recording physics of perpendicular media: hard layers

Journal of Magnetism and Magnetic Materials 241 (2002) 453–465

Recording physics of perpendicular media: hard layers

Dmitri Litvinov*, Mark H. Kryder, Sakhrat Khizroev

Seagate Research, 2403 Sidney Street, Pittsburgh, PA 15203, USA

Received 29 October 2001

Abstract

The results of both theoretical and experimental studies of some of the key issues related to the hard layer in

perpendicular magnetic recording are presented. Among the discussed issues are the guidelines and underlying physics

for choosing the optimized recording layer parameters such as thickness, specific magnetic properties, types of

recording layer material, etc. Special attention is given to the physical phenomena and parameters that define the

optimum thickness of the recording layer. To stress the specific aspects of the recording physics native only to

perpendicular recording, a comparison between perpendicular and longitudinal media is carried out throughout the

work. r 2002 Elsevier Science B.V. All rights reserved.

Keywords: Perpendicular magnetic recording; Perpendicular magnetic recording media; Recording layers; Recording physics

1. Introduction

As magnetic data storage based upon conven-tional longitudinal recording technology rapidlyapproaches areal bit densities at which super-paramagnetic instabilities begin to affect theperformance of recording systems [1], seriousattention is being given to perpendicular recording[2–10]. For the successful implementation ofperpendicular recording technology, the majoropen questions related to the design of perpendi-cular media, heads and channels should beanswered [11–16]. The purpose of this work is toconsider some of the critical issues related to thedesign of the recording layer in perpendicularmagnetic recording media.

There are two basic types of perpendicularrecording schemes. In one of the recordingschemes, a ring head with a single-layer perpendi-cular medium is used. Another perpendicularrecording scheme is based upon a single pole headand a medium comprised of a recording layer anda soft underlayer (SUL). The presence of a SULintroduces a number of additional technicalchallenges [17,18].

The primary approach to the design of aperpendicular recording layer is in many wayssimilar to the design of a conventional longitudinalrecording layer. Major goals inherent to bothlongitudinal and perpendicular recording layerdevelopment are small grain size, small grain sizedistribution, texture control, optimization of theinter-granular exchange de-coupling, etc. How-ever, some aspects of recording layer designare specific only to perpendicular recording.

*Corresponding author.

E-mail address: dmitri [email protected] (D. Litvinov).

0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

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

Information Storage: Basic and Applied

Understanding the fundamentals of these issues isthe subject of this paper.

2. Types of media

A large variety of today’s perpendicular mag-netic recording layer types can be clearly dividedinto the two major categories: (1) CoCr-alloy-based media and (2) media based on magneticmultilayers, such as Co/Pt, Co/Pd or others[4,19–25].

Material-wise, perpendicular CoCr-based alloyrecording layers are similar to conventional long-itudinal CoCr-based media, with the major differ-ence being the orientation of the magnetic easyaxis. Therefore, a significant amount of informa-tion accumulated in the course of the longitudinalmedia development can be used to control thecritical parameters such as the grain size and theinter-granular exchange coupling. At the sametime, CoCr-based perpendicular media have someopen issues. For example, it is not clear yet if it ispossible to make a CoCr-based medium withsufficiently high anisotropy to avoid superpara-magnetic instabilities at ultra-high areal densities[26]. It also has proven to be difficult to makeCoCr-alloy-based perpendicular recording layerswith a remnant squareness of 1. It is believed thata remnant squareness of 1 is necessary for low-density bit pattern stability. Also, a remnantsquareness of o1 can lead to substantial amountsof DC noise. Various magnetic alloys such as L10phases of FePt, CoPt, etc., are being studied as

higher anisotropy alternatives for the recordinglayer.

The magnetic multilayer based recording layerstypically have significantly larger anisotropy en-ergies (coercive fields of above 15 kOe have beenreported) and are thus promising to be extendableto significantly higher recording densities [27,28].Another advantage of the magnetic multilayers isthe fact that typically these materials have aremnant squareness of 1.

To compare basic magnetic properties of CoCr-alloy and mutlilayer based recording layers, typicalM–H loops by a Kerr magnetometer for a 50 nmthick perpendicular CoCr thin film and a 52 nmthick Co/Pd structure (a stack of 40 sets ofadjacent 3 and 10 (A thick layers of Co and Pd,respectively) are shown in Figs. 1a and b, respec-tively. It can be noted that in addition to theremnant squareness of 1, the Co/Pd structureexhibits nucleation fields in excess of 3 kOe, auseful characteristic to avoid data self-erasure dueto stray fields. Meanwhile, the CoCr materialshown in Fig. 1a has a squareness of 0.75. TheCoCr and Co/Pd recording layers have coercivefields and magnetizations of approximately 3 and9 kOe and 300 and 200 emu=cm3; respectively.

The direct consequence of remnant squarenesso1 is shown in Fig. 2, which compares the spectralSNR distributions for the two media types. TheCoCr medium exhibits a significant amount ofnoise at lower linear densities. This is mainly dueto the fact that the dominant contribution to thenoise at low linear density in the CoCr-basedmedium comes from the DC noise which results

-6 -4 -2 0 2 4 6

-4

-2

0

2

4

Ker

r S

igna

l (a.

u.)

Field (kOe)

-10 -5 0 5 10

-5

0

5

Ker

r S

igna

l (a.

u.)

Field (kOe)(a) (b)

Fig. 1. An M–H loop of a 50 nm thick (a) CoCr-alloy layer and (b) Co/Pd multilayer.

D. Litvinov et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 453–465454


from the relatively low value of remnant square-ness, as described below in more detail.

2.1. Continuous media

Also, it should be mentioned that there isanother type of magnetic recording medium,which, similar to a typical magneto-optical record-ing medium, due to relatively strong exchangecoupling between grains, acts as a magneticallycontinuous medium [29]. In these so-called con-tinuous magnetic materials, the bit separation isdetermined not by the grain size, but rather by thedomain wall width. The domain wall widths can beas small as a few Angstroms in these relatively highanisotropy magnetic materials. The coercive fieldsof these materials depend on the mechanisms andstrengths of the pinning of the domain walls tonaturally or artificially created defects and on thedefect size relative to the wall width. Thus far,continuous exchange coupled media have exhib-ited large transition noise. The recording layersbased upon continuous exchange coupled materi-als are therefore not covered in this paper.

3. Magnetic field calculations

Two approaches are used in this work tocalculate the magnetic fields. The analytical solu-

tion of the Laplace equation was used to calculatethe demagnetizing and stray fields for the cases oftwo-dimensional (2D) periodic bit patterns writteninto a perpendicular recording medium. Thederivation of the analytical expressions for thedemagnetizing and stray fields is presented inAppendix A at the end of this paper.

Three-dimensional (3D) boundary elementmodeling (BEM) using a commercial field solver,Amperes [30], was used to calculate the magneticfields for cases of bit patterns written into alongitudinal medium as well as to evaluate themagnetic fields generated by magnetic recordingheads. It should be noted that within the precisionof the calculations, the BEM applied to 2Dperiodic bit patterns in perpendicular media gavethe results identical to the results, which werecalculated using the analytical solution.

An approximation of an ‘‘ideal’’ SUL was usedin all calculations presented in this work. Theimplications of non-ideal behavior of a SUL arediscussed elsewhere [17,18]. It should be noted thatthe effect of the presence of an ideal SUL on thestray and demagnetizing fields generated by arecording layer is equivalent to the perfect mirror-imaging of the recording layer with respect to theSUL boundary as illustrated in Fig. 3. The fieldsabove the SUL boundary are equal to the sum ofthe fields generated by the real recording layer andby its imaginary counterpart located below theSUL boundary as shown in Fig. 3. If the spacingbetween a recording layer and a SUL is equal tozero, i.e. no buffer/exchange-decoupling layer ispresent, the use of an ideal SUL is equivalent to atwo-fold increase of the recording layer thickness.Unless specified otherwise, in most of the calcula-tions presented below, it is assumed that thethickness of the buffer layer is substantially

Fig. 3. An illustration of the mirror-imaging by an ideal SUL.

Fig. 2. SNR versus the linear density for a CoCr-alloy (hollow

circles) and a Co/Pd multilayer (hollow squares).

D. Litvinov et al. / Journal of Magnetism and Magnetic Materials 241 (2002) 453–465 455


smaller than the thickness of the recording layerand, therefore, can be assumed to be equal to zero.

It should be remembered that the use of a SULis not equivalent to the effect of mirror-imagingwhen the energies are to be evaluated. Therefore,the magnetic mirror-imaging should be used withcaution when applied to the problems that dealwith the phenomena associated with the bitenergy, such as the media thermal stability.

4. Demagnetizing fields in perpendicular recording

layer

The calculated normalized demagnetizationfields near a single ideal transition along thecentral plane of a recording layer are shown forlongitudinal and perpendicular recording layerswith and without an underlayer at two differentvalues of the recording layer thickness, 10 and20 nm, in Figs. 4a–c, respectively. (In these calcu-lations a relatively wide trackwidth is assumed.)First, it can be noticed that, unlike in longitudinal

recording, the demagnetization fields in perpendi-cular recording decrease as the thickness increases,thus promoting a larger thickness [3,10]. If aperpendicular medium with a SUL is used, theSUL effectively further increases the recordinglayer thickness. Also, unlike in the longitudinalmedium, in both types of perpendicular media, thedemagnetization fields reach their minima at thetransitions, thus promoting high-density record-ing. In this respect, it is common to notice thatalthough perpendicular recording promotes highdensities, the stronger influence of the demagneti-zation fields at lower densities is a disadvantage ofperpendicular recording.

One of the direct consequences of the strongdemagnetization fields at low densities is arelatively strong DC-noise from perpendicularmedia with a squareness of o1; as mentionedabove [26]. MFM images of wide (with respect tothe media thickness) tracks recorded into two30 nm thick CoCr alloy films with a coercive field,Hc of approximately 2 kOe and magnetizationvalues of 100 and 400 emu=cm3 are shown in

-0.04 -0.02 0.00 0.02 0.04

-2000

-1000

0

1000

2000

Ideal Underlayer

Hz (

Oe)

Distance down the track (um)

T = 10 nm T = 20 nm

-0.04 -0.02 0.00 0.02 0.04

-2000

-1000

0

1000

2000

No underlayer

Hz (

Oe)

Distance down the track (um)

T = 10 nm T = 20 nm

-0.04 -0.02 0.00 0.02 0.04

-2000

-1000

0

1000

2000 Ms = 200 emu/cc

Hx (

Oe)

Distance along the track (um)

T = 10 nm T = 20 nm

(a) (b)

(c)

Fig. 4. The demagnetization field versus the distance down the track along the central planes of 10 and 20 nm thick recording layers for

(a) longitudinal recording, (b) perpendicular recording without and (c) with a SUL.



Figs. 5a and b, respectively [31]. Smoother andmore uniform tracks in the case of the smallermagnetization indicate less DC noise than in theother case.

The maximum demagnetization fields at thecenter of a bit for three values of the recordinglayer thickness with and without a SUL versus thetrack density are shown for two values of thelinear density, 50 and 316 kfci, in Fig. 6. Ifconsidering only the magnetics of the recordingprocess, perpendicular recording is symmetric withrespect to the directions along the track and acrossthe track. For example, the demagnetization fieldand stray field contours look similar (if rotated 901in the plane) for the two sets of the linear and track

densities: (1) 316 kfci and 50 ktpi, and (2) 50 kfciand 316 ktpi. Therefore, to avoid repetition, onlyone of each of two data sets is presented. It shouldbe also noted that under the assumption of a zerospacing between the recording layer and the SUL,10 and 20 nm cases with a SUL are equivalent to20 and 40 nm cases without a SUL, respectively.

According to Fig. 6, the demagnetization fielddecreases with the increase of the track density.The rate of roll-off is determined by the effectiverecording layer thickness and by the linear density(bit length). It can be seen that to the extent thatdemagnetizing fields produce problems with ther-mal instability and/or DC noise, a larger thicknessand a higher track density are preferred. The SULincreases the effective recording layer thickness,thus reducing the demagnetization fields. In thecase that the surrounding tracks mimic the maintrack, the demagnetization field reduction with thetrackwidth reduction can not occur; therefore,special encoding might be necessary to avoidunfavorable bit patterns at relatively low densities.It is important to point out that at present, theavailable encoding schemes to accomplish the taskabove result in substantial loss in recordingdensity.

An additional insight into the nature of demag-netizing fields in a perpendicular recording layercan be obtained if the demagnetizing field isplotted against areal density for different valuesof bit-aspect ratio (BAR). The demagnetizingfields at the center of a bit in the middle and nearthe surface of the recording layer are shown inFigs. 7a and b, respectively. It can be seen thathigher values of BAR at a given areal densitypromote lower demagnetizing fields. This is incontrast to longitudinal recording where thedemagnetizing field increases as the BAR isincreased.

5. Stray fields from perpendicular recording media

It should be mentioned that in perpendicularrecording stray magnetic fields (the fields sensed bya reader) emanate not from the transitions, as inlongitudinal recording, but from the effectivemagnetic ‘‘charges’’ at the top and effective (due

Fig. 5. MFM images of tracks recorded into 30 nm thick

CoCr alloys with a magnetization of (a) 200 emu=cm3 and

(b) 400 emu=cm3:

0 500 1000 1500 2000

0.00

0.25

0.50

0.75

1.00

Dem

ag F

ield

(in

uni

ts o

f 4π M

S)

Track Density (kfci)

50kfci, 10nm 316kfci, 10nm 50kfci, 20nm 316kfci, 20nm 50kfci, 40nm 316kfci, 40nm

Fig. 6. The maximum demagnetization field along the central

line of 10, 20, and 40 nm recording layers without a SUL at a

linear density of (a) 50 kfci and (b) 316 kfci.



to the underlayer) bottom surfaces of the record-ing layer, as shown in Figs. 8a–c [14]. Outside therecording layer the fields from the top and effectivebottom charges are of opposite directions; hence,they cancel each other if the recording layerthickness is significantly smaller than the char-acteristic bit sizes. As shown in Fig. 8c, the

presence of a SUL effectively doubles (in the caseof perfect imaging) the recording layer thickness.

The net stray fields emanating from the center ofa bit in periodically written bit patterns at twovalues of the track density, 50 and 316 ktpi, versusthe linear density for media with a recording layerthickness of 10, 20 and 40 nm without a SUL, areshown in Fig. 9. It should be stressed again thatunder the assumption of a zero spacing between arecording layer and a SUL, 10 and 20 nm cases

Fig. 8. Diagrams showing the sources of stray fields in the

case of (a) longitudinal recording, and perpendicular recording

(b) without and (c) with an SUL.

0 500 1000 1500 2000

0.0

0.1

0.2

0.3

Str

ay F

ield

(un

its o

f 4π M

S)

Linear Density (kfci)

50 ktpi, 10nm 316ktp, 10nm 50ktpi, 20nm 316ktp, 20nm 50ktpi, 40nm 316ktpi, 40nm

Fig. 9. The stray field above the center of a bit in 10, 20, and

40 nm thick recording layers without a SUL at a 5 nm flying

height versus the linear density for two values of the track

density of 50 and 316 ktpi.

0 500 1000 1500 20000.4

0.5

0.6

0.7

0.8

0.9

1.0

Dem

ag F

ield

(in

uni

ts o

f 4π M

S)

Areal Density (Gbit/in2)

BAR=1:1 BAR=2:1 BAR=4:1 BAR=8:1

0 500 1000 1500 20000.00

0.25

0.50

0.75

1.00

Dem

ag F

ield

(in

uni

ts o

f 4π M

S)

Areal Density (Gbit/in2)

BAR=1:1 BAR=2:1 BAR=4:1 BAR=8:1

(a) (b)

Fig. 7. The demagnetization field at the center of a bit (a) in the middle and (b) near the surface of the recording layer for 10 nm

recording layers as function of the areal density for different values of BAR.



with a SUL are equivalent to 20 and 40 nm caseswithout a SUL, respectively. In these calculations,a flying height of 5 nm was assumed. It can benoticed that for the narrower trackwidth, thesignal can be substantial even at relatively lowlinear bit densities because no total compensationof the fields generated by the top and effectivebottom charges occurs. It is natural that at veryhigh densities, the stray fields drop because the bitarea containing the effective ‘‘magnetic’’ chargesand, thus, also the total ‘‘magnetic’’ chargebecome relatively small. Regardless of the effectiverecording layer thickness, the characteristic bitlength at which this happens cannot be smallerthan approximately the flying height. At the sametime, regardless of the linear and track densityvalues, the stray fields drop with the thicknessreduction because of the above-mentioned fieldcancellation effect due to the ‘‘magnetic’’ chargesat the top and the effective bottom surfaces of thedisk. (The latter effect is equivalent to the strayfield reduction at some finite thickness as the bitdimensions become significantly larger than thethickness value.) In between, the stray fieldsgenerated by the effective ‘‘charges’’ at the topsurface are sufficiently large and at the same timecannot be compensated by the ‘‘charges’’ from theeffective bottom surface; therefore the stray fieldhas a maximum. From the above arguments, italso can be noticed that if some encoding is notperformed to limit the maximum bit dimensions,the stray fields become negligibly small at suffi-ciently low densities. Assuming that some encod-ing is performed to avoid the low-densitydegradation of the stray field, the limiting lowerboundary value for the recording layer thickness isdetermined by the highest values of the requiredlinear and track densities. For example, aiming for200 Gbit=in2 at a 2:1 bit cell aspect ratio, the trackand linear densities would be 316 ktpi and 632 kfci,respectively. For these values of the track andlinear densities, the signal rapidly drops, as thethickness becomes smaller than approximately10 nm.

So far, it was assumed that the spacing betweenthe recording layer and the SUL was equal to zero.The effect of a non-zero spacing between therecording layer and the SUL is shown in Fig. 10. It

can be noted that the difference in the values of thestray fields between a 0 nm spacing and a 4 nmspacing can be as large as 20%. Although thiseffect does not alter any of the conclusionspresented in this work, it should be taken intoaccount when optimizing the design of a perpen-dicular recording system.

It gives additional insight into the differencebetween perpendicular and longitudinal recordingif one compares stray fields emanating fromperpendicular and longitudinal media as functionsof the areal density at different BAR values. Theperpendicular component of the stray field at a5 nm distance from the center of a bit in aperiodically written pattern for a 10 nm thick hardlayer at 3 values of BAR, 1:1, 4:1 and 8:1, is shownfor the cases of perpendicular recording with andwithout a SUL in Fig. 11. Since in the case oflongitudinal recording the directions along thetrack and across the track are not equivalent, oneneeds to consider the BAR values correspondingto both types of bits, elongated along and acrossthe track. The perpendicular component of thestray field at a 5 nm distance from the center of thetransition in a periodically written pattern for a10 nm thick longitudinal hard layer at 6 values ofBAR, 1:4, 1:2, 1:1, 2:1, 4:1 and 8:1, is shown inFig. 12.

0 500 1000 1500

0.10

0.15

0.20

0.25

0.30

Str

ay F

ield

(in

uni

ts o

f 4π M

S)

Areal Density (Gbit/in2 )

Buffer = 0 nm Buffer = 1 nm Buffer = 2 nm Buffer = 4 nm Buffer = 10 nm

Fig. 10. The stray field above the center of a bit in a 10 nm

thick recording layer without a SUL at a 5 nm flying height

versus the linear density for different values of the spacing

between a recording layer and a SUL.



The pronounced peak in the perpendicular cases(see Fig. 11) is explained by the cancellation effectdue to the fields generated by the top and bottom‘‘magnetic charges’’. It can be noticed that thereexists a certain characteristic density of B100 andB200 Gbit=in2 for the cases with and without aSUL, respectively, above and below which thestray fields depend differently on the areal bitdensity. This characteristic density increases withthe recording layer thickness decrease. The pre-sence of the SUL is equivalent to the increase ofthe recording layer thickness by a factor of two.Such sensitivity to the recording layer thickness is

explained by the nature of the ‘‘magnetic charge’’distribution in perpendicular recording (see thediscussion above). As the areal density increases,the magnitude of the stray field becomes indepen-dent of the recording layer thickness. The peakvalue of the stray field depends strongly on therecording layer thickness and is independent of theBAR (see Fig. 13).

The roll-off curves in the longitudinal case showno peaks, rather they continuously drop for allBAR values. The slowest roll-off is observed for a1:1 BAR value.

Although the stray field roll-off curves arerather complex and strongly depend on the BARvalues, it can be noticed that in perpendicularcases the stray fields roll-off significantly slowerthan in longitudinal cases. This is due to the factthat the stray field is composed of the fields fromthe top and effective ‘‘bottom’’ charges of therecording layer. The two fields are opposite to eachother such that the field emanating from the‘‘bottom’’ charges decreases the field generated bythe top charges. As the bit size becomes smaller,the relative contribution of the ‘‘bottom’’ chargesdecreases, thus slowing the overall decrease of thefield amplitude with the areal density increase.

6. Well-defined perpendicular easy axis: thicker

recording layer?

In a perpendicular recording medium the easyaxis is relatively well aligned in one direction

0 20 40 60 80 100

0.0

0.1

0.2

0.3

0.4

Max

imum

Str

ay F

ield

(uni

ts o

f 4π

MS)

Recording Layer Thickness (nm)

Fig. 12. Perpendicular component of the stray field versus the

areal density for the longitudinal recording mode.

0 500 1000 1500 2000

0.1

0.2

0.3

0.4

Str

ay F

ield

(un

its o

f 4π

MS)

Areal Density (Gbit/in2 )

BAR = 1:4 BAR = 1:2 BAR = 1:1 BAR = 2:1 BAR = 4:1 BAR = 8:1

Fig. 13. The peak value of the perpendicular component of the

stray field versus the recording layer thickness for the

perpendicular mode without a SUL.

0 500 1000 1500

0.05

0.10

0.15

0.20

0.25

0.30

Str

ay F

ield

(un

its o

f 4π M

S)

Areal Density (Gbin/in2)

BAR=1:1, no SUL BAR=4:1, no SUL BAR=8:1, no SUL BAR=1:1, SUL BAR=4:1, SUL BAR=8:1, SUL

Fig. 11. Perpendicular component of the stray field versus the

areal density for the perpendicular mode with and without a

SUL.



(perpendicular), unlike in a conventional long-itudinal medium, in which the easy axes arerandomly oriented in the 2D plane of the disk. Awell-defined easy axis potentially relaxes thestringent requirement for the trailing and sidewriting field gradient necessary to achieve sharptransitions, thus enabling the use of thicker media.

The intrinsically better alignment of perpendi-cular media helps to record narrow tracks withwell-defined transitions even into a relatively thickrecording layer. A MFM image of two adjacenttracks with a 65 nm trackpitch written into a 50 nmthick CoCr recording layer using a 50 nm widesingle pole head is shown in Fig. 14.

In this respect, it should be remembered thatpreviously it was shown that, although well-aligned perpendicular media might have a rela-tively small average angle between the magnetiza-tion and the perpendicular recording field, thetorque created is still sufficiently large to quicklyswitch the magnetization [32].

7. Utilizing the soft underlayer to advantage during

writing

If a medium with a SUL is used, to take fulladvantage of the underlayer, i.e. to generate strongrecording fields, the separation between the under-layer and the air bearing surface (ABS) of therecording head should be as small as possible[13,33]. This provides an upper limiting factor tothe recording layer thickness, because the record-ing layer is placed between the ABS and theunderlayer. This factor is determined by the writepole tip dimensions at the ABS. For example, thecalculated vertical recording fields at saturationgenerated by a write pole with a 100 nm � 200 nm

tip cross-section at the ABS at a 5 nm flying heightfor different values of the ABS to the underlayerseparation are shown in Fig. 15. It can be noticedthat in order to generate a maximum recordingfield above 2pMS of the head material, thethickness should be smaller than approximately50 nm, with a 5 nm flying height.

8. Image paradox during reading from media with a

soft underlayer

During reading from media with a SUL, due tothe image in the underlayer, the resolution can getdistorted if the separation between the ABS andthe underlayer (sum of the recording layer thick-ness and the flying height) is comparable to thereader thickness [18]. To help understand thisphenomenon a diagram of a system comprising areader, recording layer and the image head (insideof the underlayer) is shown in Fig. 16. Accordingto the reciprocity principle, the playback signal isunambiguously determined by the convolutionbetween the magnetization, M, and the sensitivityfield, H and is given by [14]

SBZ

Hðr� r0Þ �Mðr0Þ d3r0: ð1Þ

For a well-oriented perpendicular recordinghard layer where M ¼ Mz � z; Eq. (1) takes the

Fig. 14. A MFM image of two tracks with a 65 nm trackpitch.

Fig. 15. The recording field at a 5 nm flying height versus the

distance across the track under the write pole tip with a

100 nm � 500 nm cross-section for different separations be-

tween the ABS and the underlayer, 30, 35, 40, 50 and 70 nm.



following form:

SBZ

Hzðr� r0Þ � Mzðr0Þ d3r0: ð2Þ

In this case, the sensitivity field consists of thefields generated by the imaginary coils around thereal and image heads shown in Fig. 16. Fromthe diagram shown in Fig. 16, it can be noticedthat there is asymmetry between the locationsof the read head and the image head with respectto the recording layer. Due to this asymmetry, thedifference between the distances from the real headand the image head to the central line of therecording layer is equal to the thickness of therecording layer plus the thicknesses of the inter-layer, buffer layer, etc. (For simplicity, the totaleffective thickness will be denoted as d:) This is thecause of the image paradox during the readingprocess. Effectively, in comparison with the realhead, the image head is further away from therecording layer by d: As a result, in the region of

the recording layer the average sensitivity field ofthe image head is wider than the average sensitivityfield of the real head. On the other hand, theamplitude of the average sensitivity field of theimage head is smaller than the one of the real headdue to the effective spacing loss, d: Therefore,there is a trade-off between the resolution dete-rioration and the amplitude of the signal. Thefurther away the underlayer is from the ABS, theless significant is the influence of the image head,deteriorating the total resolution, and the signalreduces to a level close to the case when there is nounderlayer. On the other hand, at the otherextreme, the closer the underlayer is to the ABS,the stronger the signal from the underlayer is andthere is a less noticeable difference betweenresolutions of the real and image heads. Thisphenomenon is clearly illustrated in the calculatedPW50 and the playback signal versus the under-layer to the ABS distance, shown in Figs. 17a andb, respectively. In these calculations a fixedrecording layer thickness of 10 nm was assumed,and spacing between the bottom side of therecording layer and the underlayer was variedfrom zero to some finite values. For comparison,the dotted straight lines indicate the values for thecase when there is no underlayer.

Although, in a properly designed system thisresolution distortion can be almost completelyeliminated, it causes the resolution of a typicalread head in a system with an underlayer tobe at most as good as the resolution of anequivalent head in a system without an underlayer.Nevertheless, although, the underlayer does notimprove resolution, it definitely increases the

RealHead

ImageHead

SUL boundary Buffer layer

Recordinglayer

Fig. 16. A diagram showing the image representation of a

system with an underlayer.

Fig. 17. (a) PW50 and (b) the normalized playback signal versus the ABS to the underlayer separation. An equivalent dependence for

the case without an underlayer is shown by the dotted curve.



playback signal, which is desirable at high arealdensities.

9. Summary

Using 3D calculations and experiments, includ-ing a spin-stand, Kerr microscopy and MFMimaging, a study of recording physics aspectsrelated to perpendicular recording media, waspresented. The influence of the recording layerthickness, the presence or absence of a SUL,recording density, and BAR on various recordingcharacteristics of perpendicular recording systemswas studied. In particular, it was shown that inperpendicular recording higher values of BAR leadto the decrease of demagnetizing fields. It was alsoshown that at each given recording layer thickness,there exists a characteristic areal bit density, aboveand below which the stray fields depend differentlyon the areal bit density. It was shown that a finitethickness of the recording layer can lead to thedeterioration of the recording system resolution ifmedia with a SUL is used. For example, for a30 nm thick read element, it was shown that,although for good resolution the underlayershould be at least 40 nm away from the ABS, itshould not be further away than approximately60 nm in order to prevent non-coherent switchingand in order to maintain relatively strong record-ing fields. Also, it was shown that, in contrast tolongitudinal recording, in perpendicular recordingstray fields do not drop as rapidly at high arealdensities. The reciprocity theorem was used toshow that the playback signal in the case ofperpendicular recording, both with and without aSUL, drops slower with increasing areal densitythan it does in the case of longitudinal recording.Between the two perpendicular modes, the signaldrops faster with increasing areal density when anunderlayer is used.

Acknowledgements

The authors would like to acknowledge the helpof their co-workers at Seagate Research for useful

discussions and help with some of the experimentalarrangements.

Appendix A. Stray and demagnetizing fields gener-

ated by a 2D periodic bit pattern

As will be shown below, the Laplace equationfor the case of a 2D periodic bit pattern shownschematically in Fig. 18, can be solved analytically.The solution of the Laplace equation givesanalytical expressions for the stray and demagne-tizing fields. The presented solution is analogousto the solution of the Laplace equation for the caseof a 1D periodic bit pattern [34].

A.1. The field generated by a single surface with a

2D periodic charge

According to the Principle of Linear Super-position, the total field (stray or demagnetizing) isequal to the vector sum of the fields emanatingfrom the top and bottom surface ‘‘charges’’ of therecording layer. These fields are evaluated analy-tically below.

Due to the periodic nature of the problem, thescalar potential, f; is a periodic function withrespect to x and y: A general solution to theLaplace Equation, Df ¼ 0 is given by

f ¼Xn;odd

Xk;odd

Ank sinnpa

x� �

sinkpb

y

� �

� exp �pn

aþ

k

b

� �z

� �; ðA:1Þ

b

a

Periodic “charges”

Z

X

Y

- +

-+

δ

Fig. 18. A schematic of a periodic bit pattern.



where z ¼ 0 represents the points on the surface(see Fig. 18).

The vertical component of the field, Hz; is equalto the partial derivative of f with respect to z; i.e.Hz ¼ qf=qz; and is given by

Hz ¼ �Xn;odd

Xk;odd

pn

aþ

k

b

� �Ank sin

npa

x� �

� sinkpb

y

� �exp �p

n

aþ

k

b

� �z

� �: ðA:2Þ

At the surface for z > 0; Hz-0-2pMS: Thisgives

�Xn;odd

Xk;odd

pn

aþ

k

b

� �Ank sin

npa

x� �

� sinkpb

y

� �¼ 2pMS: ðA:3Þ

Multiplying both sides by sinððmp=aÞxÞsinððlp=bÞyÞ and integrating over �aoxoa and�boyob; gives (the left-hand side of the aboveequation is not equal to zero only for n ¼ m andk ¼ l)

Ank ¼ �32abMS

nkp2ðn=a þ k=bÞ: ðA:4Þ

Consequently, the field for z > 0 is given by

Hz ¼32MS

p

Xn;odd

Xk;odd

1

nksin

npa

x� �

sinkpb

y

� �

� exp �pn

aþ

k

b

� �z

� �: ðA:5Þ

A.2. The fields from both the top and the bottom

surfaces

If d is a recording layer thickness, the net strayfield, Hstrayz

; above the recording layer is given by

Hstrayz¼

32MS

p

Xn;odd

Xk;odd

1

nksin

npa

x� �

sinkpb

y

� �

� 1 � exp �pn

aþ

k

b

� �d

� �

� exp �pn

aþ

k

b

� �jzj

� �; ðA:6Þ

where jzj is the distance measured from the topsurface of the recording layer.

Similarly, the demagnetizing field, Hdemagz;inside the recording layer is given by

Hdemagz¼�

32MS

p

Xn;odd

Xk;odd

1

nksin

npa

x� �

sinkpb

y

� �

� exp �pn

aþ

k

b

� �jzj

� �

þ exp �pn

aþ

k

b

� �ðd� jzjÞ

� �; ðA:7Þ

where jzj; 0ojzjod; is the distance measured fromthe top surface of the recording layer into therecording layer.

As expected, it can be seen from Eqs. (A.6) and(A.7) that the stray field increases and thedemagnetization field decreases with the increaseof the recording layer thickness, d:

The dependence of the fields on a bit-aspectratio, BAR, and an areal density, AD, can bederived using the following parameter transforma-tion

a ¼

ffiffiffiffiffiffiffiffiffiffiffiBAR

AD

r; ðA:8Þ

b ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

BAD � AD

r:

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recording physics of perpendicular media: hard layers

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