Experimental demonstration of onesided flux in magnetic recording tapeP. J. Flanders Citation: Journal of Applied Physics 61, 4007 (1987); doi: 10.1063/1.338561 View online: http://dx.doi.org/10.1063/1.338561 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/61/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in OneSide Invertibility of the Weighted Shift Operators AIP Conf. Proc. 1307, 101 (2010); 10.1063/1.3527404 A thermometer whose memory is a one-sided magnet Phys. Teach. 37, 148 (1999); 10.1119/1.880199 OneSided Multipactor Discharge Modes J. Appl. Phys. 34, 3237 (1963); 10.1063/1.1729170 The OneSided Green's Function J. Appl. Phys. 22, 1054 (1951); 10.1063/1.1700100 OneSided Polarization of Ions in Vapor Molecules J. Chem. Phys. 9, 378 (1941); 10.1063/1.1750915

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Experimental demonstration of one~sided flux in magnetic recording tape P. J, Flanders Department of Physics and LRSM, University of Pennsylvania, Philadelphia, Pennsylvallia 19104

It is shown that a magnetic tape can be magnetized so that the fringing field exists on only one side of the tape, a behavior predicted several years ago but never previously confirmed by direct experiment. This one-sided flux requires a tape specially produced to have equal remanence in any direction normal to the transverse axis.

INTRODUCTiON

It has been pointed out by MaHinson,I.2 and earlier by Westmijze,3 that it is in principle possible to magnetize a planar magnetic material (a recording tape or a multi pole permanent magnet array) in such a way that fringing field exists on only one side of the plane. This phenomenon has been called "one-sided flux." The simplest such magnetiza­tion pattern is one in which a magnetization of constant am­plitude rotates about the transverse axis of the tape, with the angle of rotation varying linearly with position along the tape axis (see Figo 1).

This surprising result is most easily understood by re­garding the magnetization distribution ofFigo 1 as consisting of the superposition of two simpler distributions as shown in Fig. 2, one with the magnetization alternating in direction but always parallel to the tape axis and the other alternating in direction but always perpendicular to the tape surfacco It can be seen that the resulting fringing fields add on one side of the tape but subtract on the other. This figure is adapted from Mallinson's paper/ Mallinson also gives a formal mathematical statement of the conditions for creating a one­sided fiux.

There has apparently been no direct experimental con­firmation of one-sided flux from a recorded tape. This paper provides such confirmation.

EXPERIMENTAL PROCEDURE

The required magnetization pattern was produced by wrapping a length of recording tape around a nonmagnetic cylinder, and applying a high magnetic field in a direction perpendicular to the cylinder axis, as shown in Fig. 3. Using a cylinder of 63 mm diam, the wave length A of the rotating magnetization is 2 em. Using this method, the side of the tape that is outermost when wrapped on the cylinder be­comes the side showing one-sided flux. This is independent of the direction of winding the tape and of the direction of the applied field.

To examine the fringing fields resulting from this mag­netization pattern, the tape is stretched fiat, a Hall probe is placed above the tape surface, and the tape is moved parallel its length. The Hall probe can be oriented to measure either the component offield parallel to the tape length or perpen­dicular to the tape surface. The tape can be oriented with the

magnetic coating facing upward toward the Hall probe or downward away from the Hall probe. Measurements were made with a 3-mm spacing between the probe and the tape; at this distance the tape thickness is negligible, but the mag­nitude of the field is 0.2 Oe, which can be measured fairly easily.

Let hx and hy represent the components of measured field parallel and perpendicular to the tape length, and let primed symbols refer to the region below the tape, unprimed symbols the region above. These axes are shown in Figo 4. Then in the ideal case (see Ref 1), we can write

h, = ho sin kx~

hv = ho cos kx,

and

h ~ = aho sin kXJ

h; = aho cos kx,

where k = lIT/A.

(1)

(2)

The quantity a can vary from + 1 to - 1; a value of + 1 corresponds to the case in Fig. 2 (a) with the magnetiza­

tion confined to the plane of the tape, and a value of - 1 corresponds to Fig. 2 (b) with the magnetization always per­pendicular to the plane of the tape. The case a = 0 corre­sponds to rotation of a constant magnetization, with no field below the tape.

Figure 5 is a sketch of the predicted variation of hx and hy with position alcng the tape. The solid curves show the field above the tape surface, and the dashed curves show the field below the tape surface, for various values of a. The numerical value of a is given by the ratio h ~/hx or h .;/hy.

I o

kx

I 271

FIG. 1. One·sided flux from a magnetized recording tape. The arrows rep­resent the local magnetization in the tape. The angle of rotation varies lin­early with position along the tape.

4007 J. Appl. Phys. 61 (8),15 April 1987 0021-8979/87/084007-03$02.40 @ 1987 American Institute of Physics 4007 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

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y

t

(a)

~L~L _..s- .. ____ • ..".. -_ ...... -.. _ .. ____

J~~. (b)

--x

I o 7T

kx

I 21T

FIG. 2. Flux from tapes magnetized alternately. (a) Magnetization parallel to tape; (b) magnetization perpendicular to tape. Note that external fluxes add above the tape but subtract below the tape.

RESULTS

Use of a typical magnetic recording tape for this experi­ment does not give one-sided flux. This is because the mag­netic particles have a preferred easy axis approximately par­allel to the longitudinal axis of the tape, and because the macroscopic shape anisotropy of the tape acts to make the plane of the tape an easy plane. The result is a distribution of magnetization like that in Fig. 2(a), with h ~ zhx and h; zhy. This behavior is shown experimentally at the left of Fig. 6 for a normal y-Fez0 3 tape and ametaUic Fe tape. Tape made from Co volume-doped r-FeZ03 shows a substantial asymmetry between the upper and lower tape surface fields, and a series of Ba-ferrite tapes made with increasing values of perpendicular alignment of the particle easy axes shows a range ofbehaviorinc1uding one case (see the right-hand side of Fig. 6) where the fields below the tape are nearly zero. The numerical values of the coefficient a can be deduced directly from the measured peak field amplitudes below and above the tape, and are shown for each sample in Fig. 6. (Values of a obtained from the ratio h ~/hx agreed well with those ob­tained from h ;Ihy .) The series of Ba-ferrite tape samples gives direct experimental confirmation that the theory of Mallinson and Westmijze is correct.

SATURATING FIELD

rBOTTOM ( INNER 1 \

··-TAPE (iOcm LENGTH)

ROD (0.63 em DIA. )

FIG. 3. Geometric arrangement used to produce the magnetization pattern of Fig. l.

4008 J. AppL Phys., Vol. 61, No.8, 15 Apri! 1987

y

PERPENDICULAR , b

LONGITUC:NAL p

BEL-OW r~h~

h~

FIG. 4. Axes used to describe fields above and below tape.

The sufficient condition for achieving one-sided flux is to produce a magnetization variation in. the tape that con­sists purely of rotation of a magnetization of constant ampli­tude. This in turn should occur when the net anisotropy (the effective individual particle anisotropy plus the macroscopic shape anisotropy) is zero. As an independent measure of this net anisotropy, the remanence ratio of the tape samples was measured on short sample lengths in a vibrating-sample magnetometer, for two cases: field parallel to the tape axis and field perpendicular to the tape surface. The remanence ratios for these cases are denoted rx and yy.

We can define an orientation factor in terms of the mea­sured r values:

(3)

which is written so that r runs from negative to positive, with an isotropic sample corresponding to r = O.

Figure 7 is a plot of a vaiues, deduced from fringing field measurements above and below the tape, against r values, determined from VSM measurements of remanence and Eq. (3). It is clear that there is a good correlation between the two properties, and that one-sided flux (a = 0) corresponds to isotropic behavior of the tape remanence (r = 0) .

kX

-- TOP h"h,

---- BOTTOM h:,h',

PIG. 5. Predicted compo­nents of the external field produced by a magnetized tape. The x axis represents position along the tape axis; hx and hy are components of field parallel and perpendicu­lar to the tape surface. Solid lines correspond to fields above the tape l unprimcd quantities, Eg. (l) J; dashed lines correspond to field be­low the tape [primed quanti­ties, Eq. (2) 1 for various val­ues of the quantity a.

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Co VOLUME DOPED r Fe20 3

Be FERRITE (INCREASING PERPENDICULAR ORIENTATION - )

-0.44 I

I I \ -, ' I I \ I ( I \ (\ \ f\

\ V

TOP BOTTOM

FIG. 6. Measured components of external field above and below various sample tapes. Notation corresponds to Fig. 4 and Eqs. (1) and (2). Fields were measured 3 mm above and below tape surface; values of a were calculated from hJhx and h ;/hy.

DISCUSSION

Mallinson 1 gives a brief discussion of the possible uses of one-sided flux in magnetic recording. The recorded magneti­zation pattern can be regarded as an intermediate case between longitudinal and perpendicular recording. A tape recorded using this method would in principle give twice the recorded flux (per unit of magnetic material) as a longitudi­nally or perpendicularly recorded tape. However, this re­quires that the remanent magnetization in the tape with one­sided flux be the same as the remanence in the case of longitudinal or perpendicular magnetization, a condition unlikely to be attained in practice because the remanence cannot lie completely along a single axis.

A tape recorded with one-sided flux would have the ad­ditional advantage of reduced susceptibility to print through. It is, however, difficult to see a simple way to pro-

4009

FIG. 7. Parameter a (de­rived from fringing field measurements) vs param­eter y ! derived from re­manence ratios using Eq. (3) J.

J. Appl. Phys., Vol. 61, No.8, 15 April 1987

duce the required magnetization pattern in a practical re­cording device.

The one-sided flux configuration can be approximated by an array of individual permanent magnets, as noted by Westmijze in 1961. The same arrangement of permanent magnets is used to perturb the path of charged particles in an accelerator, where it is known as an undulator magnet.4,5 I have not found any published measurement of the magnetic field on the zero-flux side of an undulator array, probably because in practice the magnets are mounted on a heavy plate that blocks access to the zero fiux side.

ACKNOWLEDGMENTS

I thank S. Shtrikman for hi.s encouragement, enthu­siasm, and technical assistance. I thank C. D. Graham, Jr, for generous editorial help, Tapes were kindly provided by M. Sharrock of 3M Co., and David Wilson of Pfizer, Inc. The work was done in the Magnet Laboratory of the U niver­shy of Pennsylvania, Laboratory for Research on the Struc­ture of Matter, and supported in part by the National Science Foundation MRL program under Grant No. DMR-8216718.

'J. C. Mallinson, IEEE Trans. Magn. MAG-9, 678 (l973). 2J. C. Mallinson, IEEE Trans. Magn. MAG-17, 2453 (1981). 'w. K. Westmijze, U. S. Patent 2,981,871 (April 25, 1961). 4K. Halbach, Nucl. Instrum. Methods 187, 109 (1981). 5K. Halbach, paper presented at the 19811'article Accelerator Conf., Wash­ington, DC, March 11-13 (1981).

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