Surface Science 454­456 (2000) 880­884 www.elsevier.nl/locate/susc Brillouin light scattering study of an exchange coupled asymmetric trilayer of Fe/Cr P. Vavassori a,*, M. Grimsditch b, E. Fullerton c, L. Giovannini a, R. Zivieri a, F. Nizzoli a a INFM-Dipartimento di Fisica, Universita di Ferrara, Ferrara I-44100, Italy b Material Science Division, Argonne National Laboratory, Argonne, IL 60439-4845, USA c IBM Almaden Research Center, San Jose, CA 95120-6099, USA Abstract The magnetic response of a (211) oriented asymmetric Fe trilayer [Fe(100 A )/Cr(9 A )/Fe(20 A )/ Cr(20 A )/Fe(20 A )], in which the thickness of the Cr spacer layers was chosen to produce ferromagnetic coupling (F) between the two thinner Fe layers and antiferromagnetic coupling (AF) between the thicker Fe layer and the adjacent thin one, has been investigated using magnetization and Brillouin light scattering (BLS) measurements. The coupling coefficients, extracted by fitting the BLS and magnetization measurements with a theory treating the static and dynamic response on an equal footing, produced consistent values of the magnetic parameters. Our results confirm that the theoretical model used in interpreting both static and dynamic properties is valid even in systems in which F and AF coupling of the layers are simultaneously present. The theoretical model has also been extended to include the field dependence of the intensity of the Brillouin peaks. The calculated intensities are compared with the BLS spectra at different applied fields. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Green's function methods; Iron; Light scattering; Magnetic interfaces; Magnons The exchange coupling between two ferromag- well as the period of its oscillations, is now well netic thin metal films through non-magnetic met- understood. The biquadratic term is phenomeno- allic spacer layers is described by bilinear and logical and was introduced to account for the biquadratic terms (for a recent and complete observation that, under certain conditions, the review of the argument, see e.g. Ref. [1]). The magnetic moments of the two ferromagnetic layers bilinear term of the coupling is Heisenberg-like so tend to align at 90° with respect to each other. that only ferromagnetic or antiferromagnetic cou- The origin of the biquadratic coupling is quite pling between the two ferromagnetic layers is controversial and has been attributed to a variety possible. The coupling oscillates periodically of factors such as interface roughness and intrinsic between ferromagnetic and antiferromagnetic with mechanisms [1]. increasing spacer-layer thickness and its origin, as In this paper we use an experimental approach to determine the coupling coefficients based on the * Corresponding author. Fax: +39-0532-781810. fitting of Brillouin light scattering (BLS) and E-mail address: vavassor@axpfe.fe.infn.it (P. Vavassori) magnetization measurements with a theory treat- 0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0039-6028 ( 00 ) 00252-1 P. Vavassori et al. / Surface Science 454­456 (2000) 880­884 881 ing the static and dynamic response on an equal footing. This approach, successfully used in recent investigations [2­4], is here applied to a [Fe(100 A )/Cr(9 A )/Fe(20 A )/Cr(20 A )/Fe(20 A )] multilayer in which the magnetic layers have different thickness. The Brillouin cross-section is then calculated, with a procedure which is a gener- alization to a layered structure of the method of Cochran and Dutcher [5] for a single film. Our model takes into account the scattering processes which involve reflections of the incident and scat- tered light on any of the interfaces. The sample was epitaxially grown by d.c. mag- netron sputtering on a polished single-crystal MgO(110) substrate using the same procedure outlined for superlattices [6]. A 100 A Cr(211) layer was grown at 600°C. The substrate was then cooled to 180°C prior to the growth of the Fe/Cr multilayer. The thickness of the Cr interlayers was chosen to show the simultaneous presence of ferro- magnetic and antiferromagnetic coupling between the two thinner Fe layers and between the thicker Fe layer and the adjacent thin one, respectively. The complete structure was capped with a 20 A Cr layer. A calibrated quartz crystal oscillator monitored the thickness of the various layers. Under these conditions the sample grows with Fig. 1. (a) Brillouin frequencies as a function of the external Fe[211] along the surface normal and the in-plane field applied along the easy axis: experiment (dots) and fit (line) described in the text. (b) Fit (line) of SQUID loop (dots), mea- [1:11] and [01:1] directions parallel to MgO [1:10] sured with the field applied along the easy axis, as described in and [001], respectively. Magnetization studies have the text. shown that the [1:11] and [01:1] directions are the hard and easy axes, respectively. The magnetization hysteresis loops were mea- incident polarization in order to minimize the sured by SQUID magnetometry. The spin-wave intense signal of the unshifted laser radiation. All excitations were measured by BLS using 250 mW measurements were done at room temperature. of 5145 A radiation from an Ar+ laser. The scat- Fig. 1 shows the room temperature magnon tered radiation was analyzed with a tandem Fabry­ frequencies (panel a) and the magnetization results Perot interferometer [7] in 3+2 pass operation. (panel b) of our sample when the external field H The sample was mounted with its normal along is applied along the in-plane easy-axis of the the collection axis and the laser beam was incident sample. Also shown are the results of the fitting at an angle of 54° to the normal. This geometry procedure described below. As expected for three fixes the magnitude of the wave vector parallel to magnetic layers, the BLS spectra show three the surface qd at 0.98×105 cm-1. The magnetic modes: one can be viewed as the in-phase oscilla- field was applied in the plane of the sample parallel tion of the dynamic magnetization m of the three to the [01:1] direction (easy axis) and perpendicular Fe layers and the other two as the out-of-phase to the scattering plane, i.e. perpendicular to the oscillation of m of two layers with respect to the wave vector of the magnon. The polarization of third one. The splitting, observed in the calcula- the scattered light was analyzed at 90° to the tions at low fields, occurs in the regions where the 882 P. Vavassori et al. / Surface Science 454­456 (2000) 880­884 Stokes and the anti-Stokes portions of the spectra with the SQUID results. The magnon frequencies are not time reversal invariant to each other. For are obtained as excited states of the layers above larger fields, where the three layers are aligned the ground state, generalizing the formalism we with the field, no such differences exist. used in Ref. [2] to three magnetic layers. The qualitative interpretation of the magnetiza- The fitting routine involves adjusting the param- tion curve shows that at low field (0­200 Oe) the eters to produce a minimum in the difference static magnetizations M of the two thin Fe layers between calculation and experiment (x2). The error are parallel to each other, lie in the film plane and estimate for each parameter, described in detail in are along the easy-axis but antiparallel to H, while Ref. [2], involves finding the change such that the M of the thicker layer is parallel to H and thus x2, after adjusting all other parameters, increases antiparallel to those of thin layers. In this region by 50%. The best-fit parameters are listed in M/MS=(100-20-20)/140=0.43, where MS is the Table 1 where an asterisk indicates that the fit was saturation value of M. The magnetization jump insensitive to that particular parameter. (The observed at H&300 Oe is consistent with a switch- effects of the cubic anisotropy are small and it is ing of the outermost layer so that M of the middle not possible to extract reliable values for K1. layer is antiparallel to that of the other two layers. Therefore we have simply fixed the value of K Above the jump M/M 1 S=(100-20+20)/140= [2].) During the fitting of the SQUID results we 0.71. A second transition occurring between H&1 have fixed the values of the anisotropy constants and 3.5 kOe corresponds to a gradual rotation of (K1 and Ku) and of the saturation magnetization M of the central layer till all three layers are in the films (M1, M2 and M3) to the values aligned; M/MS=1. extracted from the fits to the BLS data. Fig. 1 The numerical values of the magnetic parame- shows the good agreement between the experimen- ters have been obtained by fitting the field depen- tal data and the fits. A comparison of the results dence of the magnetization and BLS results. The extracted from magnetization and BLS (Table 1) basics of the model are described in Ref. [8]; a shows that the values of Ji­j 1 and Ji­j 2 are within slightly modified version of that approach was the estimated errors. The model, therefore, pro- used in Ref. [2]. Our approach here follows vides a self-consistent description of the experimen- Ref. [2]; the energy per layer is unchanged from tal results even in this case where ferromagnetic eq. (1) of Ref. [2]; the total energy per unit area, and antiferromagnetic coupling is present. eq. (2) of Ref. [2], is generalized to three magnetic BLS peak intensities were obtained by solving layers: for the eigenmodes of the equations for the 3 dynamic magnetization (eqs. (A5) and (A6) of E= {K1di(13 cos4 hi+14 sin4 hi) Ref. [2], generalized to three layers) and the nor- i=1 malization condition requiring that the average +Kudi cos2 hi-HMidi cos(hi-hh)} energy is the same for each magnon mode. The +J1­2 dynamic magnetization m(x, t) induces small fluc- 1 cos(h1-h2)+J1­2 2 cos2(h1-h2) tuating terms in the dielectric tensor which, to +J2­3 1 cos(h2-h3)+J2­3 2 cos2(h2-h3) lowest order and for the scattering geometry used where K here, can be written [9]: de 1 and Ku are the cubic and uniaxial aniso- 21=-Km3 and tropy constants characteristic of Fe(211) films, de23=Km1, where K is the magneto-optic constant. M The reference frame, shown in the inset to Fig. 2, i is the saturation magnetization of the layer, hi and h has been taken with the x h the angles that M and H make with the 2 axis along H and the hard axis, respectively. The generalization to three x3 axis perpendicular to the surface. We have layers leads to two bilinear (J1­2 calculated the intensity of the s-polarized scattered 1 and J1­2 2 ) and two biquadratic terms (J2­3 light, given a p-polarized incident light, by solving 1 and J2­3 2 ). The equilib- rium magnetic configuration is calculated minimiz- the electromagnetic propagation equation for a ing the energy expression above and compared stratified medium, which can be written, retaining P. Vavassori et al. / Surface Science 454­456 (2000) 880­884 883 Table 1 Table summarizing the parameters extracted from the best least-square fitting of the data shown in Fig. 1. Also shown are confidence levels obtained as described in the text. Asterisks indicate parameters which are fixed during fitting K1 Ku 4pM1,2 4pM3 J1­2 1 J1­2 2 J2­3 1 J2­3 2 (×105 ergs/ (×105 ergs/ (kG) (kG) (×10-2 ergs/ (×10-2 ergs/ (×10-2 ergs/ (×10-2 ergs/ cm3) cm3) cm2) cm2) cm2) cm2) BLS 1.11 5.8±0.6 18.0±0.5 17.0±0.8 -8.0±2.5 2.5±2.0 75.0±6.0 15±4.0 SQUID 1.11 5.81 18.01 17.01 -8.5±2.0 2.5±2.0 72.0±3.0 18±2.0 This equation has been solved with the Green's function method [10], properly taking into account the electromagnetic boundary condition at each interface for the electric field of both incident and scattered light (E and dE, respectively). Finally, the differential Brillouin cross-section is calculated, as the ratio between the scattered intensity and the incident one, times the Bose­Einstein thermal factor. Fig. 2 shows the comparison between the calculated and the measured BLS spectra for H= 20 Oe (panel a) and H=4.2 KOe (panel b). The overall agreement is good; some discrepancies are observed in the anti-Stokes portion of the low field spectrum. The origin of these discrepancies may be due to the critical behavior of the cross-section far from the ferromagnetically aligned state, as already found in the case of the Fe/Cu/Fe system [8]; this issue will be addressed at a later date. Acknowledgements Work at ANL was supported by the US Department of Energy, BES under Contract W-31-109-ENG-38. The work of L.G., R.Z. and F.N. has been developed in the framework of the Fig. 2. Comparison between the calculated (solid line) and mea- INFM Project SIMBRIS. sured (dashed line) Brillouin spectra at 20 Oe (panel a) and 4.2 kOe (panel b). The inset shows the reference frame used. References the first order fluctuating terms, as v2 [1] S.O. Demokritov, J. Phys. D: Appl. Phys. 31 (1998) 925 CA- ec20+V×V×BdED and references cited therein. x2 [2] M. Grimsditch, S. Kumar, E.E. Fullerton, Phys. Rev. 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