PHYSICAL REVIEW B 1 NOVEMBER 2000-IVOLUME 62, NUMBER 17

Determination of equilibrium coupling angles in magnetic multilayersby polarized neutron reflectometry

C. H. Marrows,1,* S. Langridge,2 and B. J. Hickey11Department of Physics and Astronomy, E.C. Stoner Laboratory, University of Leeds, Leeds LS2 9JT, United Kingdom

2ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, United Kingdom~Received 14 January 2000; revised manuscript received 24 May 2000!

We have performed polarized neutron reflectometry~PNR! on Co/Cu multilayers grown by sputter deposi-tion at the first antiferromagnetic~AF! maximum of the coupling oscillation. The growth of the Cu spacerlayers was paused halfway through each layer for a variable amount of time to allow residual gases to beadsorbed onto the surface. A sample with clean Cu spacers shows good AF coupling, with low remanence andhigh saturation field. The PNR spectra show a strong1

2 -order Bragg peak and little splitting between thereflectivities for incident↑ and↓ spin neutrons at zero field, characteristic of AF ordering. Meanwhile, a moreheavily gas-damaged sample with a remanent fraction of;A2/2 has strongly spin-split PNR spectra at thecritical edge and nuclear Bragg peak, showing a significant ferromagnetic component. A strong1

2 -order Braggpeak is still present. We are able to fit accurately the magnetization and PNR data by assuming that such asample shows considerable biquadratic coupling, with moments coupled close to 90° at zero field.

ioo

hicein

r-

cahe

ud

nne-

wti-et

sfesef

hetseinioincetio

di

in-in

ennit

inntsergin a

uc-

m

Fber.ong

thein

h-es-ex-

ese

ring

ally

the

One of the most striking properties of the new generatof magnetic multilayer structures is the presenceantiferromagnetic1 ~AF! or oscillatory2 indirect exchangecoupling between magnetic layers on either side of a tnonmagnetic spacer. The oscillation in coupling with spathickness is due to the quantum interference of sppolarized wave functions,3 with the ferromagnet/spacer intefaces acting analogously to a Fabry-Perotetalon with spin-dependent reflection coefficients. A variety of theoretimethods have been employed to attempt to calculate treflection coefficients, such as RKKY-like theories,4 total en-ergy calculations,5 and quantum confinement of spin-↓holes.6 These various theories have enjoyed increasing scess in predicting the period, amplitude, and temperaturependence of the coupling.

We have been studying the interlayer coupling of omultilayer system, Co/Cu, as it exhibits a large giant magtoresistance~GMR! which is of particular scientific and technological interest.7 We previously found that relatively lowlevels of residual gas in the vacuum chamber during growould significantly reduce the GMR ratio of Co/Cu multlayers while not affecting the resistivity of the films. Thmost damaging point at which these gases could entermultilayer stack was in the bulk of the Cu spacer layer8

This was explained by a reduction of the degree of antiromagnetic character in the interlayer coupling. Subquently it became apparent that a plausible explanationthe reduction of GMR would be a smooth rotation of tequilibrium ~zero-field! angle between adjacent momenfrom p to 0 as the base pressure of the system worsen9

This noncollinear ordering of the moments requires thetroduction of a significant biquadratic term in the expressfor the free energy of the multilayer. We found that thetroduction of this biquadratic term would correctly reproduthe experimentally observed dependences of the magnetion and GMR on field and on each other across the widththe first AF peak in the coupling oscillation.10 Such noncol-linear coupling has now been observed in a number of

PRB 620163-1829/2000/62~17!/11340~4!/$15.00

nf

nr-

lse

c-e-

e-

h

he.r--

or

d.-n-

za-f

f-

ferent material systems, e.g., Fe/Cr,11 NiFe/Ag,12 andCo/Cu.13 It may be described phenomenologically by theclusion of the biquadratic second term in the expansionpowers ofS•S of the indirect exchange interaction betwespinsS in adjacent magnetic layers. The free energy per uarea,e, of a Co/Cu/Co trilayer in applied fieldH may bewritten as

e52m0mHt~cosu11cosu2!2J1cosQ2J2cos2Q, ~1!

where the Co layers are of magnetizationm and thicknesst.The moments make anglesu with the field andQ with eachother, i.e.,Q5u12u2. The interlayer exchange appearsthe form of the bilinear and biquadratic coupling constaJ1 and J2. The biquadratic term represents non-Heisenbexchange. Such coupling appears to be commonplacevariety of multilayer systems.14 With the proper sign forJ2the two energy minima can be found atQ56p/2, leading toorthogonal ordering of adjacent layer moments. By introding J1 it is possible to close up~for J1.0) or force apart~forJ1,0) the moments to reach any zero-field equilibriuangle between 0 andp. An appropriate variation ofJ1 andJ2 can therefore yield the proper decline in GMR and Acoupling with rising base pressure in the sputtering cham

In this paper we report the results of polarized neutrreflectometry15 ~PNR! performed on such samples. Amonthe many applications found for this technique, one ofmost common is determining the magnetic alignmentsmultilayer structures,16 acting in many respects as a deptselective vector magnetometer. It is therefore suited to invtigating the nature of the angular dependence of thechange interaction between the Co layers in thmultilayers.

The samples were deposited by dc magnetron sputteon 25 mm325 mm pieces of Si~001! wafer. The workinggas pressure was 3.0 mTorr. The multilayers were nominof the form $Co~10 Å!/~Cu~9 Å!%325. This Cu thicknesscorresponds to the first antiferromagnetic maximum in

11 340 ©2000 The American Physical Society

eid

uls

ye2let

ereecobgh-

antrotore

ow

ergtethvee

twAl

Oeabu

oo

ldheces

edif-hesep.

s-the

ectndtheofe

tlyhtlycingÅ.

withy-

h-n

t ofwenotssbe

ere

onsets,size-veti-re-

ate

lidsum

i-lde

PRB 62 11 341BRIEF REPORTS

oscillatory exchange coupling. The lowest base pressurthe system is achieved by cooling a Meissner coil with liqunitrogen—it is possible to raise the base pressure by not fcooling the coil. This mainly results in a higher partial presure of H2O. One sample was prepared with each lagrown continuously, in a system base pressure of31028 Torr. The growth was paused for 30 s in the middof each Cu spacer layer in the second sample, exposingsurface to a base pressure of 1.331027 Torr. Both sampleswere prepared in the same vacuum cycle of the system.

Structural characterization of the samples was performby low-angle x-ray reflectometry. Magnetization loops wemeasured by means of the magnetooptic Kerr eff~MOKE!. Magnetoresistance was measured by a four-prdc method. PNR was carried out on the CRISP time-of-flireflectometer at ISIS.17–19The instrument was operated without analysis of the spins of the exit beam of neutrons,magnetic fields were applied to the sample with an elecmagnet. A minimum applied field of 50 Oe is requiredprevent depolarization of the neutron beam. All measuments were performed at room temperature.

In Fig. 1 we show the magnetization loops for the twdifferent samples. It is immediately apparent from the loremanence that the clean sample has substantial AF ordat low fields. Meanwhile, the remanence of the gas-damasample is substantial, approximately 0.65 of the saturamagnetization. As expected the GMR of the sample withsmall remanence is much higher; indeed it is just odouble. However, the resistivity of the two samples whmagnetically saturated is very similar, 2062mV cm at roomtemperature.

It is of course possible to explain these changes inways. The gas-damaged sample may consist of perfectregions, interspersed with regions where the momentsparallel to each other that contribute nothing to the GMR.the other hand, we may set the moments at an angle toother, which will provide a net moment at remanence,also some misalignment that gives rise to GMR as the mments are closed together by an external field. It is notew

FIG. 1. Magnetization loops for the two multilayers. The solines are fits to the data. The inset is magnetoresistance meaments for nominally identical smaller samples grown in the savacuum cycle.

of

ly-r.0

he

d

tet

d-

-

ingedder

n

oF

iencht-

r-

thy that if we were to choose angles ofp for the cleansample andp/2 for the gas-damaged sample, this wouyield a GMR ratio in the clean sample of double that in tgas-damaged one, while simultaneously yielding remanenof zero andA2/2('0.7), respectively. It should also bnoted that changes in anisotropy cannot account for theferences in magnetic response we see here—generally taffect the nature of the hysteresis in the magnetization loo9

In Fig. 2 low-angle x-ray reflectivity spectra are diplayed. Since each sample has an area similar in size toracetrack of the magnetron sputter guns, we might expthat the samples are not perfectly uniform in thickness, ax-ray scans were taken at 2.5 mm intervals acrosssample.~The particular scans shown are from the centerthe wafer.! All the scans are very similar, although the valuof Q at which the bilayer Bragg peak is observed is slighhigher at the edges of the sample, corresponding to a sligthinner layer. For the clean sample the mean bilayer spais 19.4 Å with a standard deviation across the wafer of 0.6For the gas-damaged sample the mean is 19.1 Å, againa standard deviation of only 0.6 Å. A fuller structural analsis of similar samples was previously presented:20 the multi-layers were found to be extremely smooth, with rms rougnesses of;1 Å and a very high degree of vertical correlatioof the interfaces.

PNR produces very rich data sets, the most importanwhich are displayed in Figs. 3 and 4. In these two figuresshow the 50 Oe data for the two samples. Although it ispossible to perform PNR in field-free conditions due to loof polarization of the neutron beam, 50 Oe can be seen toonly a weak perturbation of the state of these samples, whthe saturation fields are much higher~see Fig. 1!. The spin-↑and -↓ labels refer to the polarization of the incident neutrbeam. There are several features common to both datasuch as the Bragg peaks, critical edges, and finite-fringes. For very lowQ, total internal reflection of the neutrons occurs and the reflectivity is unity. All the data habeen normalized in reflectivity to this point. Above the crical value ofQ the neutrons penetrate the sample. Braggflection occurs at certain values ofQ corresponding to peri-odicities within the sample. The first-order Bragg peakQ50.32 Å21 is due to the chemical periodicity of th

re-e

FIG. 2. Low-angle x-ray diffraction spectra for the two multlayers. The Bragg peak atQ5;3.2 Å21 is due to the chemicaperiodicity of the multilayer. The two scans are offset by a decaof intensity for clarity.

th

dti

gia

atdeloinrn

thpi-

ngarro

is

ostu

li-ldareableag-

-nd

ted

ula-talpa-inthedif-ular

reatn--nd

ill

thesfirstag-ro-is

tig-

tioncted

olide

or-

topleat

op-ag-

ling

gg

ea

as

11 342 PRB 62BRIEF REPORTS

sample, and yields a bilayer spacing of 19.6 Å, close tonominal value. Meanwhile the12 -order peak atQ50.16 Å21

corresponds to a doubling of the real space period and isto the AF ordering of the sample, leading to a magneperiod twice that of the chemical period. The magnetic oriof the peak peak is confirmed by its suppression as theplied magnetic field is increased, vanishing above the sration field when all the moments are closed and no AF orpersists. Meanwhile, the fringes visible in both scans beQ50.1 Å21 are analogous to Kiessig fringes observedlow-angle x-ray reflectivity spectra, arising due to interfeence of the beams reflected at the air/multilayer amultilayer/substrate interfaces.

There are a number of important differences betweentwo samples. In Fig. 3 the two spectra are only weakly ssplit, with the only splitting of any significance in the finitesize fringes. Meanwhile, in Fig. 4 there is significant splittiboth at the critical edge and at the first-order Bragg peThese are characteristic of a sample with a significant femagnetic component. The12 -order peak is not split as it isdue to AF ordering, which, without polarization analyscannot exhibit any spin dependence.

As the field is increased all these features become mpronounced: spin splitting of the critical edge, at the firorder Bragg peak, and of the finite-size fringes, and a s

FIG. 3. Polarized neutron reflectometry spectra for the clantiferromagnetically coupled sample atH550 Oe. The data arethe points; the solid lines are the results of the simulation.

FIG. 4. Polarized neutron reflectometry spectra for the gdamaged noncollinearly coupled sample atH550 Oe. The data arethe points; the solid lines are the results of the simulation.

e

uecnp-u-r

w

-d

en

k.-

,

re-p-

pression of the12 -order peak. The data set of Fig. 4 is qua

tatively very similar to that of the clean sample in a fieroughly halfway to saturation, i.e., when the momentspartly closed together. Both samples behave in a comparmanner when saturated, and are thus entirely in ferromnetic alignment. In this case the12 -order Bragg peak is entirely absent, and the critical edge, finite-size fringes, afirst-order peak are strongly spin split.

The four spin-dependent cross sections were simulausing an optical potential-type model21 and combined to pro-duce the spin-dependent specular reflectivity. The calctions were then numerically convoluted with the instrumenresolution. We averaged over two different sets of inputrameters in order to account for the slight nonuniformitythickness of the sample. In this model we assume that allintensity measured is due to specular scatter, with zerofuse component. We have recently measured the off-specscatter from several magnetic multilayers using the3He mul-tidetector on CRISP.22 In the case of these samples, whethe coupling is strong, we find little diffuse scatter, evenzero field—a weak diffuse component is just discernible uder the instrument-broadened1

2 -order Bragg peak. We therefore feel justified in neglecting this very weak scatter atreating all the intensity as entirely specular.

The Co moment is found to be;1.5mB /atom, a littlelower than the bulk value of 1.7mB /atom. This is not sosurprising given the extreme thinness of the films, which wsuppress both the magnetization and the Curie point.23 Thevalue for the zero-field coupling angleQ for the gas-damaged sample giving the best fit was 86°, while forclean sampleQ5170°. The splitting in the finite-size fringeseen in Fig. 3 can be reproduced by assuming that thefew Co layers deposited on the substrate form a ferromnetic block. Cross-sectional transmission electron micgraphs of similar samples confirm that the layering qualitypoor for the first few bilayer repeats,9 so we should expecthat the AF interlayer coupling in this region should be snificantly impaired.

It is now possible to take the thickness and magnetizavalues determined from the PNR and simulate the expemagnetic response of the samples. Settingt59.75 Å andm51.25 MA m21, and following the path of minimume, asgiven by Eq.~1!, as a function ofH, it is possible to obtainthe simulated magnetization loops of best fit shown as slines in Fig. 1 using the following coupling constants: for thclean sampleJ1520.15 mJ m22, J2520.085 mJ m22; forthe gas-damaged sampleJ1520.024 mJ m22, J2520.17mJ m22. @Note that these values include the factor of 2 crection required to transfer the trilayer model of Eq.~1! to amultilayer.# This leads to equilibrium values ofQ of 82° and180°, respectively, close to the values giving the best fitsthe PNR data. The small remanence in the clean samcomes entirely from the ferromagnetic block of five layersthe bottom of the stack in this simulation.

To conclude, we have studied by PNR the magnetic prerties of multilayers exhibiting good AF coupling, andform of coupling intermediate between AF and ferromanetic. The sample shows characteristics of both AF coup~high saturation field, appreciable GMR, and strong1

2 -orderPNR Bragg peak! and ferromagnetic coupling~high rema-nence, spin-split PNR critical edge, and first-order Bra

n

-

i

i

foen

eu

thlt

anh

ringse as

or 2peel,

s-in a

henceas-

etoof

PRB 62 11 343BRIEF REPORTS

peak!. This suggests that some sort of mixed couplingpresent. The width of the PNR Bragg peaks in Figs. 3 andyields a vertical magnetic coherence length comparable wthe size of the multilayer, so that the fluctuations in couplinmust be lateral. This means that there is the opportunitynoncollinear ordering of adjacent layer moments, as dscribed in the well-known Slonczewski coupling fluctuatiomodel of biquadratic exchange,24 where different lateral re-gions of the spacer have positive or negative coupling engies. When the lateral length scale of the fluctuations in copling strength is comparable to the exchange length ofmagnetic layers, then the magnetization cannot simuneously satisfy adjacent regions of opposite coupling. Aequilibrium angle is found partway between 0 andp, leadingto a noncollinear arrangement of moments. On the othhand, if the lateral fluctuations are long ranged, then the lers can break into domains such that the coupling conditioare locally satisfied everywhere. It is possible that as t

s4thgr-

r--e

a-n

ery-se

residual gases accumulate on the sample surface dupauses in growth they clump in particular areas, and cauchange in sign ofJ1 from negative to positive. If these areawere small compared to the exchange length, i.e., only 1nm across, then this could lead to mixed coupling of the tythat will cause a biquadratic term in the Slonczewski modand is also consistent with the gradual decrease inQ from pto zero as reported in Ref. 9. We know from Lorentz microcopy studies that on dc demagnetization the samples aresingle domain state,9 and the good agreement between tsimulations and the PNR data is further compelling evidethat there is substantial biquadratic coupling in these gdamaged samples.

C.H.M. would like to thank the Royal Commission for thExhibition of 1851 for financial support. We are gratefulthe Rutherford Appleton Laboratory for the provisionbeam time at ISIS.

*Email address: c.marrows@leeds.ac.uk1P. Grunberg, R. Schrieber, Y. Pang, M.B. Brodsky, and H. Sow

ers, Phys. Rev. Lett.57, 2442~1986!.2S.S.P. Parkin, N. More, and K.P. Roche, Phys. Rev. Lett.64,

2304 ~1990!.3P. Bruno, Phys. Rev. B52, 411 ~1995!.4P. Bruno and C. Chappert, Phys. Rev. B46, 261 ~1992!.5M. van Schilfgaarde and F. Herman, Phys. Rev. Lett.71, 1923

~1993!.6J. Mathon, D.M. Edwards, R.B. Muniz, and M.S. Phan, Phy

Rev. Lett.67, 493 ~1993!.7S.S.P. Parkin, R. Bhadra, and K.P. Roche, Phys. Rev. Lett.66,

2152 ~1991!.8C.H. Marrows, B.J. Hickey, M. Malinowska, and C. Me´ny, IEEE

Trans. Magn.33, 3673~1997!.9C.H. Marrows, B.J. Hickey, M. Herrmann, S. McVitie, J.N

Chapman, T.P.A. Hase, B.K. Tanner, M. Ormston, and A.KPetford-Long, Phys. Rev. B61, 4131~2000!.

10C.H. Marrows and B.J. Hickey, Phys. Rev. B59, 463 ~1999!.11M. Ruhrig, R. Scha¨fer, A. Hubert, R. Mosler, J.A. Wolf, S.

Demokritov, and P Gru¨nberg, Phys. Status Solidi A125, 635~1991!.

-

s.

..

12S. Young, B. Dieny, B. Rodmacq, J. Mouchot, and M.H. Vau-daine, J. Magn. Magn. Mater.162, 38 ~1996!.

13Z.J. Yang and M.R. Scheinfein, IEEE Trans. Magn.31, 3921~1995!.

14S.O. Demokritov, J. Phys. D31, 925 ~1998!.15J.F. Ankner and G.P. Felcher, J. Magn. Magn. Mater.200, 741

~1999!.16G.P. Felcher, Physica B268, 154 ~1999!.17A. Schreyer, J.F. Ankner, Th. Zeidler, H. Zabel, C.F. Majkrzak,

M. Schafer, and P. Gru¨nberg, Europhys. Lett.32, 595 ~1995!.18S. Adenwalla, G.P. Felcher, E.E. Fullerton, and S.D. Bader, Phys.

Rev. B53, 2474~1996!.19R. Felici, J. Penfold, R.C. Ward, and W.G. Williams, Appl. Phys.

A: Solids Surf.45, 169 ~1988!.20C.H. Marrows, N. Wiser, B.J. Hickey, T.P.A. Hase, and B.K.

Tanner, J. Phys.: Condens. Matter11, 81 ~1999!.21S.J. Blundell and J.A.C. Bland, Phys. Rev. B46, 3391~1992!.22S. Langridge, J. Schmalian, C.H. Marrows, D.T. Dekadjevi, and

B.J. Hickey, J. Appl. Phys.87, 5750~2000!.23C.H. Marrows, R. Loloee, and B.J. Hickey, J. Magn. Magn.

Mater.184, 137 ~1998!.24J.C. Slonczewski, Phys. Rev. Lett.67, 3172~1991!.