Micromagnetic recording model of pole-tip saturation effects

IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 6, NOVEMBER 2000 3975

Micromagnetic Recording Model of Pole-TipSaturation Effects

Jan van Ek, Martin Plumer, Hong Zhou, and H. Neal Bertram, Fellow, IEEE

Abstract—Auxiliary write-head fields, either from simpleanalytic approximations or from finite-element computations,are used to record transitions on a Landau–Lifschitz–Gilbertmodel of thin-film recording media. A micromagnetic model ofa magnetoresistive element is used to read back the transitions.Focus is on the impact of pole-tip saturation on the quality of therecorded track and subsequent playback. It is shown that withincreasing write current, the quality of the recorded transitionsdegrades much more rapidly than would be expected from theanalytical expressions for the write-head field. Specifically, headsaturation causes the transition parameter to increase. At highwrite currents, poor write field gradients at the track edges resultin a strong increase in transition parameter with read widthpercentage of the recorded track.

Index Terms—Micromagnetic recording model, track edge ef-fects, writer pole-tip saturation.

I. INTRODUCTION

B ECAUSE the medium is a crucial component in therecording process, the evaluation of a transducer design

cannot be fully performed without considering the quality ofthe recorded track. As track width and bit spacing continueto decrease, with simultaneous narrowing of the track aspectratio [1], detailed analysis of track edge effects is required forultrahigh areal density recording. In the present work, detailsof a micromagnetic recording model (MRM) are describedand the model is used in the investigation of the effects ofwriter pole-tip saturation on the quality of recorded tracks andread-back characteristics. The present study is unique due to itsexamination of writer pole-tip saturation effects on recordedtransitions and due to its use of a micromagnetic model of aGMR spin-valve sensor to study the impact of the quality ofthe transitions on the playback signal.

Early work on pole-saturation in ferrite recording heads in-clude a computational study by Bertram and Steele [2], in whichsaturation is found to be the result of a redistribution of magneticsurface charge to volume charge around the gap. Degradation ofthe field gradient is identified as the primary effect of pole-tipsaturation. Kelley [3] describes how high moment metals formetal-in-gap heads delay the onset of saturation effects. Rodéand Bertram [4] conclude that saturation effects in ferrite headscan be approximately included in linear recording models as aneffective gap length and head-to-medium separation. The results

Manuscript received June 3, 2000; revised July 28, 2000.J. van Ek and M. Plumer are with Seagate Technology, Bloomington, MN

55435-5489 USA.H. Zhou and H. N. Bertram are with CMRR, University of California at San

Diego, La Jolla, CA 92093-0401 USA.Publisher Item Identifier S 0018-9464(00)09953-2.

from all of the above studies have in common that they provideinsight into the origin and effects of pole-tip saturation in infin-itely wide heads. No track edge effects were included.

A significant number of papers in the literature exist, inwhich pieces of the recording process are examined usingthe micromagnetic method [solution of the Landau–Lif-shitz–Gilbert (LLG) equations] for thin-film media (see, e.g.,[5] and [6]). Of particular relevance to the present work is astudy of medium grain-size and thickness effects on the fittedtransition parameter with a comparison to analytic models ofthe Williams–Comstock type [7]. A cursory examination of theeffects of finite track widths on high linear density recordingwas examined in [8] using Lindholm head fields. Magneticfields derived from the finite element method (FEM) were alsoused to record transitions in an LLG model of isotropic mediawith an emphasis on the effects of the out-of-plane componentof the field [9].

In Section II, the micromagnetic recording model is de-scribed. The principal focus of Section III is to illustrate theutility of the micromagnetic recording model in the inves-tigation of pole-tip saturation effects for generic 10 Gb/inhead-medium combinations. Results for ultrahigh track densi-ties are discussed in Section IV.

II. M ODEL

For the medium, the LLG equations are solved in the highdamping limit; i.e., the precession term is neglected. Themedium is discretized into an array of either rectangular prismsor hexagonal prisms. The long-range magnetostatic interactionis accounted for explicitly through the demagnetization tensor.Fast Fourier transform algorithms without periodic boundaryconditions (square grid) or with periodic boundary conditions(hexagonal grid) are used to expedite the computation of themagnetostatic contribution to the effective field. Anisotropyand exchange fields are treated in the standard way [6].

Homogeneous external fields or write-head fields derivedfrom analytic approximations (e.g., Karlqvist or Lindholm)as well as from an FEM model of the writer can be added tothe effective field acting on the medium. Possible effects ofimaging of the medium magnetization in the writer pole tipswere not taken into account.

Read back is performed with a micromagnetic model ofan abutted junction-style GMR spin valve sensor. Imaging ofthe magnetization and sense current in the pair of shields wasaccounted for as a series of images. This model minimizesthe torque through initial simple iteration, followed by aNewton–Raphson minimization of the total energy of the

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3976 IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 6, NOVEMBER 2000

Fig. 1. Comparison betweenM -H loops for 10 Gb/in media generated withthe hexagonal (solid) and square (dashed) mesh for the LLG discretization.

discretized pinned and free layers. Out-of-plane magnetizationin the ferromagnetic layers was neglected. The signal fieldinside the read gap, at the shielded GMR sensor, is crudelyapproximated by

(1)

Here, is the exact signal field at due to themedium grain at in the absence of the shielded head(shield-to-shield spacing ). The function is an FEM-de-rived relation that describes the exponential decay of the signalfield into the read gap, along the-direction [10]. The down-track ( -direction) shielding coefficient was fixed at 0.5,such that pulsewidth at half maximum (PW) values similarto the earlier analytic results [19] were obtained. Potentially, a(two-dimensional) micromagnetic simulation of the shieldingof the stray field from transitions in the medium could improvethe model. This was not attempted here, and therefore, onlytrends in computed pulsewidths are considered reliable.

For generic 10 Gb/in applications, the medium used inthe calculations has an in-plane random uniaxial crystallineanisotropy axis distribution with Oe andemu/cc. Exchange coupling between the grains was neglected,and a uniform mesh was used on a square ( nmgrains) or hexagonal lattice (lattice constant 13 nm, mediumthickness nm). Real media has a complex structurebeing composed of randomly distributed grains of various size.In cases in which intergranular exchange coupling is weak, theprincipal effect of the grain size distribution is on medium noisepower, transition parameter, magnetization correlation length[11]–[13], and thermal decay [14], [15]. This is not consideredin the present work.

Magnetization-versus-applied-field (- ) loops generatedfrom the LLG equations for 10 Gb/inmedia are shown inFig. 1, for both the hexagonal and the square mesh. It is observedthat there is little difference between the magnetization reversalprocesses in these two cases. Both yield a coercive force of3200 Oe, a remanent magnetization value of , anda squareness of . Hexagonal discretization schemes

Fig. 2. Geometry of the writer pole tips for the notched design used in theFEM model of the head field. Relevant dimensions are indicated.

were introduced as a convenient “space-filling choice” [5],but otherwise, they have no physical basis. For the purposeof calculating the demagnetization tensor, the square latticeis preferred because all required integrals can be evaluatedanalytically.

FEM head fields were derived using a notched lower pole de-sign [16]. As schematically shown in Fig. 2, the lower pole ini-tially has the same width as the trailing pole before it flares outto the lower pole. The writer pole has a saturation magnetiza-tion of kG, with pole width equal to 0.6m and gaplength m. A head-to-medium separation of 30 nm wasassumed, and a GMR device with a sensing layer 0.6m wideand 0.3 m high was used for the read back of the recorded tran-sitions.

The medium is dc erased before writing transitions. For thepurpose of extracting trends in the remanent magnetization ofthe recorded patterns and playback characteristics, as well asfor visualization of the medium magnetization, most of therecorded patterns represent averages over ten runs. The varianceintroduced by the random uniaxial crystalline anisotropy wouldmake the comparison of the results from single runs difficult(as in actual measurements). Results presented in Section IVwere obtained from individual runs (no averaging).

III. POLE-TIP SATURATION AT 10 Gb/in

A. Lindholm and FEM Write-Head Fields

In this section, contours of the head field strength and headfield gradients in the recording medium are compared for theLindholm and the FEM model of a write head. The simplestmodel of the write field, the Karlqvist approximation, describessymmetric pole tips that are infinitely wide in the cross-trackdirection. The Lindholm head has a finite track width, but is alsoperfectly symmetric with respect to the write gap. Both of thesemodels assume a uniform distribution of “magnetic poles” onthe relevant surfaces. As such, effects due to pole-tip saturation,especially relevant at the pole corners in narrow-track recording,are absent.

VAN EK et al.: MRM OF POLE-TIP SATURATION EFFECTS 3977

Fig. 3. Contours of the field strength in the medium at the trailing pole tip for(a) the Lindholm head (H = 9:4 kOe), and (b) the corresponding FEM headfield. (c) Field gradients atH versusH at the center of the track (dashed)and track-averaged (solid) for Lindholm (circle) and finite-element-method(diamond) head fields.

Analytic expressions for the fringing field from Karlqvist andLindholm heads exist [17], [18]. The Lindholm head field ischaracterized by , the magnitude of the downtrack field com-ponent at the air-bearing surface, at the center of the track andwrite gap. The FEM software solves Maxwell’s equations for aspecific writer geometry with assumptions for the initial perme-ability and saturation magnetization of the different materials.The resulting head fields include the effect of pole-tip geometryand saturation characteristics, as well as the effects of materialproperties and current through the writer coil. In order to makea comparison between FEM and Lindholm head fields mean-ingful, in the Lindholm expression is chosen to match thevalue derived from the FEM model at each write current.

Fig. 3(a) and (b) show contours of the write field in themedium at the trailing pole tip for the Lindholm and theFEM model of the write head, respectively. The orientationof the pole tips corresponds to Fig. 2. The contours representdowntrack field strengths in the center of the medium, rangingfrom 2000–4000 Oe in steps of 200 Oe. The value offorthe Lindholm head was 9400 Oe, equal to the field at the centerof the gap, at the air-bearing surface in the FEM solution. Atthe center of the track, the FEM field gradient appears similarto the Lindholm gradient. At the pole-tip corners, at the trackedge, the gradient for the FEM-derived head field degradesfaster than for the Lindholm field. Fig. 3(c) shows head fieldgradients at the medium coercivity ( at ) asa function of ( increases with write current), both at the

center of the track and averaged over the track width. Severalobservations can be made. Both at the center of the track aswell as after averaging over the full track width, it is foundthat the Lindholm head field gradient monotonically increaseswith increasing . The FEM-derived gradient at the center ofthe track initially improves at very low write current, but thendegrades, in part due to head saturation. This is similar to theon-track corner saturation described in [2]–[4] for infinitelywide heads. Toward the track edge, the degradation of the fieldgradient with write current is more severe than at the center ofthe track [Fig. 3(a) and (b)]. Pole-tip saturation as a functionof write current is absent in the Lindholm head field. As aresult, over the field range of interest, the track-averaged fieldgradients for the Lindholm and FEM head fields follow theopposite behavior as a function of . For the Lindholm head,the gradient improves with increasing write current, whereasFEM-derived gradients degrade. Pole-tip saturation effects arethe primary focus of the present paper. Further manifestationsof pole-tip saturation are explored in subsequent subsections.

B. Effects of Pole-Tip Saturation on Recorded Transitions

Increasing the current through the writer coil serves not onlyto increase the field reaching the medium, but also enhancespole-tip saturation. FEM modeling supports the notion that suchsaturation degrades the field gradient in the medium. It is sus-pected that this can lead to a degradation in the quality of therecorded tracks, especially at the edges of the track. Fig. 4 il-lustrates this point. Dibits were recorded at a spacing corre-sponding to a linear density of 200 kbpi, using the nominalFEM 10 Gb/in writer and LLG medium (square mesh). Fourdifferent write currents were chosen to give the values ofindicated. Here, is the downtrack component of the headfield at the center of the write gap and at the point midway inthe medium thickness. In Fig. 4, the images of the LLG solutionfor the downtrack component of the magnetization vector ()clearly show track curvature, track edge distortion, and an in-creased level of percolation as the pole-tip saturation increases.Also shown are profiles of the downtrack magnetization(averaged over the pole width). The remanent magnetizationinside the dibit is reduced with write current and least-squaresfitting of the magnetization profiles to (e.g., see[7], [12], and [13]) indicates that the transition parameter in-creases with write current. Fig. 4 shows fitted magnetizationprofiles (dashed lines) as well as the effective transition param-eter extracted from the fit. In the fitting procedure, the transitionlengths for the two transitions in the dibit were forced to be thesame, and the remanent magnetization outside the dibit was im-posed as a boundary condition. Due to transition curvature in-duced by pole-tip saturation, the track-averaged magnetizationprofile is asymmetric about the center of the dibit. This is notreproduced by the fitted profile.

In order to quantify track edge effects, the following proce-dure was followed. The downtrack component of the mediummagnetization was averaged over track widths ranging from thecentral 50% of the track to the full track width. At each fractionof the full track width, the resulting downtrack magnetizationprofile was fitted (least squares) to a function,


Fig. 4. Track-averaged down-track magnetization profiles (solid curves) and images of the down-track magnetization for four different write currents. FEM headfield at the center of the media is indicated. Also shown is the result of tanh fits (dashed), and fitted transition parameters are indicated. White lines in the imagesoutline the writer pole width.

yielding the transition parameter and remanent magnetizationas a function of averaging width. This procedure establishes ameasure of the variation of the transition parameter and rema-nent magnetization across the track width, and it will demon-strate how pole-tip saturation effects degrade the quality of therecorded track, in particular at the track edges.

With increasing write current, the remanent magnetization in-side the dibit is found to degrade significantly. Fig. 5 showsthe normalized remanent magnetization inside the dibit as afunction of averaging width for write currents corresponding

to 5900 and 7580 Oe. The remanent magnetization in-side the dibit decreases significantly with increased averagingwidth, indicating poor definition of the transition toward thetrack edges. Increasing the write current further diminishes theremanent magnetization. A reduced remanent magnetization in-side the dibit, together with an increased transition length, sug-gests that the signal voltage on playback will be reduced. Thepresent results demonstrate that pole-tip saturation effects canhave a severe impact on the characteristics of the recorded tran-sitions at high track densities.


Fig. 5. Normalized magnetization(M =M ) inside the dibit as a function ofaveraging width. Inset shows the field in the medium, indicative of the level ofpole-tip saturation.

Fig. 6(a) quantitatively shows how track-edge and on-trackgradient degradation serve to increase the effective transitionparameter “.” The fitted transition parameter increases withthe percentage of the track width used for the average down-track magnetization profile. This increase is further enhanced byhigher write currents (larger ). Note that even in the centerportion of the track, an increase in write current serves to in-crease the transition length due to degradation of the on-trackfield gradient with write current. This is illustrated in Fig. 6(b),where the mean FEM head field gradient as a function of av-eraging width is shown for low and high write currents. Par-tial pole-tip saturation at the higher write current produces anon-track gradient (50% of track width) that is much worse thanat low write current. Upon increasing the averaging width, thegradient degrades roughly linearly, whereas at low current, thedependence of the mean gradient on averaging width initiallyis weaker. These results show that pole-tip saturation impactsthe gradient and, hence, the quality of the recorded transitionsacross the entire track width.

In general, it is seen that for the FEM head field, “” increaseswith increasing , from about 13 to 18 nm over the range of

(field in the medium) considered [see Fig. 6(a)]. The mi-cromagnetic results of [7] and [13] show how the grain sizeaffects, and at low flying heights, limits the reduction in tran-sition parameter. Using a linear Karlqvist head field, they ob-tain a transition parameter, using the parameters in this paperof about 11 nm. Their results are for a record current that max-imizes the head field gradient so that the slightly smaller tran-sition parameter than the result of Fig. 6(a) at low current andpercentage track width, is to be considered in good agreement.As an illustration of the effect of head field gradient, the simpleWilliams–Comstock expression is used to evaluate the transi-tion parameter [17, p. 213] for two values of . The transitionparameter decreases with increasing record field in contrast tothe simulation results. The reason is that this simple model doesnot include pole-tip saturation, and the head medium parame-

(a)

(b)

Fig. 6. (a) Fitted transition parameter versus percentage of the track width usedfor averaging. Inset shows the field in the mediumH , indicative of the level ofpole-tip saturation. Typical results from the Williams–Comstock model (WC)are shown. (b) Mean head field gradient as a function of averaging width.

ters used are such that increasing the current increases the fieldgradient [17, p. 216].

Even though the exchange interaction in the medium waschosen to be zero in this study, in real media, the exchangeinteraction cannot be eliminated entirely. The dibits shown inFig. 4 (no exchange) were regenerated, but now in the presenceof weak exchange coupling , is the in-tergranular exchange, is the uniaxial crystalline anisotropy,and is the grain size). It was found that the exchange in-teraction alters the details of the recorded magnetization pat-tern for all four write currents. However, the fitted transitionparameter, obtained from cross-track, averaged magnetizationprofiles, does not significantly change for the two lower writecurrents, whereas a small increase of about 2.5 nm is observedfor the two higher write currents. The notion of an increasedtransition parameter upon addition of weak exchange couplingappears to be consistent with the results reported in [12]. Furtheranalysis revealed that the transition length at the center of thetrack is unaffected, and thus in the present study, the increase in“ ” upon addition of weak exchange has its origin in the trackedges. Apparently, weakly coupled grains, subject to the head


Fig. 7. PW versus write current as derived from FEM write-head fields usingthe recording model. Also shown are PWfor pure Williams–Comstock andWilliams–Comstock with FEM field gradients. Error bars on the MRM curveindicate the range of pulsewidths obtained in ten runs for each write current.

field at the track edge with a poor gradient, result in a locally in-creased spatial extension of the transition when compared withmedia without exchange coupling.

Measurement of the playback voltage pulsewidth for isolatedtransitions provides another means for characterization of therecorded transitions. If the PWis large, intersymbol interfer-ence will negatively impact the playback performance of therecording system. In classic recording theory, the pulsewidthis determined by the width of the read gap (), magnetoresis-tive element thickness (), the transition length (), the head-to-medium separation (), and the medium thickness (), accordingto [19]

PW (2)

Any dependence of PW on, for instance, write current entersthrough the transition length.

Fig. 7 shows as a function of write current as de-rived with the 10 Gb/in FEM writer head field and a genericspin valve magnetoresistive sensor. Pulsewidths are estimatedfrom the average of ten runs, where the in-plane easy axis dis-tribution of the medium is regenerated for each run. The errorbars in Fig. 7 indicate the range of obtained PW-values. Alsoshown are results from the Williams–Comstock approximationfor “ ” used in (2) for the pulsewidth. In addition, results are in-cluded where FEM values for the field gradient were used in theWilliams–Comstock relation for the transition parameter. Re-sults in Fig. 7, derived with the MRM, recover the very typicaland pronounced minimum in PW as function of write cur-rent seen experimentally. On the other hand, at medium-to-highwrite current, the Williams–Comstock values for PWdependonly very weakly on the write-head field, and PWdecreasesmonotonically with write current. These results further illustratehow analytic recording models fail to capture essential featuresof high-density magnetic recording that are a consequence of

Fig. 8. Effects of increasing linear density. (a) Peak-to-peak playback signalamplitude as a function of linear density, and (b) an image of the down-trackmagnetization for a 400 kbpi dibit.

narrow track widths, pole-tip saturation effects, and, as in [12],the granular nature of real media.

C. Effects of Increased Linear Density

The FEM solution for the 10 Gb/inwriter withOe (25 mA write current) was used to record dibits at linear den-sities between 25 and 500 kbpi. Read-back with the micromag-netic spin valve model was then performed to asses the effect ofdecreasing bit spacing at high track density on the peak-to-peakamplitude of the playback signal. As shown in Fig. 8(a), in theregime between 300 and 500 kbpi, there is about a 0.15 mVreduction in signal amplitude per 50 kbpi increase in linear den-sity.

The dibit linear density, at which the signal voltage reducesto half the isolated pulse signal, is 313 kbpi ( b/nm).This linear density is the dibit equivalent of Dfor squarewave recording [17]. Along with PW-values ranging from


Fig. 9. Tracks at different linear density for the case of 0.2�m wide writer poles. The images show the down-track component of the magnetization, and thegraphs show the cross-track, averaged down-track magnetization. Averaging was performed over the width of the writer pole tip, indicated by the white lines inthe images.

177 to 193 nm (Fig. 7), the calculated PWD -productranges from 2.2 to 2.4 bits. Linear dibit pulse superposition ofa simple Lorentzian pulse shape gives PWD , whichis in good agreement with the micromagnetic results. Even forcomplicated pulse shapes due to head saturation and edge trackeffects, nonlinear percolation is sufficiently small at dibit Ddensities so that the above relation is generally expected tohold. Linear superposition of square wave recording with MRheads yields PWD [19]. For a given PW , squarewave recording yields a lower density than does dibitrecording. Thus, the general relation for square wave recordingshould also hold for complicated finite track effects and headsaturation.

Due to partial pole-tip saturation, the transitions are poorlydefined at the track edge. Despite the fact that the image of thedibit magnetization at 400 kbpi in Fig. 8(b) is the result of an av-erage of ten recording runs, percolation at the track edges can beclearly distinguished. Note that 280 kbpi corresponds to about

seven medium grains between transitions. At 495 kbpi, thereare only four grains between transitions and the local easy axisdistribution of the grains becomes increasingly important. Per-colation at high linear density is due largely to the edges of tran-sitions being ragged, a property inherent to the random in-planeorientation of crystalline anisotropy axes, as well as demagne-tizing effects in the medium.

The influence of demagnetizing fields from neighboring tran-sitions becomes less influential as decreases and the crys-talline uniaxial anisotropy increases. In order to further illustratethis point, the track-averaged magnetostatic field in the nominal10 Gb/in medium was compared for a single transition anddibits separated by ten grains (195 kbpi) and five grains (391kbpi). For the isolated transition, it was found that the magne-tostatic field switches from about500 Oe to 500 Oe close tothe transition. Inside the dibit at the larger separation, the fieldis approximately 700 Oe, whereas at the smaller separation, thefield is 1000 Oe. The quoted field strengths range from 5 to 15%


Fig. 10. Peak-to-peak playback signal amplitude as a function of linear densityfor the case of 0.2�m–wide tracks. Playback was performed on the tracks shownin Fig. 9.

of . For the grains inside the dibit, this implies only a smallexcursion from the remanent state in the- loop (Fig. 1).

IV. EXAMPLES AT ULTRAHIGH TRACK DENSITY

The MRM was used to evaluate the recording process onlongitudinal media at ultrahigh track density. The width of thewriter pole tip in the FEM model was 0.2m with high momentmaterial around the write gap. The head-to-medium spacingwas assumed to be 15 nm. Magnetic properties of a mediumthat potentially can support high track and linear density are

Oe, media thickness nm, medium grainsize of 9 nm, and emu/cc. For the magnetoresistivesensor, a generic spin valve was assumed with a physical widthof 0.2 m, a height of 0.15 m, a 15% GMR ratio, and a 4 mAsense current. Narrow tracks were recorded at 200, 400, 570,and 712 kbpi, and playback was performed.

Fig. 9 shows images of the downtrack magnetization ofthe recorded tracks (results from single runs), as well asthe cross-track, averaged downtrack magnetization. Withincreasing linear density, enhanced percolation degrades thetransitions. This percolation is a direct reflection of the localeasy axis distribution at the position of the transition. In amedium with crystalline anisotropy fields on the order of10 kOe, the magnetization of the grains will relax to alignwith the easy axis after the write field vanishes. At low lineardensity, this phenomenon causes the transitions to appearragged (Fig. 9, 200 kbpi). Superposition of ragged transitions at712 kbpi (four grains per transition) causes severe percolation.Fig. 10 shows the linear rolloff of the playback signal voltagewith increasing linear density. The signal amplitude rolloffis about 0.2 mV/100 kbpi, and D is 375 kbpi. Even withvery aggressive assumptions for the sensor properties and thehead-to-medium spacing, the expected read-back signal at highlinear density is small.

In the present investigation of ultranarrow tracks, pole-tip sat-uration effects were controlled through the assumption of veryhigh moment material in the writer pole tips. A reduction in satu-ration magnetization of the material around the write gap imme-

diately will bring about the pole tip saturation effects describedin Sections III-B and III-C. A reduction in remanent magnetiza-tion between the transitions along with an increase in transitionparameter will result in wider signal pulses and a suppressedplayback signal.

V. CONCLUSION

The effects of writer pole-tip saturation on the quality of therecorded transition at an areal density of 10 Gb/inwas inves-tigated using a micromagnetic medium model, finite elementwrite-head fields, and a micromagnetic model of a spin valvesensor. The behavior of the finite element head field gradientwith write current is opposite to what we would expect on thebasis of analytical models. Over the relevant range of write cur-rents, the finite element gradient degrades while analytical gra-dients improve. A degradation of the field gradient manifests it-self as a decrease in the remanent magnetization inside recordeddibits along with an increase in the transition parameter. At thetrack edges, pole-tip saturation causes the remanent magneti-zation inside the dibit to be lower and the transition parameterlarger than at the center of the track. Upon playback, isolatedtransitions recorded with the finite element head field yield apronounced minimum in the signal pulsewidth as a function ofwrite current, consistent with experimental observations. Overthe same range of write currents, the dependence of pulsewidthon the write current for analytical head fields is very weak.

At ultrahigh recording densities, where the width of thewriter pole tip is only 0.2 m, severe percolation was observedon high coercivity media. Even with aggressive assumptionsfor head-to-medium spacing, writer pole-tip materials, mediummagnetization, mean grain size, GMR ratio, and sense current,the playback signal voltage at high linear density was alarm-ingly small. The exact nature of writer pole-tip saturation hasyet to be examined by a detailed micromagnetic model.

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Micromagnetic recording model of pole-tip saturation effects