare the readback response of continuous and BP media both pre-programmed tracks and the results of LLG simulations were used. For the BPM, an alternating up/down magnetisation pattern was programmed into dots along a central track, whilst dots in other tracks were randomly magnetised up or down. The areal density was varied by changing the dot pitch, which was the same in the cross-track and down-track directions, and keeping the dot diameter equal to half of the dot pitch. For the continuous media, target tracks were programmed with a track width equal to the bit length, giving a bit aspect ratio (BAR) of unity. Tracks with bit lengths of 31 and 11 nm were programmed on the left and right sides of the target track, respectively; the remainder of the medium was randomly magnetised up/down. Additional data were obtained from the LLG recording simulations, using the fitted curves in Fig. 4 to find the SNR values when the bit length was equal to the track pitch. Readback waveforms were calculated using reciprocity and the sensitivity function of a MR head with a 14 nm wide sensor and a 25 nm shield-to-shield spacing. Fig. 9 shows SNR versus areal density for both media. A 5% distribution of Ms values was introduced from dot to dot or grain to grain, in line with the LLG simulations. The ‘‘Continuous: Ideal’’ data are the results for pre-programmed tracks and can be considered equivalent to recording with a head with an infinite field gradient at the track and trailing edges. At 2 Tbit/in2 the difference in SNR between the LLG data and the ‘‘Ideal’’ data was 6 dB. For the same SNR, the ‘‘Ideal’’ data had an areal density about 60% higher than the LLG data. Two sets of data for BPM are shown: one for a medium with no distributions of dot size or positions, the other with distributions of dot size (diameter), ss, and position, sp. The 8.7% dot size distribution was a Gaussian distribution and was the same as the grain size distribution in the continuous medium. The 1 nm position distribution was also a Gaussian distribution and was equal to the average

S.J. Greaves et al. / Journal of Magnetism and Magnetic Materials 324 (2012) 314–320

40

20 Continuous: Ideal Continuous: LLG BPM, σs = 0, σp = 0 BPM, σs = 8.7%, σp = 1 nm

15 SNR (Sf / Nf) (dB)

30 SNR (Sf / Nf) (dB)

319

20

10

10 5 +2 Tbit/in2 0

Cont., fcut = 0 BPM, fcut = 0 Cont., fcut = 2 GHz BPM, fcut = 2 GHz Cont., fcut = ∞ BPM, fcut = ∞

-5

σMs = 5%

0

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14 nm wide MR read head

σMs = 5% 14 nm wide MR read head

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-10 0

1

2 Areal density (Tbit/in2)

3

4

Fig. 9. Comparison of SNR for continuous media and BPM. Bit length ¼track pitch.

0

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2 Areal density (Tbit/in2)

3

4

Fig. 11. Comparison of SNR for continuous media (LLG) and BPM (ss ¼ 8:7%, sp ¼ 1 nm). Bit length¼ track pitch. Includes thermal noise in the read sensor at 300 K . fcut ¼low-pass filter noise cut-off frequency.

0.6

Signal (arb. units)

the ratio of the continuous signal to the BPM signal was less, mainly due to the fact that the width of the read head was constant and the larger BPM dots occupied more of the highest sensitivity region under the MR head. BPM size and position distributions only reduced the readback signal by about 2% for ss ¼ 8:7% and sp ¼ 1 nm, but the noise was significantly increased.

14 nm wide MR read head σMs = 5%

0.5 0.4 0.3

4.2. Effect of thermal noise in the MR sensor

0.2 Continuous: Ideal Continuous: LLG BPM, σs = 0, σp = 0 BPM, σs = 8.7%, σp = 1 nm

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Fig. 10. Comparison of output signals for continuous media and BPM. Bit length ¼ track pitch.

displacement of the seed points used to generate the grains in the continuous medium. However, the continuous media grains were represented by Voronoi cells and the seed point displacement was a uniform, not a Gaussian distribution. With no size and position distributions the BPM SNR was 14 dB higher than that of the ‘‘Ideal’’ continuous medium. With dispersions, the BPM SNR exceeded that of the ‘‘Ideal’’ continuous medium when the areal density was greater than 1.4 Tbit/in2 and was higher than the LLG data when the areal density was over 0.7 Tbit/in2. Given that current demonstrations of magnetic recording have achieved areal densities higher than 0.7 Tbit/in2 [8], if BPM can be fabricated and data correctly recorded it would appear that BPM have an advantage over continuous media, even at today’s areal densities. Although the SNR values for BPM compare favourably with those of the continuous medium, the amplitude of the readback signal should also be considered. In these examples the surface area of the BPM is mostly non-magnetic material and the readback signals may be expected to be lower than those from continuous media. Here, ‘‘signal’’ refers to the zero-peak amplitude of the calculated readback waveforms. Fig. 10 shows the calculated signals from continuous and BP media for various track pitches and bit lengths, where the track pitch equals the bit length. For a 13 nm track pitch the signal from the ideal continuous medium was more than double that of the BPM. For the continuous media tracks recorded by the LLG simulation the signal was only 45% larger than the BPM signal, the result of increased transition jitter and some grains within bits being incorrectly recorded. At larger track pitches

The difference in readback signals among the continuous and BP media leads to increased sensitivity to thermal noise in the MR sensor for BPM. Using the noise spectrum from Fig. 3 and appropriately scaling the signal and noise calculated from reciprocity to the MR head output from an isolated transition, the SNR in the presence of thermal noise was calculated. An ideal low-pass filter was assumed which removed all noise above a frequency fcut and the results for three values of fcut are shown in Fig. 11. The data for fcut ¼0 are the same as those in Fig. 9 and assume no thermal noise in the sensor. Under these conditions the BPM SNR was greater than that of the continuous medium over almost all of the range of areal densities investigated. When fcut was increased to 2 GHz, which is sufficient to allow signals from areal densities up to 4 Tbit/in2 at a velocity of 25 m/s to reach the detector, the SNR of the continuous medium was almost unchanged. This was because the continuous medium had higher signal and medium noise than the BPM and the extra thermal noise was relatively insignificant. The SNR of BPM dropped by up to 4 dB, depending on the areal density, when thermal noise up to 2 GHz was added. Nevertheless, the BPM SNR remained greater than the continuous medium SNR over most of the areal density range. If the SNR of the continuous medium at 2 Tbit/in2 is used as a guide, a transition to BPM would allow the areal density to be doubled to 4 Tbit/in2 whilst maintaining the same SNR. When all of the thermal noise was included (fcut ¼ 1) the continuous medium had the higher SNR, although the difference between the two media was at most 1.5 dB. In this case thermal noise dominates the system and the higher continuous medium signal gives higher SNR. This is not a particularly realistic scenario as much of the high frequency noise would be attenuated before it reached the detector.

5. Conclusions Continuous media are easy to write, in the sense that switching of the head field does not need to take account of grain positions, but the SNR is likely to be lower than BPM when reading back

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written data. For continuous media, control of the erase band width and grain size are the keys to improved performance. In contrast, it is difficult to write an arbitrary data sequence on BPM due to synchronisation issues. From the viewpoint of readback, BPM readback signals contain less noise due to the absence of irregular grain boundaries and erase bands. However, the generally lower amplitude readback signals from BPM dots requires that attention be paid to read sensor noise. The maximum head field gradients of around 370 Oe/nm in the centre of the recording layer would be inadequate for recording on BPM at 3.8 Tbit/in2, even if perfect BPM are assumed with no size or position distributions, as the write window was only about 2 nm across. The data show that a transition from continuous media to BPM may allow the areal density to be doubled from 2 to 4 Tbit/in2. However, the increased cost and complexity associated with manufacturing and recording on BPM will ultimately determine whether this gain is worthwhile.

Acknowledgments The authors wish to acknowledge the financial support of the Ministry of Education, Culture, Sports, Science and Technology

(MEXT) and the Storage Research Consortium (SRC). Some of the results in this paper were obtained using the resources of the Cyberscience Centre, Tohoku University.

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