IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 6, NOVEMBER 2000 3991

Effect of Secondary Gaps in Near-SaturatedMetal-in-Gap Video Heads

Desmond J. Mapps, Member, IEEE, Hazel A. Shute, and David T. Wilton

Abstract—Secondary gaps between the ferrite bulk and theSendust (AlFeSi alloy) shim may occur in metal-in-gap (MIG)heads. Finite-element models are used to explore the effect thatthese gaps have on the read/write characteristics of single- anddouble-sided MIG heads. The presence of a secondary gap isshown to cause an additional peak in the writing field and oscil-lations in the magnitude of the response during replay. The fieldand response of a double-sided MIG head is affected more thanthose of the corresponding single-sided MIG head.

Index Terms—Finite-element methods, magnetic recordingheads, magnetic reading heads.

I. INTRODUCTION

A LL ferrite video heads superceded gapped heads of highersaturation flux density but made from mechanically softer

materials, due to their better wear characteristics and reducededdy current losses. A typical ferrite, used in the manufactureof a recording head, has a saturation flux density of about 5000G. The fields generated in all of these ferrite heads are sufficientto write to tapes with coercivities of about 700 Oe, which arecurrently used for consumer analog video. The change to digitalvideo, which requires higher data densities than does analog, hasnecessitated the use of higher coercivity media, such as metalparticle and metal evaporated tapes. Helical scan systems, orig-inally developed for video, are also used to backup computerdata. The media for future generations of digital tape recorderscan be expected to be of even higher coercivities, as is the trendfor computer hard disk media, in order to increase data density.

Metal-in-gap (MIG) heads, first proposed in [1], can producefields of sufficient strength to write data onto media with co-ercivities greater than 1000 Oe [2]. A single-sided MIG headdiffers from an all ferrite head by having a layer of high satu-ration flux density material deposited on the trailing gap edge,in order to reduce saturation at that gap-edge corner during thewriting process. If high saturation layers are deposited on bothgap edges, the head is described as double-sided. Sendust is apopular choice for the MIG layers as it is less prone to erosionthan are other high saturation flux density materials, such asPermalloy (NiFe). Chemical interaction may occur at the inter-face between a Sendust layer and the ferrite bulk, which causes

Manuscript received May 17, 2000; revised July 25, 2000. This work wassupported by the EPSRC under Grant GR/M 23939.

D. J. Mapps is with the Department of Communication and Electronic Engi-neering and the Centre for Research in Information Storage Technology, Uni-versity of Plymouth, PL4 8AA Plymouth, U.K.

H. A. Shute and D. T. Wilton are with the Department of Mathematics andStatistics and the Centre for Research in Information Storage Technology, Uni-versity of Plymouth, PL4 8AA Plymouth, U.K.

Publisher Item Identifier S 0018-9464(00)09952-0.

a magnetically dead layer. The extent of the interaction dependson the parameters of the Sendust deposition process. A barrierlayer of Permalloy between the ferrite and the Sendust has beensuggested [3]. A magnetically more damaging solution to theferrite–Sendust interface problem is to deliberately form a silica(SiO ) barrier between the two magnetic materials. Hence, sec-ondary gaps of known length are created that prevent uncon-trolled degradation of the Sendust layer. Some MIG heads con-structed in this way are still manufactured [4].

To the authors’ knowledge, the effects of secondary gapsin MIG heads have not previously been fully investigated andreported in the literature. Replay experiments and approximatedtheoretical output results have been reported in [3] and [5],whereas studies of the write fields of MIG heads have assumedthat no secondary gaps occur [2], [6]–[9]. Here, finite-elementmodels [10] are used to determine the effect of secondary gapson both the reading and the writing characteristics of single-and double-sided MIG heads.

II. M ETHOD

A finite-element model of a gapped head has been created.The need for high accuracy close to the gap, which is typically1/8000 the length of the entire head, requires a large number ofelements. Hence, as MIG heads are at least 20 times as wide asthe gap length, a two-dimensional (2-D) model has been used.The validity of 2-D models for MIG heads has been confirmed[8]. The accuracy of the results from this model, for a very highconstant permeability material, has been verified by compar-ison with analytic results [11]. Variation of the material prop-erties of the head has been achieved without any change in themesh, and hence, accuracy is believed to have been maintained.The Monson model for the M–H characteristic of a ferrite headmaterial [12] has been used, assuming an initial susceptibility

of 999 and a saturation flux density of 5 kG. Sendusthas been assumed to have the same initial susceptibility but asaturation flux density of 10 kG. These virgin B–H curves areshown in Fig. 1(a). In replay, saturation of the gap edge cornersis not likely to occur. Hence, a linear M–H characteristic with

has been used to model both materials in this situa-tion.

The geometry of the MIG head appears in Fig. 1(b), and de-tails of the gap region are shown in Fig. 1(c), not to scale. Aprimary gap of length m and throat height of 16mhave been used throughout this work. The Sendust MIG layersare 4 m long and extend to the top of the throat on the trailingpole and, in the case of the double-sided MIG head, to a heightof 70 m on the leading pole. Secondary gaps varying in length

0018–9464/00$10.00 © 2000 IEEE

3992 IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 6, NOVEMBER 2000

(a)

(b)

(c)

Fig. 1. Finite-element model of a MIG head. (a) B–H characteristics. (b)General geometry (not to scale). (c) Detail of the gap region of the double-sidedMIG head (not to scale).

from zero to 30 nm and writing currents, which cause mag-netomotive forces (mmfs) of 0.25, 0.5, and 0.75 A, have beenapplied.

The field components and the gradient of the horizontal fieldhave been evaluated at intervals of m. Linear interpola-tion has permitted the evaluation of the spectral response func-tion, which is the Fourier transform of the horizontal field in thehead face plane

(1)

The limits and , which should theoretically extend to infinityin both directions, have been chosen so that over the excludedlower and upper ranges, Oe.

III. RESULTS AND DISCUSSION

Figs. 2 and 3 show the horizontal and vertical fields of single-sided MIG heads with secondary gaps ranging from zero to30 nm in length. In each case, the main gap and the Sendustlayer are 0.25 m and 4 m long, respectively, so that all of thesecondary gaps extend away from the main gap starting from

Fig. 2. Effect of increasing the secondary gap length on the horizontal field aty = 0:05 �m of a single-sided MIG head.G = 0:25 �m and mmf= 0:25 A.

Fig. 3. Effect of increasing the secondary gap length on the vertical field aty = 0:05 �m of a single-sided MIG head.G = 0:25 �m and mmf= 0:25 A.

m. Results for each field component are pre-sented at m for a driving mmf A. Hori-zontal fields of similar shape, when there is no secondary gap,have been obtained [2]. For this mmf, only slight saturation ofthe ferrite corners occurs, which is shown by the nonzero hor-izontal field for m when there is no secondarygap. Fields of at least this strength are needed to write on metalparticle tape, which has a typical coercivity of 1450 Oe withcurrent head-medium spacings of at least 0.05m.

The presence of the Sendust layer on the trailing gap-edgecauses an asymmetric field. The horizontal field is steeper abovethe trailing edge of the gap than it is above the leading one. Asecondary peak occurs above the secondary gap in both the hor-izontal and the vertical fields. As the secondary gap length in-creases, the magnitudes of the secondary peaks increase. For thehorizontal field, under this mmf, the secondary peak rises from20 Oe to 730 Oe as the secondary gap increases in length fromzero to 30 nm. A secondary peak that is greater than half the co-ercivity of the medium has been shown to degrade or even par-tially erase the recorded transition [13]. Hence, a secondary gaplonger than 30 nm, in a single-sided MIG head under an mmf of0.25 A, would be sufficient to prevent optimum recording on ahorizontally oriented, metal particle tape.

A simple analysis, assuming that a field of the same constantmagnitude occurs across each gap in an infinitely permeable

MAPPSet al.: SECONDARY GAPS IN MIG VIDEO HEADS 3993

Fig. 4. Effect of increasing the magnetomotive force and the secondary gaplength on the horizontal field aty = 0:05 �m of a single-sided MIG head.G = 0:25 �m.

head, estimates that the ratio of the peak secondary field to thatof the entire field is

(2)

as the length of the metal shim is much greater than that of thesecondary gap. This approximation underestimates the ratio forsingle-sided MIG heads by up to 10%, over the range of sec-ondary gaps considered here. The same assumptions cannot beused to model the entire field as saturation occurs at the gap edgecorners of the ferrite head parts. Both the primary and the sec-ondary fields of the vertical field are affected less by an increasein secondary gap length than are those for the horizontal field.Both field components, above the leading pole of the head, arealmost unaffected by the presence of a secondary gap.

The magnitude of the vertical field declines more rapidly thanthat of the horizontal field with increasing separation from thehead. The total field has magnitude and direction

. As the horizontal and vertical fields do nothave coincident maxima, the gain in attempting to align mediaparticles with the head field would at best only achieve slight im-provements unless tape media thickness and effective head-tapeseparation are reduced. For example, the maximum total field at

m for a single-sided MIG head with no secondarygap, under an mmf of 0.25 A is 3190 Oe. This is an 8% increaseover the maximum horizontal field for the same head, but thistotal field maximum acts at an angle 34to the direction of thehead motion. At m, the gain is only 1% because herethe maximum total field lies only 17from the direction of thehead motion.

The peak horizontal field, for a fixed primary gap length, canbe increased by applying a higher drive current. This increasesthe region of saturation at the ferrite corners. The effects of in-creasing the mmf on the horizontal fields of single-sided MIGheads with secondary gaps of zero and 30 nm in length areshown in Fig. 4. Above the leading pole, the change in magne-tomotive force has a much greater effect on the horizontal fieldthan does the presence or the absence of a secondary gap. The in-crease in saturation in the all ferrite pole as the magnetomotive

(a) (b)

Fig. 5. Effect of secondary gap length on the maximum secondary horizontalfield at y = 0:025 �m, y = 0:05 �m, andy = 0:1 �m of (a) a single-sidedand (b) a double-sided MIG head.G = 0:25 �m.

force rises causes a significant increase in the horizontal fieldabove the leading pole. The secondary peak above the trailingpole increases less with rising magnetomotive force than withsecondary gap length. Saturation in the ferrite head parts in-creases with magnetomotive force, but saturation in the metalshim remains negligible. Hence, the approximation to the ratiobetween the peak secondary field and that of the entire field (2)maintains its accuracy over this range of magnetomotive forces.

Although double-sided MIG heads are more expensive to pro-duce than are single-sided ones, they do have some advantages.Their fields are almost symmetric about the center of the maingap. Slightly more saturation occurs on the trailing pole side,due to the reduced throat height on this half of the head. Thepeak horizontal field, at m, is at least 21% higherthan that for the corresponding single-sided head, for each ofthe three magnetomotive forces tested. Similar improvementsin peak horizontal field have been reported in [2], when nosecondary gaps were present. The secondary peak above thetrailing pole is always marginally higher than that above theleading pole. In each case, the peak secondary field for a double-sided MIG head is slightly greater than that of the correspondingsingle-sided one. The approximation (2) overestimates the ratioof the peak secondary field to that of the entire field by up to 10%for a double-sided MIG head, for the range of secondary gapsconsidered here. The peak secondary horizontal fields for bothsingle-sided and double-sided MIG heads are shown in Fig. 5.Clearly, the length of any secondary gap, whether introduced bydesign or otherwise, should be minimized.

The width of a written transition is determined by the gra-dient of the field when the field strength equals the coercivityof the tape. Hence, the narrowest transitions are written on atape whose coercivity equals the head field at the point of max-imum gradient along the path of the center of the tape. Table Ishows the average of the horizontal field strength at the pointof maximum horizontal field gradient, for each of the six sec-ondary gap lengths considered here. The optimum coercivityfor the medium varies by up to 6% with secondary gap lengthfor a double-sided MIG head under a magnetomotive force of0.25 A. This variation, shown in Table I, is positive forand negative for nm. At this level of drive current,

3994 IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 6, NOVEMBER 2000

TABLE IOPTIMUM MEDIUM COERCIVITY (Oe)

TABLE IIMAXIMUM HORIZONTAL FIELD (Oe)

only the sharp corners of the ferrite saturate so that the pres-ence of the secondary gaps reduces the peak horizontal fieldand, hence, affects the horizontal field magnitude at the pointof maximum gradient. In all of the other cases that have beenevaluated, the variation in the optimum coercivity is close tothe expected accuracy of the model and, hence, cannot be reliedon, although consistently slightly higher coercivities have beenobtained from the smaller secondary gaps and the variation fallswith both increasing head–medium spacing and magnetomotiveforce.

The field above the MIG material and the primary gap is al-most unaffected by the secondary gaps if the ferrite corners aresaturated. Average peak field values are given in Table II, wherethe deviations, again only significant for a double-sided MIGhead under a magnetomotive force of 0.25 A, are positive for

and negative for nm.As well as causing significant damage to the writing process,

secondary gaps also impair replay. The spectral response func-tion describes the effect of the reading head geometry on theoutput voltage when a prerecorded sinusoidal wave is replayed.Fig. 6 shows the effect of the secondary gap length on the spec-tral response function of a single-sided MIG head. As no satu-ration has been assumed to occur during replay, these results arepresented in terms of the primary gap length by which they andall dimensions can be scaled. When there is no secondary gap,the response is virtually identical to that of an ideal ring head

Fig. 6. Effect of increasing the secondary gap length on the spectral responsefunction of a single-sided MIG head.

Fig. 7. Effect of increasing the secondary gap length on the phase of thespectral response function of a single-sided MIG head.

[14] with the first null occurring at . The presence ofa secondary gap causes oscillations in the response. The ampli-tude of these oscillations increases with secondary gap length.Similar oscillations occur in the response when a gapped headmade from a single magnetic material replays data written bya MIG head with secondary gaps that are long enough for theirfields to write onto the medium.

The response of an asymmetric head has both real and imag-inary parts. True nulls in the response of symmetric heads areassociated with abrupt phase changes by 180. Fig. 7 shows thephase of the spectral response function for three of the single-sided MIG heads considered here. When there is no secondarygap, the phase changes at and 1.9, as expected foran unsaturated gapped head. When a secondary gap is present,the phase of the response varies continuously with frequency,oscillating with the same period as the spectral response func-tion. Near frequencies corresponding to those that cause nulls inthe response of a head with no secondary gap, the amplitudes ofthe oscillations become large. The range over which this occursincreases with secondary gap length. Hence, when a secondarygap is present, the phase changes almost abruptly by up to 180

MAPPSet al.: SECONDARY GAPS IN MIG VIDEO HEADS 3995

Fig. 8. Effect of increasing the secondary gap length on the spectral responsefunction of a double-sided MIG head.

Fig. 9. Effect of increasing the secondary gap length on the phase of thespectral response function of a double-sided MIG head.

at a frequency lower than , restricting the use of thehead.

The spectral response functions and three of the cor-responding phase angles for the double-sided MIG headsconsidered here are shown in Figs. 8 and 9. The presence of asecondary gap on the leading pole as well as on the trailing polecauses even higher amplitude oscillations in the response thathave the same frequency as those for the single-sided MIG head.Hence, the phase of the spectral response of a double-sidedMIG head varies with frequency in a similar manner to thatof a single-sided one, as can be seen in Fig. 9. Oscillations inthe response of a double-sided MIG head with secondary gapshave been observed and modeled approximately [3], [5], butminor oscillations in other experimental output curves for MIGheads, for example [7], [8], [15] may be due to the presence ofsecondary gaps.

The approximate formula for the spectral response function[5], evaluated with an effective gap length of and aninfinite head permeability, has been found to be in very goodagreement with the results obtained here for , for bothsingle- and double-sided MIG heads. The error in the approxi-mation of the amplitude of the response when there are no sec-ondary gaps increases with the frequency of the replayed wave

and so does the error in the amplitude of the oscillations in theresponse when there are secondary gaps.

When no secondary gaps are present, the amplitude of thespectral response function varies by 5 dB over the range of fre-quencies less than . Secondary gaps of length 30 nmcause an increase in this variation to over 7 dB and 8 dB insingle- and double-sided MIG heads, respectively.

IV. CONCLUSION

The effects of secondary gaps on the write field and the replayresponse, in single- and double-sided MIG heads, have been ex-plored. The length of a secondary gap both affects the magnitudeof the secondary field peak, which occurs above the secondarygap during writing, and causes oscillations in the magnitude ofthe response of the head during replay.

A double-sided MIG head, with or without secondary gaps,suffers less saturation than does the corresponding single-sidedone. Hence, it produces a stronger write field; but when sec-ondary gaps are present, the associated secondary peaks arealso of greater magnitude than that of the corresponding single-sided MIG head. The response of a single-sided MIG head witha secondary gap has smaller amplitude oscillations than thatof the corresponding double-sided one. MIG heads with sec-ondary gaps are unsuitable for digital recording on high coer-civity media.

ACKNOWLEDGMENT

The authors would like to thank Informatic Component Tech-nology for their assistance and the referees for their helpful sug-gestions.

REFERENCES

[1] F. J. Jeffers, R. J. McClure, W. W. French, and N. J. Griffith,“Metal-in-gap record head,”IEEE Trans. Magn., vol. MAG-18, pp.1146–1148, 1982.

[2] Y. Kanai, M. Iizuka, T. Hatanai, and T. Konishi, “Design of ametal-in-gap head for higher coercivity media,”IEEE Trans. Magn.,vol. 27, pp. 4894–4896, 1991.

[3] C. W. M. P. Sillen, J. J. M. Ruigrok, A. Broese van Groenou, and U.Enz, “Permalloy/sendust metal-in-gap head,”IEEE Trans. Magn., vol.MAG–24, pp. 1802–1804, Mar. 1988.

[4] G. Pan, personal communication.[5] J. J. M. Ruigrok, “Analysis of metal-in-gap heads,”IEEE Trans. Magn.,

vol. MAG-20, pp. 872–874, Sept. 1984.[6] G. V. Kelly, “Write-field analysis of metal-in-gap heads,”IEEE Trans.

Magn., vol. 24, pp. 2392–2394, Nov. 1988.[7] T. Nishiyama, R. Goto, M. Yamazaki, I. Sakaguchi, S. Suwabe, and A.

Iwama, “A double-sided metal-in-gap head for 150 Mb/inrecording,”IEEE Trans. Magn., vol. 28, pp. 2632–2634, Sept. 1992.

[8] Y. Kanai and M. Iizuka, “Read-write characteristics of dual-sidedmetal-in-gap heads with various media,”IEEE Trans. Magn., vol. 30,pp. 1483–1486, July 1994.

[9] Y. Kanai and K. Ogawa, “Modeling of magnetic recording heads for2-D and 3-D finite-element analysis,”IEEE Trans. Magn., vol. 30, pp.2948–2951, Sept. 1994.

[10] Opera 2D. Oxford, U.K.: Vector Fields.[11] D. T. Wilton, “Comparison of ring and pole head magnetic fields,”IEEE

Trans. Magn., vol. 26, pp. 1229–1232, May 1990.[12] J. E. Monson, “Field analysis for nonlinear magnetic heads,”IEEE

Trans. Magn., vol. MAG-8, pp. 533–536, Sept. 1972.[13] M. Iiuzuka, Y. Kanai, T. Hatanai, T. Konishi, and K. Mukasa, “Influence

of head fields and media properties on transitions of magnetization re-versals on thin film disk,”J. Mag. Soc. Jpn., vol. 15, pp. 151–154, 1991.

3996 IEEE TRANSACTIONS ON MAGNETICS, VOL. 36, NO. 6, NOVEMBER 2000

[14] W. K. Westmijze, “Studies on magnetic recording. II field configurationaround the gap and the gap-length formula,”Philips Res. Rep., vol. 8,pp. 161–183, June 1953.

[15] Y. Sugiyama, H. Ohmori, T. Kobayashi, T. Yamamoto, M. Shoji, Y.Okazaki, and K. Hayashi, “Read/write characteristics and noise proper-ties of a thin film VCR head,”IEEE Trans. Magn., vol. 32, pp. 172–177,Jan. 1996.

Desmond J. Mappsreceived the B.Eng. degree in electrical engineering in 1966and the Ph.D. degree in magnetics in 1969, both from the University of Wales,Cardiff.

From 1969 to 1973, he researched computer memories in industry beforejoining the University of Plymouth, U.K. He is now Professor of ElectronicInformation Engineering and Head of the Center for Research in InformationStorage Technology at the University of Plymouth. Dr. Mapps is a Fellow ofthe U.K. Institute of Physics and a Fellow of the U.K. Institution of ElectricalEngineers.

Hazel A. Shutereceived the B.Sc. degree in mathematical studies in 1992 andthe Ph.D. degree in mathematical modeling in 1995, both from the Universityof Plymouth, U.K.

She is currently continuing her work on magnetic recording head read/writecharacteristics as a Postdoctoral Research Fellow at the University of Plymouth.

David T. Wilton received the B.A. degree in mathematics from the Universityof York, U.K., in 1969 and the D.Phil. degree in numerical analysis from theUniversity of Oxford, U.K., in 1974.

He spent three years at the University of Dundee, Scotland, and then threeyears with the Ministry of Defence, working on dynamic fluid-structure interac-tion problems in underwater acoustics. Since 1978, he has been lecturing math-ematics at the University of Plymouth, U.K. During 1987–1989, he spent twoyears at the City Polytechnic of Hong Kong. His main research interests arein numerical analysis and applied mathematics in the areas of electromagneticsand acoustics.