PHYSICAL REVIEW B, VOLUME 65, 064440 Magnetic interlayer exchange coupling in epitaxial FeÕSiÕFe 001... studied by polarized neutron reflectometry R. W. E. van de Kruijs, M. Th. Rekveldt, and H. Fredrikze Interfaculty Reactor Institute, Delft University of Technology, Department of Neutron scattering and Mo¨ssbauer spectroscopy, Mekelweg 15, 2629 JB Delft, The Netherlands J. T. Kohlhepp, J. K. Ha, and W. J. M. de Jonge Eindhoven University of Technology, Department of Applied Physics and COBRA Research Institute, P.O. BOX 513, 5600MB Eindhoven, The Netherlands Received 10 August 2001; published 24 January 2002 Polarized neutron reflectometry PNR has been used to investigate the magnetic interlayer coupling in a MBE-grown Fe/Si/Fe 001 sandwich at room temperature and at 10 K. Both the magnitude and orientation of the magnetic moments of the Fe layers are obtained from a rigorous analysis of the PNR data. Orthogonal configurations of the Fe magnetizations were observed, providing unambiguous evidence for the presence of a biquadratic term in the exchange coupling energy. The competition between the bilinear and biquadratic exchange couplings results in distinct orthogonal and antiparallel configurations of the Fe magnetizations at room temperature. A previously unresolved magnetic configuration in the room-temperature hysteresis curve was identified by the PNR measurements as a 180° spin-flop transition. The dominant role of the biquadratic coupling at low temperatures is evident from the orthogonal configuration of the magnetizations at remanence in the measurements at T 10 K. The magnetic configurations deduced by PNR are in good agreement with those obtained by fitting the magnetic hysteresis loops using a global energy minimum calculation. DOI: 10.1103/PhysRevB.65.064440 PACS number s : 75.25. z, 61.12.Ha, 75.60. d, 75.70. i I. INTRODUCTION application in neutron beam optics.16 The bilinear and biqua- dratic interlayer exchange in Fe/Si and their temperature de- The interlayer exchange coupling between ferromagnetic pendence have been intensively studied by several groups layers across nonferromagnetic spacers has been a topic of and were shown to depend strongly on the properties of the enormous interest in the past years. Its presence along with iron silicide that is formed by intermixing at the Fe/Si inter- the crystalline magnetic anisotropies and external magnetic faces during growth.5,10,17­22 In contrast to the oscillatory fields can lead to interesting arrangements of the magnetiza- nature common in metallic systems, a strong antiferromag- tion directions of the individual layers.1,2 These arrange- netic coupling (J1 0) was found in MBE-deposited Fe/ ments can be experimentally determined using polarized Si/Fe trilayers, with J1 exponentially decreasing for increas- neutron reflectometry PNR 3­6 with polarization analysis or, ing spacer thickness.23 An additional biquadratic contribution in a somewhat less direct way, by analyzing magnetization to the exchange coupling was also identified by a detailed loops.7­10 analysis of magneto-optical Kerr effect MOKE measure- The interlayer exchange coupling energy per unit surface ments. From the distinct temperature and exponential thick- area is generally written as E ness dependence of the derived coupling parameters J1 and ex J1cos( ) J2cos2( ), J where J 2, the exchange coupling was identified to be originated 1 and J2 are the bilinear and biquadratic coupling from ``loose spins'' in the during the deposition formed crys- coefficients, respectively, and is the relative angle be- talline iron-silicide spacer layer.7,8,20 tween the magnetizations of the ferromagnetic layers. Typi- Although the interlayer exchange in single-crystalline Fe/ cally, the Heisenberg-like bilinear coupling (J1) shows an Si/Fe 001 sandwiches has been determined by a hysteresis oscillatory dependence on the interlayer thickness. The ori- loop analysis, no direct observation of the microscopic spin gin of this oscillatory behavior can be found in the detailed orientations was obtained. Furthermore, it was recently rec- topology of the spacer Fermi surface. The biquadratic cou- ognized that fluctuations of the bilinear coupling due to fluc- pling contribution (J2) is recognized to depend strongly on tuations in the interlayer thickness both in-plane and the thickness, composition, and structure of the interlayer. Its throughout a multilayer stacking may mimic biquadraticlike origin is attributed to extrinsic factors such as fluctuations in behavior in the magnetization curves.6 In the present work, the interlayer thickness11,12 or superparamagnetic impurities we combine information obtained from PNR, grazing inci- in the spacer layer ``loose spins'' .8,13,14 An overview of dence x-ray reflection GIXR and MOKE to give a detailed these mechanisms can be found in Ref. 15. description of the magnetization configurations in exchange One system of particular recent interest is that of ferro- coupled Fe/Si/Fe 001 . The particular advantage of PNR is magnetic Fe layers nominally separated by a semiconducting that it gives vectorial information about the magnetization Si layer. The Fe/Si system is well suited for fundamental both magnitude and orientation of each layer, and hence the studies of the antiferromagnetic exchange coupling between relative angle between the magnetizations can be deter- two magnetic layers, but it is also interesting because of its mined. 0163-1829/2002/65 6 /064440 7 /$20.00 65 064440-1 ©2002 The American Physical Society R. W. E. VAN DE KRUIJS et al. PHYSICAL REVIEW B 65 064440 The layout of the paper is as follows. Section II describes the sample preparation and the experimental methods used in this work. In Sec. III the structure of the sandwich is deter- mined by GIXR. The magnetic characterization of the sand- wich is presented and discussed in Sec. IV, with Sec. IV A focussing on MOKE results and Sec. IV B focussing on PNR experiments. Finally, conclusions are presented in Sec. V. II. EXPERIMENTAL METHODS The Fe/Si/Fe sandwich was grown at the Eindhoven Uni- versity on a Ge 001 substrate in a molecular-beam epitaxy MBE system VG-Semicon V80M with a base pressure of 2 10 11 mbar. Prior to deposition of the layers, the Ge 001 substrate was cleaned by several Ar sputter and anneal treatments until a sharp (2 1)-LEED pattern was observed. The Fe layers were deposited by an e-gun source with feedback control of the flux, whereas the Si was evapo- rated from a temperature-stabilized effusion cell. All nominal FIG. 1. Normalized specular x-ray reflectivity curve of the Fe/ layer thicknesses were controlled by calibrated quartz-crystal Si/Fe 001 sandwich. Markers are shown for every fifth data point. monitors. After addition of a Si capping layer to avoid oxi- The inset shows the dispersion parameter obtained from fitting dation, the final nominal composition of the sandwich was as the model calculations to the experimental data. The discrepancy follows: Ge(001)/60 Å Fe/14 Å Si/45 Å Fe/40 Å Si. The between calculated and experimental data is shown at the bottom. nominal Si thickness of 14 Å was chosen to have a well- defined bilinear and biquadratic coupling as found earlier in ment formalism26,27 are fitted to the experimental data. The identical samples.7,8 More detailed information about the sandwich is partitioned into four slabs, corresponding to the growth dynamics, the structural quality and the Fe/Si inter- four deposited layers. The solutions of the electromagnetic diffusion can be found in Ref. 20. wave equation inside the slabs are represented by matrices In the present study, additional structural information was that depend on the thickness t and the refractive index n of gained from GIXR data accurately taken at room tempera- each slab and on the wave vector k inside each slab. The ture. A standard 2 reflectometer Philips X Pert system index of refraction n of a material consisting of different with a wavelength of 1.542 Å (CuK ,E 8.05 keV) elements i is given by was used. The reflection angle was varied between 0.5° and 5°, resulting in a wave vector transfer range of r0 2 r0 2 Q 4 sin( )/ 0.07 0.7 Å 1. The slits that define the n 1 Nifi 1 Nifi , 1 i 2 i beam size also determine the angular divergence of 0.05°, resulting in an instrumental resolution of Q 3 where r0 is the classical electron radius, and Ni and fi are the 10 3 Å 1. atom number density and scattering factor of each element. For the magnetic characterization, MOKE and PNR ex- The scattering factor consists of a real part representing the periments were performed at room temperature and at T coherent scattering of the x rays and an imaginary part rep- 10 K. The longitudinal MOKE hysteresis loops were ob- resenting the absorption of the x rays. Thus Eq. 1 is com- tained using an incident laser beam spot size of the order of monly written as 0.1 mm. The PNR experiments were carried out at CRISP, the time-of-flight reflectometer at the ISIS spallation source, n 1 i , 2 with an available wavelength range of 2 6.5 Å for po- with the dispersion Re (r0 2/2 ) iNifi and the ab- larized neutrons.24,25 The experimental settings for the fixed sorption Im (r0 2/2 ) iNifi . glancing angle of incidence and for the size of the beam slits From the sequence of all layer matrices, the reflectivity of combined to an effective instrumental resolution of Q/Q the sample is calculated as a function of the wave vector 0.10. FeCoV/TiNx super-mirrors and Drabkin spin- transfer Q 4 sin( )/ , where is the grazing angle of in- flippers were used to define the incident beam polarization cidence. The effect of interdiffusion between two deposited and perform the analysis of the reflected beam polarization. layers is incorporated by analytical expressions that describe Additionally, small guide fields were present along the flight the continuous change in the refractive index between two path of the polarized neutron beam to avoid depolarization layers by an error-function profile.28 The r.m.s. surface effects. roughness parameter quantifies the width of the error func- tion. All the calculated spectra were convoluted with the ap- III. STRUCTURE CHARACTERIZATION propriate resolution function. The fitting parameters in the data analysis are the thick- The x-ray data taken at room temperature are plotted in ness t, the dispersion , and the r.m.s. surface roughness Fig. 1. Reflectivity calculations using a standard matrix ele- for each slab in the model. The absorption parameter was 064440-2 MAGNETIC INTERLAYER EXCHANGE COUPLING IN . . . PHYSICAL REVIEW B 65 064440 TABLE I. The layer thickness t, dispersion and r.m.s. surface roughness , as refined from the fitting of model calculations to the experimental x-ray reflectivity data. The layer thickness in paren- theses is the nominal layer thickness; the dispersion in parentheses is taken from literature Ref. 29 . Layer t (Å) ( 10 6) (Å) Si 48 40 9.1 7.6 9.5 Fe 46 45 23.4 22.5 5.6 Si 9 14 16.8 7.6 9.5 Fe 59 60 21.3 22.5 3.2 Ge 15.1 14.5 0.8 taken from literature29 because the absorption of x rays in the sandwich does not play an important role in the reflectivity FIG. 2. KERR rotation of the Fe/Si/Fe sandwich at room tem- calculations. The discrepancy between the model calcula- perature with the field applied along the 100 easy axis. The round tions and the experimental data is quantified by markers indicate data points obtained from PNR experiments. The insets show the magnetic configuration as derived from the polar- 1 N ized neutron reflectivity experiments. E R j 2 N , 3 j 1 RC j the Si/Fe interface width, the model calculations showed where R( j) RC(j) RM(j) and RC(j) and RM(j) are the large discrepancies with the experimental data. When sepa- calculated and measured reflectivities at reflection angle rate interface widths were used in the fit, this discrepancy ( j). Minimization of Eq. 3 was performed in two separate disappeared, resulting in the profile shown in the inset of Fig. steps. First, a genetic algorithm GA was used to obtain a 1. Such an asymmetry in the width of the intermixing regions global minimum of E. Genetic algorithms have the distinct has been previously reported for metal/Si multilayers.32 advantage of significantly reducing the chance of hitting a local minimum and have been successfully used to analyze GIXR data in the past.30,31 Subsequent minimization by a IV. MAGNETIC CHARACTERIZATION hill-climbing algorithm HC refines the parameter values and an absolute minimum of E is reached. The fitted model A. MOKE experiments calculations are shown as a solid line in Fig. 1. In the inset of Figure 2 shows a room-temperature longitudinal MOKE the figure the depth-profile of the dispersion parameter that loop with the applied field H along the 100 easy axis. For resulted from the fitting procedure, is depicted. The values of clarity, only the branch of the down-field sweep is plotted. R/RC demonstrate that the fit is in excellent agreement The magnetization loop can be excellently fitted using global with the experimental data over the available experimental energy minimum calculations of the total relevant magnetic wave vector range. energy which is composed of the cubic magnetocrystalline Table I gives the values of the refined model parameters energy, the Zeeman energy, and bilinear and biquadratic ex- t, , and . The fitted thicknesses of both Fe layers corre- change energy contributions.8 The result of the analysis is the spond well with their nominal values and their dispersion following: As the magnetic field decreases from saturation values are also close to the bulk value of Fe 22.5 10 6. towards remanence, three distinct regions separated by sud- The increased thickness of the Si capping layer can be attrib- den jumps can be identified. The first plateau where H uted to oxidation of the sample surface. The dispersion value 17 kA/m corresponds to a saturated magnetic state with of the Si interlayer clearly differs from that expected for bulk parallel orientations of the two layer magnetizations. For Si ( Si 7.6 10 6). The fitted value of 16.8 10 6 is 10 kA/m H 17 kA/m, the magnetization of the 60 Å layer close to that of FeSi ( FeSi 18.3 10 6), and thus a clear is oriented parallel to the applied field and the magnetization indication of iron-silicide formation in the spacer layer. The of the 45 Å layer is oriented perpendicular to it, indicating reduced value of the fitted apparent interlayer thickness and a the presence of a distinct biquadratic contribution to the in- value as large as the spacer thickness are additional signa- terlayer coupling. The plateau between H 4 kA/m and tures of a completely interdiffused, e.g., iron-silicide spacer. H 10 kA/m, which includes the remanent state, is expected A more detailed study of the formation of the iron-silicide to have an antiparallel orientation of the magnetic moments interlayers in Fe/Si/Fe 001 using LEED, AES, and Mo¨ss- due to the strong bilinear AF coupling. Increasing the bauer spectroscopy was already presented in Ref. 20. But the negative field, regions with antiparallel, perpendicular GIXR data supply additional information: When the reflec- and parallel configurations are again identified. An tivity calculations were fitted to the experimental data under additional magnetic configuration is recognized for the assumption that the Fe/Si interface width was equal to 7 kA/m H 4 kA/m in the MOKE measurement, but 064440-3 R. W. E. VAN DE KRUIJS et al. PHYSICAL REVIEW B 65 064440 FIG. 4. Room-temperature Fe/Si/Fe 001 reflectivity curves as a function of neutron wave vector transfer at an applied field of 30 FIG. 3. KERR rotation of the Fe/Si/Fe sandwich at T 10 K kA/m along the easy axis. The inset shows the polarization direction with the field applied along the 100 easy axis. PNR experiments of the incident neutrons in and the direction of polarization analy- were carried out at the marked field values. Magnetic configurations sis for the reflected neutrons out . derived from PNR are shown in the insets. for the illuminated sample area. Finally, the experimental data were corrected for the efficiencies of the polarizing el- its magnetization configurations could not be identified up to ements using procedures described elsewhere36 to obtain the now by the simple simulation analysis. reflectivities R( ), R( ), R( ), and R( ). All data The magnetization behavior at low temperature is quite points that were negative or had absolute values smaller than different from that at room temperature. The down-field their estimated statistical uncertainties were excluded in the magnetization loop of Fe/Si/Fe 001 at T 10 K is shown in plots. Fig. 3. The plateaus observed in the room-temperature hys- The reflectivity curves in Fig. 4 were taken at room tem- teresis curve are missing at low temperature. From the analy- perature with an applied field of H 30 kA/m. The ( ) and sis of the hysteresis loop by global energy minimum calcu- ( ) spin-flipped reflectivities are effectively equal to back- lations of the total magnetic energy, the magnetization ground levels. The large splitting between the ( ) and ( ) reversal process is found to be a coherent rotation of the non-spin-flipped curves is indicative for a large net magneti- magnetic moments and the large remanent magnetization is zation component along the applied field direction. A large an indication of 90° alignment of the magnetizations of the net magnetization, together with the absence of any spin- ferromagnetic layers at zero applied field. flipped reflectivities, confirms the expectation that the sand- wich is saturated with the magnetizations of the 45 Å layer B. Polarized neutron reflectometry and the 60 Å layer oriented parallel to the applied field di- rection. For an applied field of H 12 kA/m, high intensity PNR experiments are carried out to directly confirm the spin-flipped signals are measured not shown . These spin- presence of bilinear and biquadratic exchange coupling in flipped intensities are related to components of the magneti- the Fe/Si/Fe 001 sandwich and obtain more detailed infor- zation perpendicular to the applied field direction and vanish mation about the magnetization reversal processes. PNR only if such components are not present. Perpendicular com- with polarization analysis of the reflected beam is unique in ponents of the magnetizations indicate the presence of a bi- its ability to extract a vectorial magnetization profile33,34 and quadratic contribution to the interlayer coupling. Measure- has been used successfully in studies of the magnetic inter- ments at H 2.5 kA/m, close to the remanent situation, show layer coupling in, for instance, Fe/Cr multilayers.3,35 only a small splitting between non-spin-flipped reflectivity At room temperature, first a saturation field of H curves, indicating a small net magnetization. Together with 250 kA/m was applied along the in-plane 100 easy axis the absence of any spin-flip scattering, this confirms a fully of the Fe/Si/Fe 001 sandwich. Subsequently, the applied antiferromagnetic configuration, showing the dominance of field was reduced in steps and PNR ``snap shots'' were taken bilinear coupling at room temperature. The last snapshot was at the field values marked in the hysteresis loop of Fig. 2. In taken at H 7.4 kA/m and the PNR spectra for this field all PNR experiments we measured the four detector intensi- setting are shown in Fig. 5. Again high intensity spin-flipped ties I( ), I( ), I( ), and I( ), where the first arrow signals are measured and the Fe magnetizations have com- between parentheses marks the direction of the incident ponents perpendicular to the applied field direction. beam polarization and the second arrow marks the direction The exact magnetic configurations can be obtained by fit- of polarization analysis of the reflected beam. The polariza- ting PNR simulations to the experimental data. Analogous to tion directions are either parallel ( ) or antiparallel ( ) with the case of x rays Eq. 1 , the index of refraction n for respect to the applied field direction. The detector intensities neutrons incident on a material consisting of elements i can are normalized to the incident beam intensity and corrected be written as 064440-4 MAGNETIC INTERLAYER EXCHANGE COUPLING IN . . . PHYSICAL REVIEW B 65 064440 experiments. To our knowledge, no analytical expressions exist that describe the influence of both the nuclear and the magnetic roughness of noncollinear systems on PNR simu- lations in a similar way as the expressions derived by Ne´vot and Croce for GIXR.28 To incorporate the effect of interdif- fusion at interfaces, additional slabs were added at the inter- face positions to describe gradual changes in the nuclear den- sity and in the magnetization vector. It turns out that the effect of interdiffusion on the neutron reflectivity calcula- tions is negligible in the experimentally available neutron wave vector transfer range. The model calculations are fitted to the experimental data by minimization GA followed by HC of 1 N E R j 2 N , 5 j 1 UR j where R( j) is the difference between calculated and mea- sured reflectivity for neutrons of wavelength ( j) and UR(j) is the statistical uncertainty in the measured reflectivity. The parameters that were refined are the nuclear scattering length density Nb iNibi in each layer, and the size M and ori- entation ( ) of the magnetization in both Fe layers. The nuclear scattering length density profile at the start of the fitting procedure was obtained from the GIXR results pre- sented in Sec. III. The experimental data at high Q are not of sufficient quality to resolve details in the nuclear and mag- netic SLD profiles, making the fit procedure rather insensi- tive to small changes in the SLD profiles. The number of FIG. 5. Non-spin-flipped a and spin-flipped b reflectivities as fitting parameters could be reduced by setting the values of a function of wave vector transfer at room temperature with H Nb and M to the same value for both Fe layers, without 7.4 kA/m along the easy axis. affecting the overall quality of the fit. The fit procedure is much more sensitive to changes in the orientations of the Fe magnetizations. Such changes affect the reflectivity over the 2 entire Q range and change the relative contributions of the n 1 Ni bi pi , 4 spin-non-flipped and spin-flipped signals. Model calculations i were fitted simultaneously to all the room-temperature ex- perimental data by using a common nuclear SLD profile in where bi is the bound coherent nuclear scattering length and all model calculations. In this way, the influence of system- pi C i is the magnetic scattering length, with C 0.2695 atical errors in separate data-sets on the fitting procedure is 10 4 Å/ B and i is the net magnetic moment per scat- reduced. Furthermore, instead of fitting the spin-asymmetry terer in units of Bohr magnetons. Nibi and Nipi are com- function that is defined in Ref. 37, we fit model calculations monly referred to as the nuclear and magnetic scattering to all four reflectivities R( ), R( ), R( ), and R( ). length densities SLD of element i. In general, bi is a com- Fitting all spin-dependent reflectivity curves simultaneously plex quantity with a real and imaginary part respectively is in general a more sensitive procedure than fitting only the representing the scattering and the absorption of neutrons. spin asymmetry function. The sign in Eq. 4 refers to the incident polarization of It was impossible to obtain good fits to the experimental the neutrons, either parallel or antiparallel ( ) to the data with a single-domain configuration i.e., the magnetiza- applied field direction. tion M in each Fe layer is that of the magnetization at satu- The nuclear density profile and vector magnetization pro- ration MS). A good fit could be obtained only with a system- file of the Ge 001 /Fe/Si/Fe/Si sample are approximated by a atic reduction of the fitted size of the magnetization at lower four-slab model, with each slab representing a deposited fields, with M/MS dropping to 0.88 at the near-remanent layer. The solutions of the particle wave equations in these state. This can be explained by the formation of a multido- slabs are implemented in a matrix formalism that calculates main state at low fields, where the neutrons coherently probe the spin-dependent neutron reflectivities of magnetically the averaged magnetization due to their in-plane coherence noncollinear media as a function of the neutron wave vector length of the order of 100 m. A similar reduction in mag- transfer Q 4 sin( )/ .37 The influence of absorption netization at low field was found when PNR experiments on imaginary part of bi) on calculations of the reflectivity is Fe/Cr/Fe sandwiches were analyzed, although the reduction negligible in the wave vector range used in the present PNR is more pronounced in Fe/Cr/Fe.4 The stronger reduction re- 064440-5 R. W. E. VAN DE KRUIJS et al. PHYSICAL REVIEW B 65 064440 TABLE II. The effective magnetization M/MS and the angles of TABLE III. The effective magnetization M/MS and the angles the 45 and 60 Å layer magnetizations ( 45 , 60) relative to the ap- of the 45 and 60 Å layer magnetizations ( 45 , 60) relative to the plied field direction, determined by PNR measurements at room applied field direction, determined by PNR measurements at T temperature. The normalized Kerr rotation estimated from Eq. 6 10 K. Also listed is the normalized Kerr rotation estimated from has also been listed. Eq. 6 . H 45 60 M/MS Kerr H 45 60 M/MS Kerr kA/m deg. deg. deg. kA/m deg. deg. deg. 30.2 0 0 0 1.0 1.0 45.0 49 12 61 0.94 0.80 12.0 74 14 88 0.93 0.66 20.0 68 11 79 0.93 0.70 2.5 180 0 180 0.88 0.21 2.5 82 7 89 0.92 0.63 7.4 92 110 158 0.89 0.22 rections of the 45 and 60 Å Fe layers and the applied field ported in Fe/Cr/Fe is explained by the fact that the average direction. The markers in Fig. 2 correspond with the normal- domain size in the poly-crystalline Fe/Cr/Fe samples is much ized Kerr rotation that is calculated by Eq. 6 , using the smaller than in the single-crystalline Fe/Si/Fe samples. fitted values of M, t45 , t60 , 45 , and 60 . Good agreement After the introduction of a reduced magnetization of the is found between the predicted and measured normalized Fe layers at low applied fields, the fitted model calculations Kerr rotation values, confirming the magnetic configurations are in good agreement with the experimental data. The fitted derived from the PNR experiments. values of Nb 7.5 10 6 Å 2 for the Fe layers and Nb PNR experiments at low temperature were carried out 2.4 10 6 Å 2 for the Si capping layer are in good agree- with the sample mounted in a helium flow cryostat between ment with those found for Fe and Si in literature:38 NbFe the poles of an electromagnet. Experiments were performed 8.1 10 6 Å 2 and NbSi 2.1 10 6 Å 2. For the inter- at applied fields corresponding to the positions marked in the layer, the fitted value of Nb 6.2 10 6 Å 2 was close to hysteresis loop of Fig. 3. Model calculations were fitted to that expected for iron silicide NbFeSi 5.6 10 6 Å 2. Al- the experimental data and a good agreement was obtained. though these PNR results generally confirm the interpretation The data analysis of the experiments at T 10 K was per- of the x-ray data, a higher transversal resolution of the formed separately from the data analysis of the room tem- nuclear density profile was obtained by GIXR due to the perature experiments to reduce the time needed by the fitting higher maximum momentum transfer and the better overall algorithm. A recent simultaneous fit to all data sets at both quality of the x-ray data. temperatures does not show any distinguishable differences The refined values of the size and the orientations of the in the refined model parameters, confirming the absence of Fe magnetizations are given in Table II, with the correspond- systematical errors in the data sets taken at different tempera- ing magnetic configurations shown in the insets of Fig. 2. tures. The configuration for H 12 kA/m clearly proves the pres- The refined parameters for the T 10 K measurements are ence of a 90° coupling between both Fe layers. The domi- given in Table III. The formation of a multidomain state is nance of the bilinear coupling at room temperature is con- again implied by the decrease in the value of M/MS . The cluded from the 180° coupling near remanence. An magnetic configurations determined by PNR are shown in additional magnetic state was recognized in the room- the insets of Fig. 3 and indicate a coherent rotation of the temperature hysteresis loop for 7 kA/m H 4 kA/m, magnetizations from parallel alignment at saturation to per- which configuration could previously not be deduced from pendicular alignment at remanence. The markers in Fig. 3 analyzing the MOKE data. The PNR results show that this indicate the Kerr rotation calculated from the PNR results by field region corresponds with a spin-flop transition from an- Eq. 6 and agree well with the results found by MOKE. The tiparallel coupled Fe layers oriented parallel to the applied presence of a 90° coupling of the Fe layers at remanence field, to antiparallel coupled Fe layers oriented perpendicular confirms the strong increase of the biquadratic coupling with to the applied field. decreasing temperature that was postulated in Ref. 8. The room-temperature MOKE signal for a specific mag- netic configuration can be estimated from the PNR experi- ments. The normalized longitudinal Kerr rotation is propor- V. CONCLUSIONS tional to the net magnetization component along the applied We have systematically studied the magnetization reversal field direction and may be written as in an exchange coupled Fe/Si/Fe 001 sandwich by combin- ing information from PNR, GIXR, and MOKE. Room- t temperature MOKE loops show a distinct steplike behavior Kerr 45Mcos 45 t60Mcos 60 that is indicative for the presence of interlayer coupling. In t45M t60M , 6 certain field ranges, the PNR results show an orthogonal ar- rangement of the magnetizations that is due to a significant where t45 and t60 are the Fe layer thicknesses, and 45 and biquadratic contribution to the total magnetic energy. The 60 are the respective angles between the magnetization di- antiparallel magnetic alignment at remanence shows that the 064440-6 MAGNETIC INTERLAYER EXCHANGE COUPLING IN . . . PHYSICAL REVIEW B 65 064440 dominant coupling at room temperature is bilinear. At T ACKNOWLEDGMENTS 10 K, the PNR analysis indicates an orthogonal remanent This work was financially supported by the Netherlands magnetic configuration that becomes parallel at saturation Organization for Scientific Research NWO and the Dutch through a coherent rotation of the magnetizations, demon- Technology Foundation STW. We thank Niels van Dijk for strating the dominance of the biquadratic coupling at low careful reading of the manuscript and gratefully acknowl- temperatures. edge Sean Langridge for support at the CRISP beamline. 1 M. Maccio , M.G. Pini, P. Politi, and A. Rettori, Phys. Rev. B 49, 21 J. Dubowik, F. Stobiecki, B. Szyman´ski, Y.V. Kudryavtsev, A. 3283 1994 . Grabias, and M. Kopcewicz, Acta Phys. Pol. 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