PHYSICAL REVIEW B VOLUME 55, NUMBER 2 1 JANUARY 1997-II Mimicking of a strong biquadratic interlayer exchange coupling in Fe/Si multilayers J. Kohlhepp Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands and Department of Physics, Eindhoven University of Technology (EUT), 5600 MB Eindhoven, The Netherlands M. Valkier and A. van der Graaf Interfaculty Reactor Institute, TU Delft, 2629 JB Delft, The Netherlands F. J. A. den Broeder Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands Received 10 July 1996 The antiferromagnetic interlayer exchange coupling properties of sputtered Fe/Si multilayers have been studied by magnetometry and spin-polarized neutron reflectometry. Both the degree of antiferromagnetic alignment of adjacent ferromagnetic layers at zero field and the strength of the coupling are found to depend on the position in the multilayer stack. It is shown that these interlayer coupling variations are able to imitate an apparent strong biquadratic coupling. S0163-1829 97 50102-0 The discoveries of an antiferromagnetic AF exchange Originally, such a biquadratic-type coupling has been dis- coupling between two ferromagnetic FM films across a covered by domain microscopy studies of Fe/Cr/Fe trilayers nonmagnetic metallic interlayer,1 the giant magnetoresis- where the 90° alignment of the Fe films at certain Cr thick- tance GMR effect associated with such a coupling,2 and the nesses was directly observed.12 Quite apart from the fact that oscillatory behavior of the magnetic coupling3 have initiated the origin of such a high biquadratic contribution concluded a huge amount of both experimental and theoretical investi- to be present in Fe/Si FeSi ML's is still unclear, an indirect gations during the past decade. Whereas in metal/metal mul- and quantitative determination of biquadratic coupling by tilayers ML's the coupling is understood quite well,4 the simply fitting the magnetization loops of magnetic multilay- situation for ML's with semiconducting spacers is still un- ers seems to be at least questionable. clear. Soon after the discovery of a very weak oscillatory The present paper is concerned with the nature of the exchange coupling between Fe layers across amorphous Si apparent strong biquadratic interlayer exchange observed in deposited at low temperature,5 a very strong nonoscillatory sputtered Fe/Si ML's. By means of the magneto-optical Kerr AF coupling has been observed in sputtered Fe/Si MLs.6 In effect MOKE and spin-polarized neutron reflectometry this case the interlayer was found to be a crystalline interdif- PNR measurements we were able to establish a strong de- fused FeSi alloy. Subsequently it was concluded that the AF pendence of the coupling characteristics on the position in coupling could be converted to FM coupling by cooling to the multilayer stack. It is mainly this striking phenomenon low temperature, at which the AF coupling could surpris- which causes the occurrence of remanences and pronounced ingly be restored by light irradiation.7 It was suggested that rounding offs in the measured magnetizations loops and charge carriers, which are excited thermally or optically from which is thus able to mimic a strong biquadratic interlayer the valence band, or alternatively from localized impurity exchange. states in the narrow band gap of a semiconducting -FeSi The Fe/Si ML's were prepared by dc-magnetron sputter- interlayer, mediate the exchange coupling.7,8 Recently, how- ing (pbase 5 10 5 Pa) at 50 °C onto thermally oxidized ever, we have shown that the AF exchange coupling strength silicon oxi-Si at an Ar pressure of 1 Pa. To allow optical in sputtered Fe/Si FeSi ML's strongly increases with de- access from the substrate side to the magnetic ML's, in some creasing temperature.9 This is in clear contrast to the ex- cases glass substrates have been used. For the experiments pected behavior of the excitation mechanism, where a de- described here the individual Fe layer thicknesses were fixed crease of the temperature should result in a weakening of the at tFe 30 Å whereas the nominal Si thicknesses varied be- AF coupling strength. tween 8 and 40 Å in the (tFe Fe/tSi Si N multilayers, where Realizing the negative temperature coefficient of the AF N is the number of bilayers and tFe(tSi) are the nominal coupling strength, the original supporters of the excitation Fe Si thicknesses. No structural differences were found at mechanism have very recently reinterpreted their earlier all between the growth on glass and on oxi-Si, respectively. temperature-dependent results10 and performed additional In low-angle x-ray diffracton XRD measurements Cu experiments.11 Based on a temperature-dependent analysis of K ) Bragg peaks were observed up to 2 10° for all Si the measured hysteresis loops10 or the saturation fields thicknesses, which is a clear indication of well-defined lay- HS ,11 both groups concluded that a strongly temperature- ering with smooth interfaces. However, the measured dependent biquadratic-type coupling component favoring a multilayer period was considerably shorter than the actu- 90° alignment of adjacent FM layers is responsible for the ally expected sum of the individual Fe and Si thicknesses appearance of a remanent magnetization at low temperatures. deduced from low-angle XRD measurements on calibration 0163-1829/97/55 2 /696 4 /$10.00 55 R696 © 1997 The American Physical Society 55 MIMICKING OF A STRONG BIQUADRATIC . . . R697 least-squares fit of the calculated to the measured loops thus gives J1 and J2. For the majority of our experiments we could indeed find suitable combinations of J1 and J2 which were able to reproduce the remanences and the loop shapes in a satisfactory manner see for example Figs. 1 a and 1 b . Various possible mechanisms causing a biquadratic con- tribution have been proposed recently. But neither intrinsic interlayer properties,17 nor extrinsic factors such as interlayer thickness fluctuations in connection with short-period AF-FM oscillations,18 super paramagnetic impurities ``loose spins'' in the interlayer or at the interface to the FM layers,19 nor magnetic-dipole fields created by magnetic lay- ers with uncorrelated roughness20 are able to explain the strength and the strong temperature dependence of J2 ob- served in our experiments. We can resolve this puzzle by introducing an alternative mechanism which is responsible to contribute at least partly FIG. 1. Normalized hysteresis loops for a 30 Å Fe/11 Å to the rounding of the loop shapes and the occurrence of Si 20 left part and a 30 Å Fe/14 Å Si 20 multilayer right part remanence, namely a dependence of the exchange coupling grown on glass, measured with VSM and longitudinal MOKE at properties on the position in the ML stack. A first hint for the 295 K. The thick solid lines in the VSM loops a and b are fits existence of such a phenomenon is given by studies of ML's resulting in J1 0.679 and J2 0.398 mJ/m2 for 11 Å Si and with different numbers of bilayer repetitions N.16,21 These J1 0.504 and J2 0.098 mJ/m2 for 14 Å Si. showed a remarkable decrease of the remanent magnetiza- samples. Such a contraction of results from a large de- tion from nearly 90% for an Fe/Si/Fe sandwich to almost crease of the Si atomic volume in an Fe environment caused zero for N 60. Additionally, a change from a strongly con- by iron-silicide formation. In agreement with earlier growth vex curved magnetization loop to a more linear one, charac- studies on sputtered Fe/Si multilayers, our own high-angle teristic for almost pure bilinear coupling, was observed. In XRD measurements confirmed a complete (110) order to check the variation of the coupling characteristics bcc-textured growth with typical perpendicular coherence lengths around with the position in the multilayer stack in more detail, we 200 Å for a nominal t took advantage of the limited information depth of MOKE to Si up to 16 Å. Above tSi 16 Å an amorphization of the interlayer starts, indicated by a distinct measure loops both from the surface front side and from broadening of the 110 main peak corresponding to a coher- the glass substrate side back side , independently. Figure 1 ence length limited by a single Fe layer and the disap- shows the results of such an investigation for two different pearence of high-angle satellite reflections. The most prob- ML's with 11 and 14 Å nominal Si thicknesses. Here, the able explanation for the crystalline interlayer growth below vibrating-sample magnetometer VSM loops could be fitted t excellently with the bilinear/biquadratic coupling model, al- Si 16 Å is the aforementioned iron-silicide formation dur- ing growth. Especially the nonmagnetic CsCl-structure B2 though the longitudinal MOKE loops definitely show that FeSi phase seems to be a good canditate for the crystalline both the degree of ferromagnetic alignment of adjacent FM interlayer due to its excellent lattice match to bulk bcc-iron. layers and the rotation process depend on the position in the Recently, it has been shown that this metastable silicide ML stack. At the bottom of the ML, close to the substrate, phase can be stabilized in thin films.13 B2-FeSi is metallic14 the FM layers are weakly AF coupled, while the high rema- and is now held responsible for mediating the interlayer ex- nence is indicative for a very substantial degree of FM cou- change coupling between adjacent Fe layers in Fe/Si-based pling. On the other hand, the top layers show a strong AF systems.15 coupling with almost no remanence. Besides the appearance of a remanent magnetization an- In order to support our MOKE observations we addition- other striking feature is observed in the hysteresis loops of ally performed polarized neutron reflectivity PNR measure- antiferromagnetically coupled Fe/Si ML's.9,10,16 They exhibit ments at the time-of-flight reflectometer of the Interfaculty a distinct convex shape see Figs. 1 a and 1 b . Phenom- Reactor Institute IRI in Delft.22 In our PNR experiments enologically this behavior can be described by the presence the reflected neutron intensity was measured as a function of of a so-called biquadratic coupling term E the incident neutron wave-vector component normal to the bq , favoring a 90° alignment of adjacent FM layers, in addition to the bi- sample surface, q0 2 sin / , where is the neutron wave- linear Heisenberg-type AF coupling term E length, and is the angle of incidence, and as a function of bl 180° align- ment in the interlayer exchange energy:12 the polarization state of the incident neutron beam with re- spect to an applied magnetic field. Unfortunately, with the E experimental setup an exit-beam polarization analysis was ex Ebl Ebq J1cos J2cos2 . 1 not possible. Here is the angle between two adjacent FM layers and Shown in Fig. 2 are reflectivity data taken at room tem- J1 (J2) is the bilinear biquadratic coupling parameter. perature in three different fields applied parallel to the sur- Theoretical magnetization loops can be calculated by simply face of a 30 Å Fe/14 Å Si 20 ML with the incident neutron minimizing the total magnetic energy of the multilayers. A beam polarized parallel ( ) or antiparallel ( ) to the field. R698 J. KOHLHEPP et al. 55 FIG. 2. Polarized neutron reflectivities for a 30 Å Fe/14 Å Si 20 multilayer in different applied magnetic fields H at room tem- perature. The solid open symbols are the measured and the solid FIG. 3. Magnetic scattering length density ( m) profiles corre- long-dashed lines are the calculated reflectivities for the neutron sponding to nonspin-flip reflectivity calculations of Fig. 2. In the spin parallel antiparallel to the field. Only the incident beam was framework of our model m is proportional to the magnetization polarized and spin-flip scattering was neglected in the calculations. of a layer which lies parallel ( ) or antiparallel ( ) with respect to The short dashed curve 60 kA/m is the calculated reflectivity the applied field. neutron spin parallel at the AF peak for a magnetic order limited only by the structural coherence length. n(z) m(z) n0(z) b(z) p(z)..., with n0 the atomic num- ber density, b the nuclear and p the magnetic scattering The most important feature in the low-field spectrum is the length. Here n(z) is the nuclear SLD and m(z) is the presence of a strong Bragg reflection at q0 0.44 nm 1, magnetic SLD which is proportional to the in-plane average which corresponds to a magnetic periodicity mag twice the magnetization parallel ( ) or antiparallel ( ) to the neutron chemical modulation length deduced from low- and high- spin. angle XRD. Such a Bragg peak is expected for an AF order- The theoretical reflectivity was calculated using the so- ing of subsequent FM layers and thus confirms the existence called matrix method,23 and convoluted with the experimen- of an AF exchange coupling across the FeSi interlayer in our tal resolution. For this purpose, the sample was divided into sample. The drop of the intensity of the AF Bragg peak slabs alternatingly composed of 9 Å of a nonmagnetic iron observed with increasing field strength is simply the effect of silicide with a n very close to Fe50Si50 and 27 Å of an an enhanced Zeeman energy in competition with the cou- iron-rich Fe100 xSix (x 15) magnetic alloy for more de- pling energy, causing a decrease of AF alignment and con- tails see Ref. 24 . Keeping this nuclear SLD profile of the sequently a decrease of the magnetic contrast between adja- ML constant, the measured reflectivities for the different cent FM layers. Remarkable is the considerable width of the magnetic field values were fitted by adjusting the magnetiza- AF Bragg peak, which is a clear sign of a poor magnetic tion profile of the sample. Figure 3 shows the resulting mag- coherence length and thus an additional indication of a netic non-spin-flip SLD profiles exemplarily for the PNR strongly depth-dependent coupling behavior along the ML. spectra of Fig. 2. Here, the solid dashed lines in Fig. 2 For a magnetic order limited by the structural coherence of represent the optimum fits of the calculated reflectivities to the ML one would expect much narrower AF peaks, which is the measured data points symbols for the neutron spin par- exemplarily shown for one field 60 kA/m and one spin allel antiparallel to the applied magnetic field. Inspecting in direction by the short-dashed curve in Fig. 2. Fig. 3 the low-field 60 kA/m m(z) profile, a strong depen- However, due to the missing exit-beam polarization dence of the magnetic alignment of FM layers on the posi- analysis in our setup, a separation between spin-flip and non- tion in the ML becomes evident. While the magnetizations of spin-flip scattering was not possible. Thus, vector magne- the top layers show a nearly perfect AF alignment, the cou- tometry could not be performed and quantitative statements pling in the bottom half of the sample is predominantly FM, about the magnetic structure of the ML cannot be made. which is in agreement with the interpretation of our MOKE Nevertheless, with the help of some simplifications concern- measurements. Applying an increasing external field see for ing the magnetic structure, at least some qualitative conclu- instance H 318 and 581 kA/m in Fig. 3 results in an in- sions can be drawn. In the following it is assumed that the crease of the magnetizations parallel to the field direction. magnetic moments of the magnetic layers are always aligned But once again, this process is not homogeneous, it is in turn parallel or antiparallel to the applied field. Therefore only depending on the position in the ML stack. It is obvious that perfect FM or AF aligned regions domains are allowed one needs much more field to achieve a magnetic saturaton between the adjacent FM layers, and consequently spin-flip for layers close to the sample surface than for those in the scattering cannot take place. The reflectivities depend bottom half of the ML. Thus, not only the zero-field align- on the scattering length density SLD , (z), which in ab- ment, but also the coupling strength is depth dependent. sence of spin-flip scattering can be written as (z) All in all, we have measured the PNR reflectivities and 55 MIMICKING OF A STRONG BIQUADRATIC . . . R699 these individual loops results in macroscopic hysteresis curves with FM fractions and nonlinear slopes. A variation of the interlayer exchange coupling in the vertical direction can thus imitate an apparent strong biquadratic interlayer ex- change and can lead to serious misinterpretations of experi- mental results. Naturally, the question arises as to which mechanism causes this inhomogeneous coupling behavior. Probably, the growth of the first few layers on the amorphous substrate is strongly disturbed, resulting in local ferromagnetic short cir- cuits, which strongly influence the loop shapes and the cou- pling strength.25 This interpretation is supported by an addi- tional experiment where the first Fe/Si layers have been replaced by a Cr/Si ML with an identical growth behavior.16 FIG. 4. Comparison of the normalized magnetization loops of a A single Fe/Si/Fe sandwich grown on top of such a simu- 30 Å Fe/14 Å Si 20 multilayer measured by vibrating sample lated Fe/Si base ML already showed a predominantly AF magnetometry VSM and polarized neutron reflectivity PNR ex- coupled magnetization loop. Besides usual pinholes, as for periments. instance grain boundaries filled with a ferromagnetic phase, subsequently determined the m(z) profiles for 13 different also chains of nearest-neigbor Fe atoms in the not perfectly magnetic fields. Correspondingly, an averaging of the mag- ordered FeSi interlayer which percolate the magnetization netizations in the magnetic SLD profiles as a function of the between adjacent Fe layers are able to mediate FM coupling. applied magnetic field provides us with the magnetization In the present case especially, these percolation bridges may loop of the sample. Figure 4 shows the loops deduced from become successively ferromagnetic on cooling, explaining our PNR study and measured by depth-insensitive vibrating the observed remarkable temperature dependences of the re- sample magnetometry. The excellent matching of the PNR manences and the loop shapes. data with the VSM curve is striking and supports at least in In conclusion, we have shown that the degree of antifer- a qualitative way the validity of our depth-dependent model, romagnetic alignment of adjacent ferromagnetic layers and despite the serious simplifications which have been made. the coupling strength definitely depend on the position in the A depth-dependent coupling provides a natural explana- Fe/Si ML stack. 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