PHYSICAL REVIEW B VOLUME 55, NUMBER 6 1 FEBRUARY 1997-II Orientation dependence of interlayer coupling and interlayer moments in Fe/Cr multilayers M. A. Tomaz and W. J. Antel, Jr. Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 W. L. O'Brien Synchrotron Radiation Center, University of Wisconsin-Madison, 3731 Schneider Dr., Stoughton, Wisconsin 53589 G. R. Harp Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 Received 5 September 1996; revised manuscript received 15 October 1996 The relationship between indirect exchange coupling and interlayer d-electron magnetic moments is studied using magnetometry and x-ray magnetic circular dichroism XMCD in Fe/Cr multilayers. Multilayers are simultaneously prepared with growth axes along different crystallographic orientations to determine the ori- entation dependence of these properties. We find the Cr moments are antiparallel to the Fe, and that a Cr thickness (tCr) of 1 ML has a moment of 0.7 B , 50% larger than the Cr moment developed in Fe-based dilute Cr alloys. For larger tCr the Cr moment decays very quickly with distance from the Fe interface, while the Fe moment remains bulklike at all Cr thicknesses. It is found that for tCr 10 Å there are slight differences in the indirect oscillatory exchange coupling between Fe layers depending on crystallographic orientation. Intuitively, one would also expect an orientation dependence to the induced Cr moments, but we find them to be orientation independent. The orientation independence of the Cr moments correlates well with the orienta- tion independent coupling which has been previously observed for tCr 10 Å. S0163-1829 97 01306-4 I. INTRODUCTION multilayers are predicted to depend on crystallographic orientation.6 Additionally, their detailed behavior also de- Advances in preparation techniques now allow the pro- pends on the nature of the Fe/Cr interface and the Fe moment duction of ferromagnetic and/or nonmagnetic superlattices configuration9,8,6 that is, whether the Fe layers are arranged comprising layers only a few atoms thick. This enables the ferromagnetically, antiferromagnetically, or otherwise . very interesting possibility of inducing magnetic moments in For the 100 orientation, there is extensive literature on materials not normally magnetic by placing them in close the magnetic ordering of Cr thin films deposited on the sur- proximity to a ferromagnetic layer. These ``interlayer'' mag- face of Fe.10­13 For nearly perfect Fe 100 substrates and netic moments are ultimately responsible for the oscillatory high quality Fe/Cr interfaces, layer antiferromagnetism is ob- exchange coupling which is often observed in these served in the Cr film,10­12 which gives rise to ``short period'' systems.1 This occurs as follows: hybridization at the ferro- antiferromagnetic coupling between Fe 100 films separated magnetic and/or nonmagnetic interface induces a magnetic by Cr.14 Imperfect interfaces, however, can suppress the Cr moment net spin polarization in the electrons belonging to spin density wave15 and the short period coupling9 between the interlayer atoms. This spin polarization decays and oscil- Fe layers. lates in sign as one moves away from the interface. At the Much less work has focused on Cr moments in Fe/Cr subsequent interface, the ferromagnetic layer interacts with multilayers, and orientation dependent measurements of mo- the remnant of this spin polarization leading to a decaying ments in Fe/Cr have not been performed until now. These and oscillating exchange coupling between the ferromagnetic induced interlayer moments are crucial to our understanding layers. Another way in which interlayer moments may con- of RKKY exchange coupling. The measurement of interlayer tribute to exchange coupling is as ``loose spins,'' which are moments is challenging because the ferromagnetic layer mo- important to one model2 for biquadratic 90°) exchange ments overwhelm the very small interlayer moments. An coupling.3 element-specific probing technique is required. Here we ap- Indirect exchange coupling is generally expected to be ply x-ray magnetic circular dichroism XMCD to determine orientation dependent, since in an RKKY model it depends the layer-averaged values of the Fe and Cr moments in Fe/Cr on the magnitude of the Fermi wave vector parallel to the multilayers both as a function of interlayer thickness and growth axis.4 This has been verified specifically in Fe/Cr crystallographic orientation. Because XMCD is measured at through first-principles calculations of multilayers in various the ``white line'' absorption features, it measures mainly the orientations.5,6 Thus, a recent result which shows an orienta- d-band component of the atomic magnetic moment. This al- tion independence of the ``long'' period coupling in Fe/Cr lows us to probe the correlation between the d-band mo- 100 and 211 multilayers7 is rather surprising. It is pos- ments and the exchange coupling. But because the sible that the experimental result is caused by a coincidental d-derived moments dominate the magnetic moments in tran- equality of the coupling period for the two orientations.8 sition metals, for convenience we shall simply refer to the When calculated directly, the interlayer moments in Fe/Cr XMCD results as measuring the atomic moments. 0163-1829/97/55 6 /3716 8 /$10.00 55 3716 © 1997 The American Physical Society 55 ORIENTATION DEPENDENCE OF INTERLAYER . . . 3717 II. SAMPLE PREPARATION The multilayers were prepared in a new sputter deposition system at Ohio University using established recipes.7,16,17 This system has a base pressure of 1 10 9 Torr, and mag- netron sputtering was performed at 3 10 3 Torr. MgO 100 , MgO 110 , and Al 2O3 112¯0 substrates were in- serted together and initially heated to 550 °C for 20 min, followed by growth of the buffer layer Cr 25 Å . The sub- strates were then allowed to cool to 100 °C ( 4 h at which time a multilayer with structure Fe 7.5 Å/ Cr tCr/Fe 7.5 Å ]40 was deposited, followed by a protective Al 20 Å capping layer. Here tCr 1.5, 3, 4.5, 6, 7.5, 9, 12, 15, and 20 Å. Only multilayers with tCr 1­20 Å were studied since, as shown below, the Cr atoms are most strongly polarized at the Fe interface, and the average Cr moment is maximized for thin Cr layers. The substrate holder was rotated at 1 Hz during deposition to ensure uniform thicknesses across the different substrates. It was found that with an Al 20 Å capping layer, no detectable oxidation of the Fe or Cr was evident in any of the films as determined by x-ray absorption spectroscopy . Such oxidation was problematic in a previous study of Fe/V.18 III. STRUCTURAL CHARACTERIZATION FIG. 1. Specular left x-ray diffraction scans from three Fe/Cr Following deposition, the samples were removed from multilayers grown simultaneously on MgO 100 lower , vacuum and characterized by x-ray diffraction. The specular MgO 110 middle and Al2O3 112¯0 upper substrates with struc- diffraction scans indicated a single vertical orientation corre- ture: Substrate/Cr 25 Å/Fe 7.5 Å/ Cr 7.5 Å/Fe 7.5 Å]40/Al 20 Å. On sponding to 100 , 211 , or 110 for films deposited on each substrate only a single crystallographic orientation is observed, MgO 100 , MgO 110 , and Al corresponding to the bcc 100 , bcc 211 , and bcc 110 growth axes, 2O 3 112 ¯0 , respectively. Rep- resentative x-ray scans are presented in Fig. 1 from the Fe/Cr respectively. To the right of each specular scan, rocking curves 7.5 Å samples. Here we observe only those diffraction fea- through the strongest multilayer peak are displayed. Rocking curves tures associated with 100 , 211 , or 110 orientations of typically have FWHM of 1°. the respective Fe/Cr multilayers i.e., no other orientations are present . Beside these scans, x-ray rocking curves those with t through the strongest Fe/Cr features are presented for each of Cr 12 Å showed low remanence and very high saturation fields independent of the azimuthal orientation. the films. We observed rocking curve full width at half This is indicative of antiferromagnetic coupling between the maxima FWHM of 1° in the 100 and 211 oriented Fe layers. Such AF coupling for Cr 12 Å layers agrees with films. The 110 rocking curve FWHM were sometimes previous results on Fe/Cr 100 and Fe/Cr 211 multilayers.7 broader; the widest one was observed for the Fe/Cr 110 15 From easy-axis loops such as those in Figs. 2­4, we de- Å multilayer and was over 2°. termined the applied field required to bring each film to 80% of its saturation magnetization. This 80% saturation field is IV. MAGNETOMETRY plotted in Fig. 5 for all of the samples. The filled data points were taken from loops that were not saturated even in the The samples were characterized using the magneto- largest field applied in our instrument 8 kOe . Therefore, optical Kerr effect MOKE loops along various in-plane azi- these data points represent lower limits for the 80% satura- muthal orientations for each sample. From these loops, the tion field. We find that this saturation field exhibits a strong easy and hard axes of each sample were determined. Al- peak centered near tCr 10 Å for every orientation of our though we could not determine which in-plane crystallo- Fe/Cr films, indicative of AF coupling. graphic direction is associated with the easy axis in each However, the minimum Cr thickness where nonferromag- sample, it was possible to verify that each sample's anisot- netic coupling occurs is different in each orientation. A ropy showed the symmetry corresponding to its epitaxial ori- dashed vertical line is drawn in the figure to highlight this entation. Thus the 100 samples showed a fourfold magnetic feature. Nonferromagnetic coupling begins at tCr 4.5 Å in anisotropy two easy-axes in-plane separated by 90°), while Fe/Cr 110 , 6 Å in Fe/Cr 100 , and 7.5 Å in Fe/Cr 211 . the 110 and 211 samples showed a twofold in-plane mag- Because the three orientations were deposited simulta- netic symmetry. neously, there is no possibility that layer thickness variations Representative MOKE loops are presented in Figs. 2­4. are responsible for these differences.19 We observe that the difference between easy- and hard-axis In Fig. 6, we present another method for visualizing the loops is prominent only in samples having strong ferromag- coupling. Here we plot the ratio M600 /M8000 : the magneti- netic coupling between Fe layers. Some samples, such as zation of each sample in 600 Oe applied field divided by its 3718 TOMAZ, ANTEL, O'BRIEN, AND HARP 55 FIG. 2. Magnetization loops along the easy and hard axes of FIG. 4. As in Figs. 2 and 3, but for Fe/Cr 110 films. Here the three Fe/Cr 100 multilayers having Cr layer thicknesses of 1.5, 12, in-plane anisotropy is again twofold, with easy and hard directions and 20 Å. Very strong antiferromagnetic coupling is observed in the related by a 90° in-plane rotation. 12 Å film. At 1.5 and 20 Å, ferromagnetic coupling permits the to occur first in Fe/Cr 110 , second in Fe/Cr 100 , and last of observation of the in-plane anisotropy of the films. The easy and hard axes were related by a 45° in-plane rotation fourfold . all in Fe/Cr 211 . We point out that the orientation depen- dence OD of the exchange coupling reported here is not magnetization in 8000 Oe. Filled symbols indicate which inconsistent with the orientation independent coupling ob- samples were not saturated in 8000 Oe. For the thinnest and served in Ref. 7 since the previous study focused mainly on thickest films, M multilayers with larger t 600 / M 8000 1, indicating the films were Cr . fully saturated in 600 Oe applied field. For tCr near 10 Å, M600 /M8000 is much smaller than 1, indicating AF coupling. Once again, the onset of nonferromagnetic coupling appears FIG. 5. Plot of the 80% saturation field for Fe/Cr 100 , 211 , and 110 multilayers as a function of tCr . Each orientation shows a peak near tCr 10 Å, indicating antiferromagnetic coupling. The filled symbols indicate samples which could not be saturated in 8 FIG. 3. As in Fig. 2, but for Fe/Cr 211 films. Here the in-plane kOe. The vertical dashed line highlights the result that there is an anisotropy is twofold, and the easy and hard axes are related by a orientation dependence to the interlayer coupling in the low thick- 90° in-plane rotation. ness regime. 55 ORIENTATION DEPENDENCE OF INTERLAYER . . . 3719 FIG. 6. Plot of the Kerr effect at 600 Oe divided by the Kerr effect at 8 kOe for all the films in this study. Filled symbols indicate films which were not saturated in 8 kOe. In this figure, it is even more evident that there is an orientation dependence to the onset of nonferromagnetic coupling in these films. While we observe a definite OD to the coupling, one must FIG. 7. Absorption spectra and XMCD difference spectrum at keep in mind that this OD could be due either to intrinsic or the Fe edge from an Fe/Cr 100 film with tCr 20 Å. The XMCD extrinsic factors. Examples of extrinsic factors include OD of data circles are compared with a scaled version of the XMCD layer roughness, OD of Fe-Cr interdiffusion, etc. Indeed, from a standard sample filled line . From the scaling factor of the Folkerts and Hakkens20 found that Fe/Cr 110 superlattices filled line, the average Fe magnetic moment in the 20 Å film is spontaneously facet to present 100 and 010 faces, which determined. have a lower surface energy. Presumably, similar faceting would not occur on the 100 orientation since there is no We deduce the projected magnetic moment from the energy advantage. Such extrinsic factors could move the ef- XMCD spectra in the following way. The spectra from all fective Fe/Cr interface relative to the nominal interface, mak- ``unknown'' samples are compared to a ``standard'' sample. ing the Cr layers behave as if they were thinner or thicker as The standard sample is chosen to be one for which we know regards coupling. Another way roughness can affect cou- the absolute magnetic moment by some other method. First, pling is through the enhancement of biquadratic coupling.2 r( ) and l( ) of the standard and unknown are nor- This might explain the large biquadratic coupling that has malized to a per-atom basis. We then compare the XMCD, recently been observed in Fe/Cr 110 by Elmers et al.21 m ( r l), of the unknown to that of the standard. More Whatever the cause of the OD of the interlayer coupling specifically, we determine the value of M which minimizes observed here, Fe/Cr presents a good system for the study of U S the OD of the induced interlayer moments. This is because 2 i m,i M m,i 2, 1 the OD of the indirect exchange coupling occurs in an inter- where U and S denote the unknown and standard, and the layer thickness range where we expect the strongest XMCD sum on i is taken over all data points in the photon energy signal. In the following section, we discuss the measurement range near the absorption edge. M represents the projected and results for the interlayer moments. average magnetic moment in the unknown multilayer in units of the standard moment. We also obtain an estimate of V. ELEMENT SPECIFIC MAGNETOMETRY the statistical error bar in M by determining what variation of M is required to change 2 by 10% from its minimum A. Determining magnetic moments value. There is also a systematic error which is dominated XMCD studies were performed at the Synchrotron Radia- by the magnetic dipole contribution to the XMCD and is of tion Center on the 10M toroidal grating monochromator. order 15% of M.22 The magnetic moments are then cor- This monochromator is equipped with a scanning vertical rected if necessary using the MOKE loops so that they aperture which allows the selection of linearly 100% or correspond to the moment at 600 Oe. circularly ( 85% polarized radiation. XMCD measure- The above method for determining magnetic moments ments were made at the Fe and Cr 2p absorption edges using was developed especially for cases where the induced mag- a new system which allows the application of 0­1.5 kOe netic moment is small. Instead of just reporting the ``peak'' fields in the sample plane. The photon beam was incident at dichroism as is sometimes done, we compare dichroism sig- an angle of 45° and the projection of the photon wave vector nals over the entire spectrum. Statistically, this provides the into the sample plane was either parallel or antiparallel to the best estimate of the magnetic moment. applied field direction. The applied magnetic field was As an example of this process, we display in Figs. 7 and 8 switched at each photon energy, and in this way two absorp- the absorption spectra and XMCD from an Fe/Cr 100 tion spectra were obtained, r( ) and l( ). Samples multilayer. We present data from a tCr 20 Å sample to were measured in remanence where possible, or in field highlight the sensitivity of our measurements since this is the when the remanent magnetization was low. The x-ray ab- ``worst case,'' where the Cr dichroism signal is lowest as sorption spectra, obtained using a total yield technique, were compared to its absorption coefficient. In the upper portion normalized to the incident photon flux. of these figures, we display r and l at the Fe and Cr 3720 TOMAZ, ANTEL, O'BRIEN, AND HARP 55 FIG. 8. As in Fig. 7, but at the Cr edge. Here the XMCD is much weaker due to the small induced moment on the Cr inter- layers. Three scaled versions of the standard Cr spectrum are dis- played, indicating the best fit and the upper and lower bound of our statistical error bar for the average magnetic moment of Cr atoms in this film see text for details . FIG. 9. Summary of the projected Fe moments in 600 Oe ap- plied field as determined by XMCD. Statistical error bars are absorption edge, respectively. In the lower panel, shown, although the systematic error bars may be larger see Ref. m is dis- played circles . Superimposed on 22 . For comparison, all graphs display a dashed line at the bulk Fe m are three scaled ver- sions of the standard dichroism spectrum for that element. moment and a starburst symbol representing data from an Fe94Cr6 alloy. These curves look strikingly similar to those of Fig. 6. This These three standard spectra correspond to the best fit, and indicates that while the net Fe moment is often reduced by AF the upper and lower limit of the error bar. In the Fe case, the coupling, individual Fe layers possess bulklike moment magni- fit is of such high quality that the separate standard dichro- tudes. ism spectra are indistinguishable. ality constants28 from Fe and from V, which nicely bracket Cr in the Periodic Table . The constants for Fe were found B. Element-specific magnetic moments above, and those for V were determined from an Fe94V6 Figure 9 displays the XMCD results for the projected Fe alloy, where previous hyperfine field23 and neutron moments. The Fe spectra were compared to an Fe 250 Å diffraction24 studies indicate a V magnetic moment of thick film deposited on MgO 110 with the usual Al capping 0.3 0.2 B averaging the results from the two publica- layer, for which we assume a moment of 2.2 tions . This analysis concluded that the alloy Cr moment was B . It is seen that for thin interlayers the Fe magnetic moment is close to 0.4 B using Fe coefficients and 0.6 B using V or slightly enhanced over that of bulk Fe. For larger Cr thick- coefficients . As a compromise, we assigned an average ness, the projected Fe moment falls due to the onset of non- value of 0.47 B to the alloy Cr moment. ferromagnetic coupling. XMCD measurements were not per- In the multilayers, we found that the layer averaged Cr atomic moments were always aligned antiparallel to the Fe, formed for most of the tCr 9 and 12 Å samples since the as shown in Fig. 10. Note that we plot the negative of the Cr antiferromagnetic coupling was so strong as to preclude moment. Remarkably, the induced Cr moment is higher in meaningful measurements. the 1.5 Å Cr layers than in the Fe The Fe curves look very similar to those of Fig. 6. This is 94Cr 6 alloy. The alloy is indicated with a starburst at the horizontal position corre- expected, since the Fe moments dominate the MOKE signal sponding to a multilayer with the same composition. Alloys in Fig. 6. But the similarity of Figs. 6 and 9 provides one with more Cr are expected to show even lower Cr moments. important piece of information: it indicates that the Fe This is compared with the tCr 1.5 Å multilayer which has atomic moments deviate little from the bulk value in any of an average composition of Fe 84Cr16 . This result is indepen- these films. This result agrees well with previous calculations dent of the exact vertical scale since it comes from a direct where the interface Fe moments are slightly suppressed and comparison of the XMCD from the multilayers and the alloy. the interior Fe layers are slightly enhanced giving little net We conclude that layering Cr with Fe is more effective at change in the average Fe moment from its bulk value.6 inducing interlayer moments than alloying Cr with Fe, for a Moving to the Cr moments, Cr XMCD spectra were com- given average composition. This is in agreement with previ- pared to the ``standard'' spectrum of an Fe ous theoretical studies see, e.g., Ref. 6 . 94Cr 6 alloy where previous studies23,24 indicate a magnetic moment of 0.4 0.4 VI. DISCUSSION B . Because of the large error bars in the previ- ous studies, we made an independent determination of the In the multilayers, the magnitude of the Cr moments fol- alloy moment using a ``transfer'' of the XMCD proportion- lows a pattern which is a product of the projected Fe moment 55 ORIENTATION DEPENDENCE OF INTERLAYER . . . 3721 coupling is orientation dependent and is thought to be medi- ated by the interlayer moments.4 Moreover, this does not agree with the results of recent calculations which predict an OD of the induced Cr moments.6 Yet in all cases XCr is the same for the three crystallographic orientations to within ex- perimental error. XCr decays with increasing tCr in a manner reminiscent of a dilution effect, or 1/tCr dependence. We conclude that only Cr atoms close to the Fe interface acquire a significant mag- netic moment, and that the moments of atoms in the layer interior are negligible. This decay is quantified with a simple model. Suppose that a Cr atom at position z is exchange coupled to the adjacent Fe layers with a strength that decays exponentially with distance from the Fe layer: A MCr z 2 M1exp z/ Cr M2exp tCr z / Cr , Cr 3 where M1 and M2 are the vector magnetizations of the Fe layers located at z 0 and z tCr , respectively, and A and Cr are arbitrary constants. In the case of nonferromagnetic coupling, we assume that both Fe layers are aligned sym- metrically about the applied field direction. FIG. 10. Similar to Fig. 9 but displaying Cr moments. We ob- To obtain the average Cr moment, MCr(z) is projected serve that the Cr moments follow the trend of the Fe moments, but onto the measurement direction and then integrated over the with an additional decaying factor with increasing tCr . Remarkably, thickness of the layer. Finally we divide by t the Cr moments developed in multilayers with t Cr to obtain the Cr 1.5 Å average average Cr moment per atom, composition Fe84Cr16) are larger than is developed in the Fe94Cr6 alloy see text . M Mave A Fe 1 exp tCr / Cr , 4 times a function which decays with increasing t Cr t Cr . The de- Cr pendence on the Fe moment is expected since in the absence where M of Fe, the Cr would be paramagnetic.25 To remove this trivial Fe is the projected Fe moment of either of the Fe layers. We divide by M dependence of the Cr moment on the projected Fe moment, Fe , and obtain an expression that can be compared with X we define the ``interlayer susceptibility,'' X Cr , and this is done in Fig. 11 solid Cr , defined as26 line . Besides its evident simplicity, this model was chosen be- M ave X Cr cause it has the correct asymptotic behavior: M is finite as Cr Cr M . 2 Fe tCr 0, and it decays as 1/tCr for large tCr . In Fig. 11, the parameters A and X Cr have been adjusted to obtain the best Cr is plotted in Fig. 11. fit. The model simulates the data well, and allows us to ex- Figure 11 shows that XCr does not depend on crystallo- tract the exchange coupling decay length, graphic orientation. This is somewhat surprising since the Cr 1.1 Å. To help visualize Eq. 4 , we plot in Fig. 12 the model results for Cr moments in Fe/Cr 100 multilayers having 1, 3, 5, and 7 monolayers of Cr. Along other orientations, the results would be qualitatively the same, but with somewhat different moment values in each layer due to the different thicknesses associated with a monolayer along each direc- tion . In each case, the Cr layers are assumed to be bracketed by ferromagnetically aligned Fe layers with moments of 2.2 B . Note that the Cr moments decay rapidly toward the interior of the layer. Beyond 7 ML, thicker Cr only results in the addition of nonmagnetic Cr layers to the center of the Cr layer. The interface Cr atoms always have about the same moment ( 0.35 B) except for 1 or 2 ML thicknesses ap- proximately 1.5 or 3 Å where the interface Cr atoms acquire a larger moment up to 0.7 B for 1 ML Cr . FIG. 11. The Cr interlayer susceptibilities, X It is instructive to compare the Cr moment magnitudes Cr for all the films. Surprisingly, X with those obtained for Cr films on Fe 100 . One direct com- Cr falls on a universal curve independent of crystal- lographic orientation. This is distinct from the predictions of previ- parison can be made to the work of Idzerda et al.,13 who also ous calculations. The solid line is the fit of a model described in the used XMCD as a probe. For 0.25 ML Cr on Fe they saw an text. XMCD to absorption peak ratio of 7.2% for Cr. Using a 3722 TOMAZ, ANTEL, O'BRIEN, AND HARP 55 be limited, since certain multilayer effects survive, including the long period exchange coupling. Another multilayer effect is the enhancement of the in- duced Cr moments for multilayers above those observed in alloys with similar composition. This is in agreement with a previous theoretical study.6 One way of understanding this is that in a multilayer, the Cr atoms are segregated from the Fe atoms and thus interfere less with the Fe magnetic moments. It is known that in alloys with greater Cr concentration, the Fe moments are suppressed.27 Likewise, Cr atom segregation may reduce Fe interference in the development of the Cr moments. Both of these effects are likely to lead to higher induced Cr moments for multilayers as compared with al- loys. The OD of the indirect exchange coupling is not reflected in the interlayer moments. An assumption that the exchange coupling is intrinsically orientation dependent would indicate that the d-band moments are not the dominant mediators of long-period coupling for tCr 10 Å. In this case, the sp-derived bands would appear to dominate the coupling. Even though the sp moments are small and not measurable in the present experiment , they can dominate the coupling in Mo 100 and Nb 100 spacer layers as was pointed out by Koelling.8 Ironically, in the same article Koelling concludes FIG. 12. The Cr moments as a function of tCr for Fe/Cr 100 as that the long coupling period in Fe/Cr 100 could only be deduced from the fit of Fig. 11. The Cr moments crosshatched due to d-band electron states. bars have been multiplied by 5 in order to bring out their detail in The simplest resolution of this dilemma is to suppose that the presence of the Fe moments filled bars . the OD of the indirect exchange coupling is caused by an OD of extrinsic factors such as interface roughness. Another pos- different standardization method to that used here, they ar- sibility is that while the sp bands are important to coupling rived at a Cr moment of 0.6 0.2 for small t B for this film. This is Cr , the sp-band effects become weak for tCr 10 comparable to our observation of a 7.7% XMCD to absorp- Å. This kind of behavior has been seen in recent calculations tion ratio for 1 ML Cr sandwiched between Fe after correct- of Co/Cu multilayers by Samant et al.,28 who report that the ing for the finite angle of incidence and incomplete circular sp-band moments decay much more quickly away from the polarization , for which we arrive at a Cr moment of interface than do the d-band moments. 0.7 For greater Cr layer thicknesses, the exchange coupling is B . The excellent agreement of XMCD to magnetic moment scaling factors in these two studies lends credibility orientation independent, at least for the 100 and 211 ori- to both of them. entations as shown by Fullerton et al.7 This is in good agree- Idzerda et al.13 find a rapid decay of the Cr moment with ment with the orientation independence of the d-band inter- increasing Cr layer thickness, with the moment dropping to layer moments observed here. This also supports the 0.2 conclusion of Koelling8 that the long period coupling is de- B for a 1 ML Cr film. In contrast, Turtur and Bayreuther12 find that the first two Cr monolayers have a pendent on d-derived states. In that article, Koelling argues constant Cr moment of 3 that the d-band ``lens'' of the Cr Fermi surface gives rise to B . The differences between the two studies may have to do with sample preparation. It is the long period coupling, and that the shape of this lens is difficult to compare Cr thin films which have one Fe inter- such that the long coupling period is the same along 100 , face to Cr in multilayers with two Fe interfaces. However, 211 , and 110 orientations. doing so suggests that the present study is qualitatively more similar to the study of Idzerda. VII. CONCLUSIONS In the present work, the localization of the induced Cr moment to the interface is evidence for frustration of the Our results show that there is a slight orientation depen- interior Cr moments by 1 interface roughness and 2 the dence to the long period exchange coupling in Fe/Cr in the fact that we force the Fe layers into ferromagnetic alignment low thickness regime. In the same films, however, the inter- for XMCD measurements, even when the ground state is an layer moments are identical to within experimental error antiferromagnetic configuration. Both of these factors are across three different growth orientations: 100 , 211 , and known to suppress layer antiferromagnetism, short period 110 . The induced Cr moments are antiparallel to the Fe exchange coupling, and the magnitude of Cr magnetic mo- moments, and for interlayers 1 ML thick, have a magnitude ments in Fe/Cr multilayers. These issues have been discussed of about 0.7 B per atom. By direct comparison, we ob- in Refs. 9, 15, and 6. Note that Eq. 4 neglects the effects of serve that these multilayers have 1.5 times the Cr moment roughness in these films. Because we have no information developed in dilute Cr-Fe alloys, establishing that the quantifying the roughness, we have chosen to ignore it in our multilayer geometry is more effective at inducing interlayer analysis. We point out, however, that such roughness must moments in Cr than the alloy geometry. 55 ORIENTATION DEPENDENCE OF INTERLAYER . . . 3723 The thickness dependence of the Cr moments agrees with gests that the long period coupling in Fe/Cr is mediated by a model assuming an exponential decay of the moment as a d-derived electron states, as was suggested by calculations.8 function of distance from the Fe interface, with a decay con- stant of 1.1 Å. The Fe atomic moments remain close to that ACKNOWLEDGMENTS of bulk Fe. The orientation independence of the d-derived The authors gratefully acknowledge the support of the moments observed here correlates well with the orientation Ohio University Research Council and the National Science independence of the interlayer exchange coupling for Foundation under CAREER Award No. DMR-9623246. The tCr 10 Å which was observed in a previous study.7 This Synchrotron Radiation Center was supported by the National relationship between d moments and interlayer coupling sug- Science Foundation under Award No. DMR-9212658. 1 S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. 64, 22 This method implicitly assumes that the shape of the dichroism 2304 1990 . signal is independent of the sample composition and/or orienta- 2 J. C. Slonczewski, J. Appl. Phys. 73, 5957 1993 . tion. To estimate what systematic error this assumption will in- 3 M. Ru¨hrig, R. Scha¨fer, A. Hubert, R. Mosler, J. A. Wolf, S. troduce, consider that the dichroism signal consists of three Demokritov, and P. Gru¨nberg, Phys. Status Solidi A 125, 635 parts: the spin moment, the orbital moment, and the magnetic 1991 . dipole correction term. The sum of the orbital and spin moments 4 For a recent review of the theory of exchange coupling see K. 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