Optical probing of magnetic inert layers

Dror Sarid, Merritt N. Deeter, and Vincent Kahwaty

The thickness of a magnetic inert layer on top of a ferrite head sample was measured by probing thelongitudinal Kerr effect as a function of the angle of incidence of a laser beam. Our computerized measuringsystem used a simple single-detector setup to derive polarization information from a Kerr-reflected beam asthe incident angle was scanned. The results were analyzed using a general theory of reflection from magneticstratified media. The experimental results indicate that the possible inert-layer thickness values are given by(50 + 10) + 60 X N nm, where the order N equals 0, 1, 2, 3, or 4.

1. Introduction

The performance of ferrite recording heads has beenobserved to depend on the surface quality of the headmaterial.1 2 Specifically, formation of a nonmagneticsurface layer (the so-called inert or dead layer) is asso-ciated with a decreased level of performance once itsthickness is >100 nm, the effect worsening with theaging of the device. Either abrasion on the headcaused by particles embedded in magnetic tape, in-duced mechanical stress, or oxidation are believed toproduce these undesired surface layers. Obviously, atechnique to characterize such layers accurately ishighly desirable.

Various techniques have been used to detect surfacelayers on ferrite materials, including high-resolutionfield measurements,34 ellipsometry,2 and the polarKerr effect.1 Estimated inert-layer thicknesses fromfield measurements are of the order of several tenths ofa micrometer.34 The ellipsometric method actuallyonly detects changes in optical properties (that is, therefractive index) unlike magnetooptic methods, whichare directly affected by magnetic properties in thesurface region. The magnetooptic work done thus far1has produced inert-layer estimates of <0.1 Am; howev-er, no magnetooptic techniques, such as the Kerr ef-fect, have been used to characterize dead layers in thecontext of a general theoretical model.

Vincent Kahwaty is with IBM General Products Division, Tucson,Arizona 85744; the other authors are with University of Arizona,Optical Sciences Center, Tucson, Arizona 85721.

Received 15 January 1987.0003-6935/87/153153-05$02.00/0.© 1987 Optical Society of America.

Nevertheless, other models based on magnetooptictheory have succeeded in other applications. Tanaka5

measured the angular dependence of the longitudinalKerr effect to determine the magnetooptic constant ofPermalloy. Sprokel6 developed a matrix methodbased on the polar Kerr effect to calculate the magne-tooptic properties of multilayers for use in optical stor-age.

In this paper, we show that angular measurements ofthe longitudinal Kerr effect can be correlated with amathematical model to provide information on thedepth of the nonmagnetic surface layer. The modelcalculates the Kerr reflectivity of a system composedof a single uniform nonmagnetic layer on a magneticsubstrate, and a computerized measuring system usesa fairly simple optical layout to derive the relevantquantities from the reflected elliptically polarizedbeam.

11. Theory

The general case of the reflection of a laser beamfrom magnetic stratified media at arbitrary incidentangle is a complicated problem. For this reason, thegeneral magnetooptic interaction is usually brokendown into three cases, namely, the transverse, polar,and longitudinal geometries. The transverse geome-try occurs when the magnetization vector M is parallelto the film surface but perpendicular to the plane ofincidence; the polar geometry exists when M is normalto the film plane; and the longitudinal geometry occurswhen M lies both in the film plane and the plane ofincidence, as shown in Fig. 1.

The geometry of the interaction in this experimentconsists of a magnetic substrate on which a nonmag-netic surface layer has been formed. Using Smith'stheory,7 we can calculate the Kerr reflectivity as afunction of incident angle for such a system. We as-sume a dielectric tensor with equal diagonal elements:

1 August 1987 / Vol. 26, No. 15 / APPLIED OPTICS 3153

1 -iq 0[e] = iq 1 0 1

o 1(1)

Air: n=1, q=O

where = ErEO is the dielectric constant in the absence ofgyrotropic effects, and q is the gyroelectric constant,both quantities being in general complex. The z axishas been chosen as the gyrotropic axis, that is, the axisof magnetization. Solutions of Maxwell's equationsfor such a medium lead to the construction of a four-by-four scattering matrix that yields the s and p reflec-tivities as well as the Kerr reflectivity. Matrix meth-ods have long been used in calculating reflectivitiesfrom dielectric film structures. However, they gener-ally utilize two-by-two matrices.8 For multilayerstructures, the system scattering matrix is simply thematrix product of matrices representing each layergiven by

[C],tta = C]1 [C12 ... [Clk[A]ub.

Magnetic substrate:

n=n~ub. q=q'+iq"

ki(nl)

/ >t' ansverse

Mlongitudinal

Fig. 1. Dead-layer geometry: in the polar case, the magnetizationM is normal to the film plane, while in the longitudinal case it lies

both in the film plane and the plane of incidence.

(2)

For the case of longitudinal magnetization, the gen-eral matrix for a magnetooptic film is given by

f x. 1

[Cliong =

cos(b) iN sin(a) 0

i sin(a) cosMN csl

iM2,q -

2

2NiNS2 2

yq-6&yq -2 COW()

i2 yq- 2M

0i sin(6)

M

-iM sin(S)

cosW5)

l (3)

where = n-ydic = 2rnyd/Xo; M = ocfln; N = ocAn; and y are the direction cosines of the k vectorrelative to the y and z axes, respectively; n is the bulkindex of refraction; d is the film thickness; and X0 is thevacuum wavelength of incident radiation. The matrix[A]5 ub for a transmitting substrate takes the form

yN u = Jt~c -(14)

In terms of the system matrix [C]toi, the amplitudereflection coefficients are

(C11 + NC21)(C33 + MC43) - (C + NC23 )(C31 + MC41)A I

2m(C31 C4 3 - C4 1C3 3 )A

(C33 - MC 4 3)(C11 - NC 21) - (C 3 1 - MC4 1)(C13 - NC2 3 )

A

1

[Alsub = zNx-fz

IM_

where

c± = n2 = . (1 -qA +24

pr = AY X1 y

f bI f±

A = _prYt

1 f11 -fr.-

1 _N_ N+ N+

-fzx 1 1 ,

fx 1 l1M_ M+ M+_

q4)

(4)

=2m(ClIC 23 - C 13 C21)

A I I

A = (C11 - NC 21) (C33 + MC43) - (C13 - NC 23) (C3 1 + MC41),

where m = oc/n, M = m, and N = m/3, n and iBreferring to the incident medium.

To summarize briefly, the mathematical model com-(5) putes the system matrix corresponding to the case of

an isotropic nonmagnetic (q = 0) layer on top of a(6) magnetic substrate having the same bulk dielectric

constant. From this matrix, both the s and p reflecti-vities and the Kerr reflectivity can be computed as afunction of incident angle and inert-layer thickness.

(8) Note, however, that because we assume the dielectricconstant to be the same in the inert (nonmagnetic)

(9) layer as in the bulk, the p and s reflectivities (bothamplitude and phase) will not be affected by the pres-ence of the inert layer.

(10) Next, we show how the presence of an inert layeraffects magnetooptic measurements. Specifically, we

(11) consider how a single polarizer can be used to analyze a

3154 APPLIED OPTICS / Vol. 26, No. 15 / 1 August 1987

Y

Z

ly this term in which we are interested. We now definethe Kerr signal I, as

)= ftr,(0)11k,(0)1 cos[A(O)]J sin(2q).IO

(22)

Fig. 2. Experimental system: note that 0 is the angle of incidenceand 0 the angle between the analyzer transmission axis and the p-

polarization plane.

Kerr-reflected beam of light. The goal of this sectionis to show that data from these magnetooptic measure-ments can be manipulated to provide information thatmay be compared to the predicted values from themathematical model. We now calculate the ampli-tude and intensity transmission of a Kerr-reflectedbeam (elliptically polarized) through a linear polarizer,assuming an incident beam (on the sample) of s polar-ization. Here we let 0 be the angle of incidence and 0be the angle between the polarizer transmission axisand the p-polarization plane, as in Fig. 2. Thus 0 = 0corresponds to the case of crossed polarizers. Thereflected beam consists of two components, the stan-dard s-polarized reflected component with amplitudeIrJ1 and phase a and the Kerr-reflected componentwith amplitude k,1 and phase 1s,, which is polarized inthe opposite sense, that is, in the p plane. The ampli-tude transmission through the polarizer is just the sumof the projections of the two components on the polari-zer's transmission axis. Following Lissberger, 9 we letA be the dimensionless amplitude transmittedthrough the polarizer and thus obtain

A = [rJI exp(ia,)]sinq + [Jk 8Iexp(i#,l)]cos0, (20)

where r, a, k, and As all depend on 0, the incidentangle. The normalized intensity I/Io is just the ampli-tude transmittance times its complex conjugate,

I/I, = Ir,12sin2 o + Ik12 cos20 + Ir11^kJ sin(2,O) cos(A), (21)

where I/Io = AA*, Io is the incident intensity, and A =

Now consider the effect of modulating k, for exam-ple, let k = IkOI sin(cot). Because k is proportional tothe magnetization, modulation can be accomplishedby using an ac eletromagnet. The three terms on theright-hand side of Eq. (21) then in general have differ-ent time dependencies. The first term is independentof 1k81 and, therefore, acts as a dc term. The secondterm oscillates at 2w because of the square dependenceon 1k,1. The third term oscillates at w, and it is primari-

In our model, the inert-layer thickness d affects boththe Kerr amplitude k,(0)I and the phase termcos[A(O)]. According to Eq. (22), measurement of thesignal at frequency co enables us to measure the prod-uct of these terms as a function of incident angle 0 butnot each term individually. Separate measurementsof k,(6)I and cos[A(0)] are possible but require a morecomplicated optical scheme.10 Nonetheless, thismethod uses more available information than mea-surement of Ik,(0)12 alone, as would be done withcrossed polarizers (that is, 0 = 0). In addition, because1r8 (O) I >> lk 8(0) , measurement of the 2w signal results ina much smaller SNR than is possible with measure-ment of the c signal.

111. Experiment

A. Setup

The experimental setup is shown in Fig. 2. A micro-computer controls a motorized stepper rotation stage,which in turn controls the angle of incidence with aresolution of 1/100 of a degree. The analyzer/detectorarm is driven by a belt system that rotates the arm sothat the reflected beam is constantly directed towardthe detector regardless of incident angle. The electro-magnet has a gap of 5 mm and is wrapped with 100windings of copper wire. The ferrite samples are helddirectly against the magnet face. Such a geometryprovides efficient coupling of the magnetic flux intothe sample but also makes field measurements imprac-tical because of the lack of an air gap in the magneticcircuit. Alternating currents of 300-400 mA from anaudio amplifier (co _ 2 kHz) produce the necessarylongitudinal magnetic field.

The basic optical system consists of a laser source,polarizer, analyzer, and detector. The laser used is astabilized He-Ne (X = 633 nm). The polarizer used isa standard prism-type polarizer, although the analyzeris of the plastic sheet-type because of weight and spaceconsiderations. The detector is a silicon photovoltaicwith an integrated lens to compensate for small dis-placements of the reflected beam.

The electrical signal from the detector is first passedto a current-to-voltage preamplifier and then to a lock-in amplifier. The output from the lock-in is fed to adigital voltmeter, which digitizes the analog signal.Finally, the digitized signal is sent to the host comput-er over an interface bus. After a reflection scan iscompleted, the computer stores and/or plots the signalvalues (i.e., I,, rsI2, or rpI2) as a function of angle ofincidence.

B. Procedure

The samples tested were NiZn ferrite with pre-formed inert layers created by mechanical polishingwith varying grit sizes. Mechanical polishing is

1 August 1987 / Vol. 26, No. 15 / APPLIED OPTICS 3155

thought to resemble the process by which inert layersform on actual magnetic recording heads.1 In addi-tion, portions of each sample were chemically etched toremove the inert layers. For these etched regions, weassume that the material can be characterized by thebulk values of e and q; that is, we assume d = 0 for theseregions. This assumption allows us to use the etchedportions as standards by which the inert layer areascan be characterized. The experimental procedurethen consists of two parts: substrate characterization(that is, etched region) and inert-layer characteriza-tion.

Characterization of the substrate consists of the de-termination of n = n' + in"(E = n2) and q = q + iq".However, it can be shown that (0) cc IqI. Because weare only able to measure the shape of I() and not itsabsolute magnitude (due to calibration problems), weneed not know IqI as long as we determine the phase ofq[Oq = tan'1(q"/q')], which is invariant and stronglyaffects the shape of I(0). This reduces the number ofmaterial constants that must be determined to three.Determination of n' and n is done by matching thepredicted p-reflection curve from the mathematicalmodel with the measured p-reflection curve until abest fit is obtained. This method is particularly sensi-tive when comparing the p-reflection curves in thevicinity of the Brewster angle, for here we find that theminimum value of rp depends principally only on n",while the angle at which this minimum occurs OB de-pends mainly on n'. Using a best eyeball fit with thismethod, we find that we can estimate n' and n towithin +0.01. After n' and n' have been determined,it is straightforward to determine 10q. From Eq. (22)we observe that

lI"(O)12- c, s Ik.,(0)12 COS2[A(O)]. (23)

Ir'(O)I12

Thus the left-hand side of Eq. (23) is calculated usingexperimental data from a region with no dead layerand then compared to calculated theoretical curves ofthe right-hand side for a specific kq. As mentionedalready, I,, is not measured absolutely (that is, relativeunits), so that each theoretical curve must be normal-ized to have the same mean value (or equivalently thesame integrated area) as that of the experimental data.By iterating until the two curves agree (using either abest eyeball fit or a minimum mean-squared-errormethod), 'kq can be estimated to 1.

Inert-layer characterization follows substrate char-acterization. Because our model assumes that n' andn" remain the same in the inert layer as in the bulk, theonly remaining unknown is d, the inert-layer thick-ness. Again, we use the computer model to generatetheoretical curves of Ik,(0)12 cos2 [A(0)], this time fordifferent values of d. We then estimate the inert-layerthickness by observing what value of d produces thebest match between theory and experimental data.

IV. Discussion

Figure 3 shows the theoretical and experimental preflectance measured in the vicinity of the Brewster

.02

D

40a

,c01o

.S

060 67. 5 75

Incident Ange, B

Fig. 3. Theoretical and experimental p reflectance IrpI2 measuredin the vicinity of the Brewster angle for a typical sample. The

theoretical (solid) curve was calculated for n = 2.57 + A0.15.

0

00U,

0

U

16

!S<1

IA

or

0

0 45Incident Angle, 8

90

Fig. 4. Comparison of the experimental curve of lIj(0)12/Irs(O)12(solid) for a typical sample without an inert layer and mean-normal-ized theoretical curves of Ik,(0)12 cos2[A(O)] calculated for no inert

layer and ,q values of 9, 11, and 130.

angle for a typical sample. The solid (theoretical)curve was generated assuming a complex index n =2.57 + iO.15. This value agrees with ellipsometricvalues obtained by Wada,2 although he fails to saywhatwavelengthwas used for his measurements. Thenear overlap of the experimental p-reflectance curvesfor the etched and inert layer regions of the sampleindicates that the inert layer has nearly the same indexof refraction (and thus nearly the same dielectric con-stant) as the substrate.

Figure 4 compares an experimental curve of II,(0)2/Jrs(0)12 for a typical sample with no inert layer withthree theoretical curves of 1k,(0)12 cos2[A(0)] calculatedfor d = 0 and different kq values (9, 11, and 130). Allthree theoretical curves were normalized to have thesame mean value as the data. Despite the presence ofnoise, the data clearly fit best with a kq value of 11°,indicating that this value of 'q is appropriate. Theestimated error in qfq is +10.

Before the dead-layer experimental data may beanalyzed, it is important to understand how the theo-retical curve is affected by the dead-layer thickness.

3156 APPLIED OPTICS / Vol. 26, No. 15 / 1 August 1987

-#q 9 de - -/ I. 13 dei *-

X~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/1~~~~~~~~~~~~~~~~~

-- 4-~~~~~~~~~~~

'a -90 6rni-- /M u1260rni ~ f

0 45 90Incident Angle,

Fig.5. Peak-normalized plots of|k,(0)12 COS2[A(O)] for dvalues of 0,30, 60, 90, and 120 nm.

U,

0

--<1

I00

0 45Incident Angle, 8

90

Fig. 6. Typical experimental curve of JIj(0)j2/jrs(O)j2 for data ob-tained from an inert-layer sample along with mean-normalized theo-retical curves of lks(O)2 cos2[A(O)] calculated for n = 2.57 + iO.15,kq =

110, and d values of 51, 169, 295, and 424 nm.

When we plot peak-normalized curves of IkM(0)12cos2[A(0)] for dead-layer thickness between 0 and 500nm, for example, we observe an oscillatory behavior inthe shape of the curves in which the angular position ofthe signal peak appears to have a period of -60 nm.Figure 5 illustrates theoretical normalized peak curvesof 1k,(0)12 cos2 [A(0)] for d values of 0, 30, 60, 90, and 120nm. Thus we see that the occurrence of similar curvesis periodic in the inert-layer thickness, spaced by -60nm. It is interesting to note that the periodicity is dueto the fact that it takes four passes of the depolarizedray in the inert layer (as opposed to two passes, as inconventional thin-film optics) to give rise to construc-tive interference.

Figure 6 compares an experimental curve of I4(0)12/1r8(6)12 from a typical dead-layer sample with theoreti-cal curves obtained for d values of 51, 169, 295, and 424nm corresponding to the first-, third-, fifth-, and sev-enth-order best-fit values (using a minimum mean-squared-error approach). The curves correspondingto the second-, fourth-, and sixth-order best-fit valueswere omitted for clarity. In Fig. 6 we see that the first-and third-order d values give acceptable fits with theexperimental curve, while the fifth and higher orders

deviate from the experimental data and can, therefore,be excluded. For each of the first five best-fit inert-layer thicknesses, we find that a shift in d from thebest-fit value by ±10 nm produces a noticeably poorerfit to the data.

V. Conclusion

We have demonstrated that angular measurementsof the longitudinal Kerr effect are quite sensitive tomagnetically inert surface layers on ferrite materials.The information is contained in both the amplitudeand shape of the Kerr signal curves as a function of theincident angle. Qualitative agreement was found be-tween theory and experiment assuming material con-stants of n = 2.57 + iO.15 and Oq = 110. We estimatethat the dead-layer thickness of our NiZn ferrite sam-ple is given by (50 + 10) + 60 X N nm, where the orderN equals 0, 1, 2, 3, or 4.

The ambiguity in the determination of the thicknessof the dead layer, using our technique, is due to theperiodic occurrence of similar shapes of the Kerr sig-nal. The ambiguity might be solved by improving theexperimental SNR, which decreases the number ofpossible orders. Alternatively, our present techniquecould be combined with other methods of lower resolu-tion, which would distinguish between the differentorders.

We would like to thank E. J. Ozimek for suggestingthe topic and D. I. Paul, T. W. McDaniel, J. M. Schmal-horst, and J. L. Nix for helpful discussions.

This work has been supported by a grant from theIBM Corp.

References1. J. A. L. Potgiesser and J. Koorneef, "Wear of Magnetic Heads,"

IERE Conf. Proc. (1973).2. T. Wada, "An Improvement of Ferrite Substrates," IEEE

Trans. Magn. MAG-16, 884 (1980).3. J. P. J. Groenland and J. H. J. Fluitman, "Measurement System

for Two-dimensional Magnetic Field Distributions, Applied tothe Investigation of Recording Head Fields," J. Phys. E 14, 503(1981).

4. A. W. Baird, C. D. Lustig, and W. F. Chaurette, "High-Resolu-tion Field Measurements near Ferrite and Thin-Film RecordingHeads," IEEE Trans. Magn. MAG-16, 1631 (1980).

5. S. Tanaka, "Longitudinal Kerr Magneto-Optic Effect in Perm-alloy Film," Jpn. J. Appl. Phys. 2, 548 (1963).

6. G. J. Sprokel, "Reflectivity, Rotation and Ellipticity of Magne-tooptic Film Structures," Appl. Opt. 23, 3983 (1984).

7. D. 0. Smith, "Magneto-Optical Scattering from MultilayerMagnetic and Dielectric Films," Opt. Acta 12, 13 (1965).

8. 0. S. Heavens, Optical Properties of Thin Solid Films (Dover,New York, 1965).

9. P. H. Lissberger, "Kerr Magneto-Optic Effect in Nickel-IronFilms," J. Opt. Soc. Am. 51, 948 (1961).

10. M. Ruane, M. Mansuripur, and R. Rosenvold, "Measurement ofReflectivities for Magnetooptical Media," Appl. Opt. 25, 1946(1986).

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