PHYSICAL REVIEW B VOLUME 62, NUMBER 17 1 NOVEMBER 2000-I Determination of equilibrium coupling angles in magnetic multilayers by polarized neutron reflectometry C. H. Marrows,1,* S. Langridge,2 and B. J. Hickey1 1Department 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 spacer layers was paused halfway through each layer for a variable amount of time to allow residual gases to be adsorbed onto the surface. A sample with clean Cu spacers shows good AF coupling, with low remanence and high saturation field. The PNR spectra show a strong 12 -order Bragg peak and little splitting between the reflectivities for incident and spin neutrons at zero field, characteristic of AF ordering. Meanwhile, a more heavily gas-damaged sample with a remanent fraction of 2/2 has strongly spin-split PNR spectra at the critical edge and nuclear Bragg peak, showing a significant ferromagnetic component. A strong 12 -order Bragg peak is still present. We are able to fit accurately the magnetization and PNR data by assuming that such a sample shows considerable biquadratic coupling, with moments coupled close to 90° at zero field. One of the most striking properties of the new generation ferent material systems, e.g., Fe/Cr,11 NiFe/Ag,12 and of magnetic multilayer structures is the presence of Co/Cu.13 It may be described phenomenologically by the in- antiferromagnetic1 AF or oscillatory2 indirect exchange clusion of the biquadratic second term in the expansion in coupling between magnetic layers on either side of a thin powers of S*S of the indirect exchange interaction between nonmagnetic spacer. The oscillation in coupling with spacer spins S in adjacent magnetic layers. The free energy per unit thickness is due to the quantum interference of spin- area, , of a Co/Cu/Co trilayer in applied field H may be polarized wave functions,3 with the ferromagnet/spacer inter- written as faces acting analogously to a Fabry-Perot e´talon with spin- dependent reflection coefficients. A variety of theoretical 0mHt cos 1 cos 2 J1cos J2cos2 , 1 methods have been employed to attempt to calculate these reflection coefficients, such as RKKY-like theories,4 total en- where the Co layers are of magnetization m and thickness t. ergy calculations,5 and quantum confinement of spin- The moments make angles with the field and with each holes.6 These various theories have enjoyed increasing suc- other, i.e., 1 2. The interlayer exchange appears in cess in predicting the period, amplitude, and temperature de- the form of the bilinear and biquadratic coupling constants pendence of the coupling. J1 and J2. The biquadratic term represents non-Heisenberg We have been studying the interlayer coupling of one exchange. Such coupling appears to be commonplace in a multilayer system, Co/Cu, as it exhibits a large giant magne- variety of multilayer systems.14 With the proper sign for J2 toresistance GMR which is of particular scientific and tech- the two energy minima can be found at /2, leading to nological interest.7 We previously found that relatively low orthogonal ordering of adjacent layer moments. By introduc- levels of residual gas in the vacuum chamber during growth ing J1 it is possible to close up for J1 0) or force apart for would significantly reduce the GMR ratio of Co/Cu multi- J1 0) the moments to reach any zero-field equilibrium layers while not affecting the resistivity of the films. The angle between 0 and . An appropriate variation of J1 and most damaging point at which these gases could enter the J2 can therefore yield the proper decline in GMR and AF multilayer stack was in the bulk of the Cu spacer layers.8 coupling with rising base pressure in the sputtering chamber. This was explained by a reduction of the degree of antifer- In this paper we report the results of polarized neutron romagnetic character in the interlayer coupling. Subse- reflectometry15 PNR performed on such samples. Among quently it became apparent that a plausible explanation for the many applications found for this technique, one of the the reduction of GMR would be a smooth rotation of the most common is determining the magnetic alignments in equilibrium zero-field angle between adjacent moments multilayer structures,16 acting in many respects as a depth- from to 0 as the base pressure of the system worsened.9 selective vector magnetometer. It is therefore suited to inves- This noncollinear ordering of the moments requires the in- tigating the nature of the angular dependence of the ex- troduction of a significant biquadratic term in the expression change interaction between the Co layers in these for the free energy of the multilayer. We found that the in- multilayers. troduction of this biquadratic term would correctly reproduce The samples were deposited by dc magnetron sputtering the experimentally observed dependences of the magnetiza- on 25 mm 25 mm pieces of Si 001 wafer. The working tion and GMR on field and on each other across the width of gas pressure was 3.0 mTorr. The multilayers were nominally the first AF peak in the coupling oscillation.10 Such noncol- of the form Co 10 Å / Cu 9 Å 25. This Cu thickness linear coupling has now been observed in a number of dif- corresponds to the first antiferromagnetic maximum in the 0163-1829/2000/62 17 /11340 4 /$15.00 PRB 62 11 340 ©2000 The American Physical Society PRB 62 BRIEF REPORTS 11 341 FIG. 2. Low-angle x-ray diffraction spectra for the two multi- layers. The Bragg peak at Q 3.2 Å 1 is due to the chemical periodicity of the multilayer. The two scans are offset by a decade FIG. 1. Magnetization loops for the two multilayers. The solid of intensity for clarity. lines are fits to the data. The inset is magnetoresistance measure- ments for nominally identical smaller samples grown in the same thy that if we were to choose angles of for the clean vacuum cycle. sample and /2 for the gas-damaged sample, this would yield a GMR ratio in the clean sample of double that in the oscillatory exchange coupling. The lowest base pressure of gas-damaged one, while simultaneously yielding remanences the system is achieved by cooling a Meissner coil with liquid of zero and 2/2( 0.7), respectively. It should also be nitrogen-it is possible to raise the base pressure by not fully noted that changes in anisotropy cannot account for the dif- cooling the coil. This mainly results in a higher partial pres- ferences in magnetic response we see here-generally these sure of H2O. One sample was prepared with each layer affect the nature of the hysteresis in the magnetization loop.9 grown continuously, in a system base pressure of 2.0 In Fig. 2 low-angle x-ray reflectivity spectra are dis- 10 8 Torr. The growth was paused for 30 s in the middle played. Since each sample has an area similar in size to the of each Cu spacer layer in the second sample, exposing the racetrack of the magnetron sputter guns, we might expect surface to a base pressure of 1.3 10 7 Torr. Both samples that the samples are not perfectly uniform in thickness, and were prepared in the same vacuum cycle of the system. x-ray scans were taken at 2.5 mm intervals across the Structural characterization of the samples was performed sample. The particular scans shown are from the center of by low-angle x-ray reflectometry. Magnetization loops were the wafer. All the scans are very similar, although the value measured by means of the magnetooptic Kerr effect of Q at which the bilayer Bragg peak is observed is slightly MOKE . Magnetoresistance was measured by a four-probe higher at the edges of the sample, corresponding to a slightly dc method. PNR was carried out on the CRISP time-of-flight thinner layer. For the clean sample the mean bilayer spacing reflectometer at ISIS.17­19 The instrument was operated with- is 19.4 Å with a standard deviation across the wafer of 0.6 Å. out analysis of the spins of the exit beam of neutrons, and For the gas-damaged sample the mean is 19.1 Å, again with magnetic fields were applied to the sample with an electro- a standard deviation of only 0.6 Å. A fuller structural analy- magnet. A minimum applied field of 50 Oe is required to sis of similar samples was previously presented:20 the multi- prevent depolarization of the neutron beam. All measure- layers were found to be extremely smooth, with rms rough- ments were performed at room temperature. nesses of 1 Å and a very high degree of vertical correlation In Fig. 1 we show the magnetization loops for the two of the interfaces. different samples. It is immediately apparent from the low PNR produces very rich data sets, the most important of remanence that the clean sample has substantial AF ordering which are displayed in Figs. 3 and 4. In these two figures we at low fields. Meanwhile, the remanence of the gas-damaged show the 50 Oe data for the two samples. Although it is not sample is substantial, approximately 0.65 of the saturated possible to perform PNR in field-free conditions due to loss magnetization. As expected the GMR of the sample with the of polarization of the neutron beam, 50 Oe can be seen to be small remanence is much higher; indeed it is just over only a weak perturbation of the state of these samples, where double. However, the resistivity of the two samples when the saturation fields are much higher see Fig. 1 . The spin- magnetically saturated is very similar, 20 2 cm at room and - labels refer to the polarization of the incident neutron temperature. beam. There are several features common to both data sets, It is of course possible to explain these changes in two such as the Bragg peaks, critical edges, and finite-size ways. The gas-damaged sample may consist of perfect AF fringes. For very low Q, total internal reflection of the neu- regions, interspersed with regions where the moments lie trons occurs and the reflectivity is unity. All the data have parallel to each other that contribute nothing to the GMR. On been normalized in reflectivity to this point. Above the criti- the other hand, we may set the moments at an angle to each cal value of Q the neutrons penetrate the sample. Bragg re- other, which will provide a net moment at remanence, but flection occurs at certain values of Q corresponding to peri- also some misalignment that gives rise to GMR as the mo- odicities within the sample. The first-order Bragg peak at ments are closed together by an external field. It is notewor- Q 0.32 Å 1 is due to the chemical periodicity of the 11 342 BRIEF REPORTS PRB 62 pression of the 12 -order peak. The data set of Fig. 4 is quali- tatively very similar to that of the clean sample in a field roughly halfway to saturation, i.e., when the moments are partly closed together. Both samples behave in a comparable manner when saturated, and are thus entirely in ferromag- netic alignment. In this case the 12 -order Bragg peak is en- tirely absent, and the critical edge, finite-size fringes, and first-order peak are strongly spin split. The four spin-dependent cross sections were simulated using an optical potential-type model21 and combined to pro- duce the spin-dependent specular reflectivity. The calcula- tions were then numerically convoluted with the instrumental resolution. We averaged over two different sets of input pa- rameters in order to account for the slight nonuniformity in FIG. 3. Polarized neutron reflectometry spectra for the clean thickness of the sample. In this model we assume that all the antiferromagnetically coupled sample at H 50 Oe. The data are intensity measured is due to specular scatter, with zero dif- the points; the solid lines are the results of the simulation. fuse component. We have recently measured the off-specular scatter from several magnetic multilayers using the 3He mul- sample, and yields a bilayer spacing of 19.6 Å, close to the tidetector on CRISP.22 In the case of these samples, where nominal value. Meanwhile the 12 -order peak at Q 0.16 Å 1 the coupling is strong, we find little diffuse scatter, even at corresponds to a doubling of the real space period and is due zero field-a weak diffuse component is just discernible un- to the AF ordering of the sample, leading to a magnetic der the instrument-broadened 12 -order Bragg peak. We there- period twice that of the chemical period. The magnetic origin fore feel justified in neglecting this very weak scatter and of the peak peak is confirmed by its suppression as the ap- treating all the intensity as entirely specular. plied magnetic field is increased, vanishing above the satu- The Co moment is found to be 1.5 B /atom, a little ration field when all the moments are closed and no AF order lower than the bulk value of 1.7 B /atom. This is not so persists. Meanwhile, the fringes visible in both scans below surprising given the extreme thinness of the films, which will Q 0.1 Å 1 are analogous to Kiessig fringes observed in suppress both the magnetization and the Curie point.23 The low-angle x-ray reflectivity spectra, arising due to interfer- value for the zero-field coupling angle for the gas- ence of the beams reflected at the air/multilayer and damaged sample giving the best fit was 86°, while for the multilayer/substrate interfaces. clean sample 170°. The splitting in the finite-size fringes There are a number of important differences between the seen in Fig. 3 can be reproduced by assuming that the first two samples. In Fig. 3 the two spectra are only weakly spin few Co layers deposited on the substrate form a ferromag- split, with the only splitting of any significance in the finite- netic block. Cross-sectional transmission electron micro- size fringes. Meanwhile, in Fig. 4 there is significant splitting graphs of similar samples confirm that the layering quality is both at the critical edge and at the first-order Bragg peak. poor for the first few bilayer repeats,9 so we should expect These are characteristic of a sample with a significant ferro- that the AF interlayer coupling in this region should be sig- magnetic component. The 12 -order peak is not split as it is nificantly impaired. due to AF ordering, which, without polarization analysis, It is now possible to take the thickness and magnetization cannot exhibit any spin dependence. values determined from the PNR and simulate the expected As the field is increased all these features become more magnetic response of the samples. Setting t 9.75 Å and m pronounced: spin splitting of the critical edge, at the first- 1.25 MA m 1, and following the path of minimum , as order Bragg peak, and of the finite-size fringes, and a sup- given by Eq. 1 , as a function of H, it is possible to obtain the simulated magnetization loops of best fit shown as solid lines in Fig. 1 using the following coupling constants: for the clean sample J1 0.15 mJ m 2, J2 0.085 mJ m 2; for the gas-damaged sample J1 0.024 mJ m 2, J2 0.17 mJ m 2. Note that these values include the factor of 2 cor- rection required to transfer the trilayer model of Eq. 1 to a multilayer. This leads to equilibrium values of of 82° and 180°, respectively, close to the values giving the best fits to the PNR data. The small remanence in the clean sample comes entirely from the ferromagnetic block of five layers at the bottom of the stack in this simulation. To conclude, we have studied by PNR the magnetic prop- erties of multilayers exhibiting good AF coupling, and a form of coupling intermediate between AF and ferromag- netic. The sample shows characteristics of both AF coupling FIG. 4. Polarized neutron reflectometry spectra for the gas- high saturation field, appreciable GMR, and strong 12 -order damaged noncollinearly coupled sample at H 50 Oe. The data are PNR Bragg peak and ferromagnetic coupling high rema- the points; the solid lines are the results of the simulation. nence, spin-split PNR critical edge, and first-order Bragg PRB 62 BRIEF REPORTS 11 343 peak . This suggests that some sort of mixed coupling is residual gases accumulate on the sample surface during present. The width of the PNR Bragg peaks in Figs. 3 and 4 pauses in growth they clump in particular areas, and cause a yields a vertical magnetic coherence length comparable with change in sign of J1 from negative to positive. If these areas the size of the multilayer, so that the fluctuations in coupling were small compared to the exchange length, i.e., only 1 or 2 must be lateral. This means that there is the opportunity for nm across, then this could lead to mixed coupling of the type noncollinear ordering of adjacent layer moments, as de- that will cause a biquadratic term in the Slonczewski model, scribed in the well-known Slonczewski coupling fluctuation and is also consistent with the gradual decrease in from model of biquadratic exchange,24 where different lateral re- to zero as reported in Ref. 9. We know from Lorentz micros- gions of the spacer have positive or negative coupling ener- copy studies that on dc demagnetization the samples are in a gies. When the lateral length scale of the fluctuations in cou- single domain state,9 and the good agreement between the pling strength is comparable to the exchange length of the simulations and the PNR data is further compelling evidence magnetic layers, then the magnetization cannot simulta- that there is substantial biquadratic coupling in these gas- neously satisfy adjacent regions of opposite coupling. An damaged samples. equilibrium angle is found partway between 0 and , leading to a noncollinear arrangement of moments. On the other C.H.M. would like to thank the Royal Commission for the hand, if the lateral fluctuations are long ranged, then the lay- Exhibition of 1851 for financial support. We are grateful to ers can break into domains such that the coupling conditions the Rutherford Appleton Laboratory for the provision of are locally satisfied everywhere. It is possible that as the beam time at ISIS. *Email address: c.marrows@leeds.ac.uk 12 S. Young, B. Dieny, B. Rodmacq, J. 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