perpendicular recording: the promise and the problems

Journal of Magnetism and Magnetic Materials 235 (2001) 1–9

Invited paper

Perpendicular recording: the promise and the problems

Roger Wooda,*, Yoshiaki Sonobeb, Zhen Jinc, Bruce Wilsonb

a IBM Storage Technology Division, CUY/0282, 5600 Cottle Road, San Jose, CA 95193, USAb IBM Almaden Research Center, San Jose, CA, USA

cCenter for Magnetic Recording Research, UC, San Diego, CA, USA

Abstract

Perpendicular recording has long been advocated as a means of achieving the highest areal densities. In particular, inthe context of the ‘superparamagnetic limit’, perpendicular recording with a soft underlayer promises several keyadvantages. These advantages include a higher coercivity, thicker media that should permit smaller diameter grains and

higher signal-to-noise ratio. Also, the sharper edge-writing will facilitate recording at very high track densities (lower bitaspect ratio). Recent demonstrations of the technology have shown densities comparable with the highest densitiesreported for longitudinal recording. This paper further examines the promise that perpendicular recording will deliveran increase in areal density two to eight times higher than that achievable with longitudinal recording. There are a

number of outstanding issues but the key challenge is to create a low-noise medium with a coercivity that is high and ismuch larger than the remanent magnetization. r 2001 Elsevier Science B.V. All rights reserved.

Keywords: Perpendicular recording; Areal density; Head fields; Granular media; Off-track performance

1. Introduction

For the past 25 years, perpendicular recordinghas been advocated as a means of achieving thehighest areal densities. However, despite consider-able research and significant development effort,there have been no successful products made usingperpendicular technology. Now suddenly, with the‘super-paramagnetic limit’ looming, there is muchrenewed interest in this technology as a means ofextending areal densities. Recent demonstrationsof the technology [1,2] boasted densities arecomparable with the highest densities reportedfor longitudinal recording. This paper will further

examine the promise that perpendicular recordingwill deliver an increase in areal density betweentwo to eight times higher than that achievable withlongitudinal recording [3–5]. Against this weacknowledge the challenge of achieving the desiredmedia characteristics and of dealing with the manysystems issues that arise.

2. The promise and the problems

In the environment where the areal density islimited by the grain-size in the recording mediumas dictated by thermal stability issues, perpendi-cular recording promises several key advantages:

1. A pole-head/soft-underlayer configuration cangive about twice the field that a ring head

*Corresponding author. Tel.: +1-408-256-4131; fax: +1-

408-256-263.

E-mail address: [email protected] (R. Wood).

0304-8853/01/$ - see front matter r 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 2 9 0 - 6

produces. Higher head fields allow the use ofmedia with high coercivity and high anisotropyenergy density, Ku: This in turn allows mediawith ‘grains’ (switching units) that have smallervolume and can thus support higher arealdensities.

2. Sharp transitions can be supported on relativelythick media. For media with coercivity muchgreater than saturation magnetization and withhigh intrinsic squareness, the demagnetizingfields do not necessarily act to broaden thetransitions during writing and storage. Also, thehead fields and field gradients are bettermaintained into the depth of the medium andin the vicinity of the soft-underlayer. Thickermedia allows more grains per unit area for agiven grain volume, and hence higher arealdensity.

3. The edge effects during writing are wellconfined. The field configuration off the edgeof the head is similar to that in the down-trackdirection. The fact that there is a sharp track-edge with minimal erase band will facilitate thelow bit aspect ratios anticipated for the highestareal densities

4. Short wavelengths are relatively easy towrite and to maintain in perpendicular media.This is advantageous because of the difficulty inmaintaining strong writing fields at high fre-quencies and because of the severe short-wavelength losses that have to be overcomeduring readback. During writing, for example,the effects of the demagnetizing fields are suchas to increase the transition separation in anisolated dibit and thus compensate for poorfield risetime.

5. Perpendicular media can naturally have astrong uniaxial orientation (longitudinalmedia tend to have an orientation that israndom in-plane). This should lead to a tightswitching-field distribution and sharperwritten transitions. There should also behigher signals and lower noise in well orientedmedia.

The key challenge is the creation of the newrecording medium with the required properties.However, there are a number of issues identified

that are of concern. Summarizing the key problemareas:

1. A new medium is required that is significantlymore complex than the current media. Not onlydo we have to perfect a very high coercivity,low-noise recording layer, but we also have tocreate a soft underlayer that is effective in writingand reading and yet does not contribute sig-nificant noise or otherwise degrade the system.

2. A pole write head is preferred. It is expected tobe similar in complexity to a thin-film ring headand may in some respects be easier to manu-facture. Head field gradients are poorer thanthose for the horizontal component of a ringhead. Also, there are issues regarding side-writing especially in the context of head-skewfrom a rotary actuator.

3. A conventional dual-shielded MR head, whenused with a soft underlayer, produces a wave-form looking much like the integral of thesignal from longitudinal media. The ‘resolution’of this system is intrinsically quite low, raisingconcerns about the dynamic range and linearityrequired of the sensor.

4. Since the readback response is dramaticallydifferent, a new equalization strategy is requiredand there may be changes required in thedetector target response. Several researchers havesuggested that a modulation code that strictlylimits run-lengths and/or Dc-content could helpto reduce the peak demagnetizing fields.

5. Unless Hc � 4pMs is large, the magnetization inthe medium will be susceptible to disturbancesfrom a variety of mechanisms (as well asthermal decay). In particular, stray ambientfields that get strongly concentrated in the gapbetween the soft underlayer and the read/writehead structures will cause signal erasure.Similarly, there is a risk that the fieldsassociated with the return pole will interferewith the magnetization on adjacent tracks.

3. Head fields and field-gradients

The maximum field generated in a pole/soft-underlayer configuration can be approximately

R. Wood et al. / Journal of Magnetism and Magnetic Materials 235 (2001) 1–92

75% higher than that generated by a conventionalring head. Fig. 1 shows the fields from a conformalmapping solution (assuming that a similar ‘deepgap field’ can be generated in either case). Thehigher field from the pole-head configuration isbelieved to provide one of the primary advantagesof perpendicular recording.In addition to the absolute value of the fields,

the field gradients are also critically important,since these help to determine the sharpness of therecorded transitions. The normalized field gradientfor the pole head, QP ¼ ðdHy=dxÞ=ðHy=dÞ; issomewhat lower than that for the ring head, QR ¼ðdHx=dxÞ=ðHx=dÞ; where d is the distance from thehead. The horizontal field component from a ringhead dies away particularly rapidly over thetrailing pole. However, in longitudinal recording,the vertical field also plays a small role. Assumingthat the internal vertical field is reduced by asusceptibility of approximately unity, the effectiveswitching field becomes Heff ¼ OfH2

x þ ðHy=2Þ2g:

Finally, taking the highest coercivity to be 75% ofthe maximum field (since we are interested inwriting the highest coercivity), we estimate thenormalized gradients to be QP ¼ 0:39 for perpen-dicular with the pole head vs. QR ¼ 0:51 forlongitudinal with the ring head.An alternate view of these same fields is shown

in Fig. 2. Here the fields are plotted as a trajectory

in polar form. Besides the larger magnitude, astriking feature of the pole-head/soft-underlayerconfiguration is that the orientation of the headfield remains close to perpendicular during theentire write process. Onto this figure is super-imposed the switching astroid for a Stoner–Wohlfarth particle (interpreted as either long-itudinally or perpendicularly oriented, as appro-priate). From this perspective we see that thecoercivity that can be switched with a pole-head/soft underlayer is onlyB15% greater than that fora ring head with a highly oriented longitudinalmedium.Further detracting from the advantage of

perpendicular recording is the inherent shearingof the B–H loop. The field required to switch the‘last grain’ is Hc þ ð1�NdÞMs; where Nd is thedemagnetizing factor for the shape of an isolatedgrain (assuming 100% packing factor). In long-itudinal recording, the corresponding effect tendsto tighten the switching field distribution.In practice, it does seem possible to write

considerably higher coercivity with perpendicularrecording [6]. Ultimately, the advantages in Hc willonly be determined as more experiments areconducted and as we gain a better understandingof the writing process.

Fig. 1. Comparison of fields for a pole-head/soft-underlayer

configuration and a conventional ring head (dist. from head,

d ¼ 1; pole to soft-underlayer=1.5d, gap of ring-head=3d).

The field from a pole head is 75% greater.

Fig. 2. Head fields from Fig. 1 replotted in polar form. The

switching astroid of a Stoner–Wohlfarth particle is super-

imposed. This picture implies that a pole head has an advantage

of only B15% in coercivity that can be written.

R. Wood et al. / Journal of Magnetism and Magnetic Materials 235 (2001) 1–9 3

4. Thermal stability

Higher head fields imply higher anisotropyenergy density Ku in the medium. However,thermal stability is enhanced only if the mediumhas an appropriate level of magnetization. Theenergy required to reverse the magnetization in anideal Stoner–Wohlfarth grain in the presence of asmall demagnetizing field is [7]:

EbDm0½MsHk=2�MsHdðcos yþ sin yÞVg ð1Þ

where Ku ¼MsHk=2 is the anisotropy energydensity, Hd the demagnetizing field acting at angley; Vg the effective grain volumeSince the demagnetizing field can be expressed

as a demagnetization factor multiplied by themagnetization, Hd ¼ NmMs; we find that there is adistinct maximum in energy barrier as a functionof Ms [4]. Depending on the values assumed forthe angles and demagnetizing factor (say Hc ¼Hk=2; NdD1) we find that the energy barriermaximizes when Ms is only 1/2–1/3 of Hc (in SIunits). Note, this is in sharp contrast to recent highareal density demonstrations [1,2] for whichHc=MsD1: Low values of Hc=Ms lead to excessivedemagnetization fields reducing stability and leav-ing the medium susceptible to various inadvertenterasure mechanisms.

5. Transition widths

Using a simple Williams–Comstock formulationwhere perfect squareness, S ¼ 1; is assumed, wecompare the transition parameters that can beachieved for longitudinal and perpendicular re-cording. The demagnetizing field gradient at thetransition center is assumed equal and opposite tothe head field gradient, dHd=dx ¼ �dHh=dx: Forlongitudinal and perpendicular recording we haverespectively (SI units):

HdL ¼Msð2=pÞftan�1 ðx=aÞ � tan�1 ½x=ðaþ t=2Þg

HdP ¼Msð2=pÞftan�1½x=ðaþt=2Þ

þtan�1½x=ðaþ 3t=2Þg;

where a is the arctangent transition parameter, t isthe medium thickness, with no spacing betweenmedium and soft-underlayerEquating field gradients:

QLHc=ðd þ t=2Þ ¼Msð2=pÞfðt=2Þ=½ðaÞðaþ t=2Þg;

QPHc=ðd þ t=2Þ

¼Msð2=pÞfðaþ tÞ=½ðaþ t=2Þðaþ 3t=2Þg;

giving aL ¼O½2lLðt=4Þ þ ðt=4Þ2 � t=4; aP ¼ ðlP=2Þf1þO½1þ ðt=lPÞ

2g � t; where l ¼ ðMs=HcÞ ð2=pÞðd þ t=2Þ=Q:We note (in contrast to longitudinal recording)

that, if

Hc=Ms > ð4=3pÞð1þ 2d=tÞ=Qp

then the worst-case demagnetizing field gradient(a ¼ 0) is lower than the head field gradient and,according to this simple theory, a sharp transitioncan be written.Fig. 3 shows calculated ‘a-parameters’ compar-

ing perpendicular and longitudinal recording. Forthe parameters shown, it is clear that perpendi-cular recording has a considerable advantage if ahigh ratio of Hc=MsD3 can be maintained(reinforcing the comments in the preceding sec-tion).

Fig. 3. Transition width for perpendicular and longitudinal

systems is critically affected by Hc=Ms: For high Hc=Ms;transition sharpness in perpendicular media is not limited

by demagnetizing fields. Field configuration as in Fig. 1,

QL ¼ 0:51; QP ¼ 0:39; S ¼ 1; media thickness=1, distance

to midplane, d ¼ 1:


6. Media: granular vs. multilayer

Perpendicular media should provide high mediaSNR (small grains), high coercivity, and a highratio of Hc=Ms (or equivalently, a high ‘nucleationfield’Fthis being the minimum field required tocause any significant demagnetization). Twooptions are discussed widely in the literature:granular (CoCr-type) media and ‘continuous’multi-layer media (typified by Co/Pd multilayers).The former exhibits good SNR and has beenused in the recent high areal density demonstra-tions. Its disadvantage lies in the difficulty ofobtaining a high value for Hc and a high ratio ofHc=Ms: So far, this media shows no advantageover longitudinal media and shows some suscept-ibility to thermal decay. In contrast, continuousmultilayer systems are eminently tunable withrespect to parameters such as Hc; Ms; and S;but have not demonstrated such good SNR. Thetwo categories of media are well illustrated in Ref.[8] by Ouchi.A recent suggestion has been to try to combine

these two media approaches. A granular CoCr

based medium is first deposited. On top of this isbuilt up a multilayer Co/(Pd,Pt) structure. Thisstructure is referred to as CGC media (CoupledGranular and Continuous), as shown in Fig. 4(a).Typical Kerr loop of a CGC medium is shown inFig. 4(b), as compared with a granular CoCrPtmedium and a multilayer Co/Pt medium. A CGCmedium with a large nucleation field, Hn; and asmall saturation field, Hs; shows promise forthermal stability and writeability. Simulationsshow that the properties of the multilayer filmcan be tuned to provide an appropriate amount ofexchange coupling [9]. Small amounts of exchangecoupling improve the loop shape and appear toinhibit thermal decay by preventing grain reversalsin DC magnetized regions. Experimental work hasbeen conducted that confirms the improvedstability but more work is needed to furtherimprove SNR [10].

7. Readback responses

Readback is generally assumed to be accom-plished using a conventional double-shieldedmagneto-resistive head. However, the readbackresponses for conventional longitudinal, single-layer perpendicular, and 2-layer perpendicular(with soft underlayer) are dramatically different.The readback responses for the three different

recording configurations are obtained using ananalytic 2-D frequency-domain approximation.Following Potter [11] and Ruigrok [12], we obtainan expression for the isolated transition response,PðkÞ; that factors conveniently in the frequencydomain:

PðkÞ ¼ fjk sinhðkðdsh � dÞ � jyþ gsÞ=

sinhðkdsh þ ðgs þ ghÞÞg

f2 sinhðkd=2Þ=kdg

fMrdðp2ka=4Þ=sinhðp2ka=4Þg

feh sinðkg=2Þsinðkðgþ tÞ=2Þ=

½ðkg=2Þðkðgþ tÞ=2Þgf2=jkg;

where j ¼ O� 1; k is the wavenumber, d thespacing from head to mid-plane of medium, dsh isspacing from head to soft underlayer, y is the angle

Fig. 4. (a) Structure of CGC medium, (b) typical Kerr loop of

CGC medium, as compared with a granular medium and a

multilayer Co/Pt medium.


of magnetization (y ¼ 0 is longitudinal)

gs ¼ �ð1=2Þlnððms � 1Þ=ðms þ 1ÞÞ;

where ms is permeability of the soft underlayer

gh ¼ �ð1=2Þlnððmh � 1Þ=ðmh þ 1ÞÞ;

where mh is permeability of the head shields, d themedia thickness, Mr the remanent magnetizationof the medium, a the transition parameter for ahyperbolic arctangent, transition, tanhð2x=paÞ), ehthe readback ‘efficiency’ in terms of output perunit magnetization in the medium, g the gapbetween the MR element and the shield, t thethickness of the MR element.The five consecutive factors above can be

thought of as representing: an elementary responsefunction; a thickness ‘loss’; the writing resolution(for a tanhð2x=paÞ transition), the MR Potter-typereadback response, and finally an isolated transi-tion.Fig. 5 shows the readback responses for the

three different configurations where the transition,parameter (a ¼ 1), media-thickness (d ¼ 1), read-back gap (g ¼ t ¼ g ¼ 1), and spacing to themedia mid-plane (d ¼ 1) are all held constant.Starting with longitudinal recording, a rotation ofthe magnetization to perpendicular does notchange the magnitude of the frequency responsebut does have a dramatic effect on the phase andon the transition response in the spatial-domain(time-domain). Bringing in a soft underlayer(m ¼ 100) roughly doubles the sensitivity of thehead to the perpendicular magnetization, thoughonly at relatively long wavelengths. Larger signalsfrom the medium are, of course, desirable,particularly in terms of signal to head-noise. Thetransition response now takes the form of a stepresponse rather than an isolated pulse. Themagnitude ratio between the largest readbacksignals and the short-wavelength response isgreatest for 2-layer perpendicular recording. Thisis an issue with respect to the dynamic range of thesensor and ultimately to the signal-to-head-noiseand the head linearity. Fig. 6 plots the familiar‘roll-off’ curve for the three configurations andhighlights the relatively poor resolution character-istic of perpendicular recording with a soft under-layer.

Fig. 5. Readback responses in the frequency and spatial or time

domains for three different recording configurations all with the

same media thickness. Note the increased long wavelength

response of the perpendicular system with soft underlayer

(2-layer).

Fig. 6. ‘Roll-off’ curves illustrating the relatively poor resolu-

tion of perpendicular recording with soft underlayer. (Normal-

ized by maximum amplitude).


8. Systems issues

Many of the systems issues have been discussedabove. In particular, there are dramatic differencesin the appearance of readback waveforms and inthe nature of the sidewriting/sidereading phenom-ena.Although readback waveforms from perpendi-

cular recording do look dramatically different, thebasic techniques for equalization and detection arewell understood. Current equalizers are adequatealthough there may be practical issues such asbuilt-in constraints on tap values. Also, no bigchanges in precompensation are expected. Non-linear transition-shift (NLTS) is generally small inperpendicular media since magnetostatic effectsoppose risetime effects. Perpendicular recordingwith a soft underlayer does have much strongerlong wavelength content and several researchershave suggested alternate target responses such asð1þDÞn that would better match the spectralcontent of the signal [13]. However, the advantagesof changing the target may be quite limited if weremain dominated by media noise (which is alsomuch stronger at long wavelengths).Much of the concern over perpendicular record-

ing relates to the intense demagnetizing fields thatarise in regions written with DC magnetization.These effects may be mitigated with the use of anappropriate channel code. Imposing an RLL ‘k’-constraint or a DC-free constraint that strictlylimits the DC runs and/or the DC content of thecode could be quite beneficial. On the negativeside, of course, this implies a higher channeldensity (closer transitions) and a higher channelclock rate.The move to perpendicular recording is expected

to be associated with a push towards much lowerbit aspect ratio (BAR). Good side reading and sidewriting characteristics at extreme track-densitieswill be crucial. In this respect the perpendiculartwo-layer configuration is attractive. The readbacksensitivity function is well confined because of thepresence of both the shields and the soft under-layer.There is a distinct difference in writing with a

pole head compared with a ring head. With thepole head, writing takes place over the entire pole

face rather than just along the gap. The naturalhead-skew that arises from the use of a rotaryactuator can therefore easily create problems asthe edges of the poleface overlap adjacent tracks.Various solutions are proposed ranging from there-introduction of linear actuators to the design ofa tapered pole tip (where the taper angle must begreater than the worst case skew).Aside from this geometric problem, perpendi-

cular recording with a soft underlayer is otherwisecharacterized by sharp track-edges and by anabsence of erase-band. (In the past, at high bitaspect ratio, the absence of erase-band has beenquoted as one of the disadvantages of perpendi-cular recording. However, as track-densities arepushed to the extreme there is simply no room foran erase band.) The sharp sidewriting has beenshown to be very advantageous in generating agood position error signal [14].In the context of a medium with low nucleation

field, BHc �Ms; it will be important to preventspurious fields from demagnetizing the medium.Fortunately, the fields from a pole head arerelatively well-confined at the track-edges (other-wise we might have to contend with severeadjacent-track erasure/interference even in theabsence of head-skew). However, the head struc-ture must still be carefully designed to minimizethe concentration of field in the small gap betweenthe head and the soft underlayer.

9. A ‘747’ curve at 1 terabit/sq.in

Ref. [4] speculated about a perpendicularrecording system that approached an areal densityof 1Terabit/sq.in. Concern was expressed aboutthe across-track resolution and whether it wouldsupport the claimed density. Recent work by Jinet al. [15] gives encouraging results in this respect.It should be noted, however, that, althoughrealistic 3-D writing fields and read head sensitiv-ity functions are used, there are no interactionsbetween grains and no other source of readbacknoise. Fig. 7, showing a ‘747 curve’ produced by a‘grain-by-grain’ simulation, confirms that ade-quate off-track margins could exist even at lessthan the quoted 47 nm target track-pitch.


10. Discussion

Perpendicular recording offers considerablepromise with respect to the thermal limit. Inparticular, the ability to write higher coercivity,thicker media, and sharp track-edges, shouldpermit considerably higher densities to beachieved. Assuming continuing advances in thebase technologies (servo-tracking, track-widthdefinition, flying-height, head resolution, signalprocessing), areal densities approaching 1Terabit/sq.in. are conceivable, at low data-rates.We should also note that many of the key

advantages listed above have not yet been fullyrealized. Although very high coercivities,>10 kOE, have been obtained in, for example,CoPt multilayer media, the best SNR and systemperformances are still being achieved with low-

coercivity, 2.6 kOE, CoCr-type granular media[1,2]. A new structure, ‘CGC media’, which addsa continuous multilayer medium on top of a moreconventional granular CoCr medium offers somepromise. Obtaining a high value of Hc; a high ratiofor Hc=4pMs; and a small effective grain-size arebelieved to be critical to the success of perpendi-cular recording.

Acknowledgements

The authors gratefully acknowledge the con-tributions of H.N. Bertram, T. Olson, H. Mur-aoka, M. Williams, and D. Wilton.

References

[1] H. Takano, Y. Nishida, M. Futamoto, H. Aoi, Y.

Nakamura, Possibility of 40Gb/in2 perpendicular record-

ing, IEEE Inter-mag Conference (AD-06), April 10–13,

2000, Toronto, Canada.

[2] Read-Rite and Samsung Electronics Record 60 Billion Bits

per Square Inch Using Perpendicular Magnetic Recording,

http://www.readrite.com/html/whatnew/101600a.html,

Press release from Read-Rite Corp. on October 16, 2000.

[3] H.N. Bertram, M. Williams, IEEE Trans. Magn. MAG-36

(1) (2000) 4–9.

[4] R. Wood, IEEE Trans. Magn. MAG-36 (1) (2000) 36–41.

[5] R. Victora, National Storage Industry Consortium Winter

Meeting, Jan. 12–14, 2000, San Diego, CA.

[6] E.E. Fullerton, et al., Growth, characterization and

recording performance of Co-X/Pd multilayer recording

media, Paper #25pA-01, PMRC 2000, Sendai, Japan.

[7] R. Wood, J. Monson, T. Coughlin, JMMM 193 (1999)

207–212.

[8] K. Ouchi, N. Honda, IEEE Trans. Magn. 36 (2000) 16–22.

[9] S.J. Greaves, H. Muraoka, Y. Sonobe, M. Schabes, Y.

Nakamura, Pinning of written in composite perpendicular

media (simulation), Paper #26pA-10, PMRC 2000, Sendai,

Japan.

[10] Y. Sonobe, Y. Ikeda, D. Weller, M. Schabes, K. Takano,

Novel perpendicular recording medium with an exchange

coupled layer on a granular host layer, Paper #26pA-11,

PMRC 2000, Sendai, Japan.

[11] R. Potter, IEEE Trans. Magn. MAG-10 (3) (1974) 502–

508.

[12] J. Ruigrok, Short-Wavelength Magnetic Recording: New

Methods and Analyses, Pergamon Press, New York, 1990.

[13] Y. Okamoto, H. Osawa, H. Saito, H. Muraoka, Y.

Nakamura, Performance of PRML Systems in Perpendi-

Fig. 7. A ‘747 Curve’ simulated for the ‘Terabit system’

described in Ref. [4] provides a measure of the ability of a

system to withstand tracking errors. The curves are obtained by

grain-by grain simulation for 80,000 bits, each of 8 ‘squeeze’

distances and 12 off-track read positions. Realistic 3-D writing

fields and read head sensitivity functions are used but there are

no interactions between grains and no other source of readback

noise. The ‘747’ contour (solid) is set as the bit error-rate giving

10�15 block failure after error correction [15].


cular Magnetic Revording Channel with Jitter-like Noise,

Paper #26aA-05, PMRC 2000, Sendai, Japan.

[14] Z. Jin, H.N. Bertram, Modelling of PES Noise in

Perpendicular Recording, National Storage Industry

Consortium Winter Meeting, Jan. 12–14, 2000, San

Diego, CA.

[15] Z. Jin, H.N. Bertram, B. Wilson, R. Wood, IEEE Trans.

Magn. 2001, to be submitted.


perpendicular recording: the promise and the problems

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