~ Journal of mnal nellsm magnetic maleflais ELSEVIER Journal of Magnetism and Magnetic Materials 196-197 (1999) 67-69 Brillouin light scattering study of Co/Cr/Co trilayers J.A. Cowen a, J.G. Booth a'*, J.W. Boyle a, K.M. Booth a, A.D. Boardman a, S.M. Thompson b, M. Jackson b, J.S.S. Whiting b a Joule Laborato~, Department of Physics, University ofSalford, Salford, M5 4WT, UK bPhysies Department, University of York, York, YOI 5DD, UK Abstract Spin-wave excitations have been observed in Co(212 ~,)/Cr(do)/Co(200 ~)/Si trilayers for 5 < do < 35 A. Two modes, symmetric and antisymmetric, showed a frequency variation with applied in-plane magnetic field (0.1 < H < 5.0 kOe). The small frequency changes with Cr thickness at high and low fields indicate that exchange coupling is small. Values of 4riM S typical of bulk values were obtained from fits to theory. No in-plane orientational frequency dependence was observed. © 1999 Elsevier Science B.V. All rights reserved. Keywords." Brillouin light scattering; Co/Cr/Co; Trilayers; Exchange coupling Magnetic coupling in magnetic/non-magnetic/mag- probe with the optical power at the sample being of the netic trilayers continues to be of interest. Stray dipolar order of 250 mW. Measurements were carried out with fields between neighbouring magnetic layers interact and a scattering angle of 45 ° corresponding to an in-plane for thin spacer layers exchange coupling occurs. The magnon wavenumber of 1.73 × 105 cm- 1 and two modes latter has been widely investigated since the discoveries were detected. No frequency shift was detected for differ- of antiferromagnetic coupling [1] and oscillatory inter- ent in-plane orientations for any of the samples and the layer exchange [2]. spin-wave frequency was measured as a function of the Co/Cr/Co trilayers have received little attention [3] applied magnetic field H, where 0.1 < H < 5.0 kOe for although both ferromagnetic and antiferromagnetic each sample. MOKE measurements indicated that most coupling have been observed. The present study exam- of the samples were saturated in fields of ~ 65 Oe al- ines the effect of Cr spacer thickness on the coupling, by though two required more than 100 Oe, the lowest ap- observation of the spin-wave mode frequencies. plied field used here. Brief details of the sample preparation are as follows. In the dipolar case where the effects of exchange are Growth was by electron beam evaporation in UHV on neglected and with no anisotropy the analytical solution silicon (1 1 1) substrates with a thick amorphous SiO2 for the spin-wave frequencies is given by [4] surface layer giving rise to polycrystalline growth. The Co layers are nominally 200/~ thick as the top Co layer 09 = 7[H(H + 4rtM) + 4rt2M2(1 + 1/C)] 1/2, (1) oxidises to a depth of 12/~. where C is a constant. The two values of C can be found Brillouin light scattering measurements used a back- from the quadratic relation scattering geometry with the applied field in the plane of the sample and perpendicular to the incident light. An C 2 exp( - 2kud2) + C exp[2ku(dl - d2)] Argon ion laser operating at 5145 ~ was used as the - C exp( - 2kudo) + C exp[ - 2kv(d2 + do)] + C exp[2ku(dl - do)] - C exp[2kn(dl - d2 - do)] * Corresponding author. Tel.: + 44-161-295-5259; fax: + 44- 161-295-5197; e-mail: j.g.booth@physics.salford.ac.uk. + C + exp(2ktfll) = 0, (2) 0304-8853/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S0304-8 8 53(98)00664-7 68 ZA. Cowen et al. /Journal of Magnetism and Magnetic Materials 196-197 (1999) 67-69 50 N 40 s _ _ ~ j ~ - - ~. 30 ~ - i - j ' ~ j ~ g .~r..f j a ~ 20 "~ l0 50 0 -50 Frequency shill / GHz I 2 3 4 Fig. 1. Brillouin spectrum for Co/Cr/Co trilayer where Applied field., kOe do(Cr) = 35 A in a field of 2.0 kOe. Fig. 2. Spin-wave frequency versus applied field for Co/Cr/Co trilayer where do = 35 A. where k, is the in-plane m a g n o n wavenumber, do is the thickness of the spacer layer, and dl and d2 are the The values of 4xM~ are all of the order of ~ 17 kG which thicknesses of the magnetic layers. The two modes at compares favourably with the bulk value of 17.6 kG. The different frequencies are referred to as symmetric (S) and fitted value of the constant C is generally of the same antisymmetric (A), which refers to the spin-wave ampli- order of magnitude as the calculated values. Any dispar- tudes in the two magnetic layers being parallel (S) or ity probably arises from a lack of precision about the real antiparallel (A). A typical spectrum is shown in Fig. 1 for thickness of the layers, since Co and Cr alloy. However, do = 35 ~, where the two modes are observable on the no general trend was observed for different spacer thick- Stokes and anti-Stokes sides of the spectrum. nesses. The results of the measurements of the spin-wave fre- In dipolar coupled layers anti-parallel alignment of the quency versus applied field are shown for the film for spin-wave amplitudes is favoured and the A mode is the which do = 35 ~ in Fig. 2. The solid lines represent fits to lower frequency mode. It has been shown [5] that ex- Eq. (1) for the two values of C. For the A mode 7, 4xM, change coupling modifies only the frequency of the and C were all used as variables but the S mode required A mode. As the spacer thickness is reduced, the frequency the calculation of C to obtain realistic values for 7 and of the exchange affected A mode increases, and may 4~M~. Results of the fits are shown in Table 1. become higher than the S mode. For all samples the value of 7 lies in the range 2.95- The results of the measurement of the spin-wave 3.08 G H z / k O e which corresponds to a g-value of 2.1-2.2. frequency versus Cr spacer layer thickness at various Table 1 Values of gyromagnetic ratio 7, saturation magnetisation 4xMs and constant C for different Cr thicknesses do. Crdo(A) Mode type ~,(GHz/kOe) 4xM~(kG) C(calc) C(fitted) 5 S 3.01 17.23 0.7576 A 3.04 16.85 5.85 x 10 3 7.06 × 10 2 10 S 3.01 17.33 0.7562 A 2.98 17.52 1.16×10 2 1.02x10 z 15 S 3.02 16.88 0.7548 A 2.92 18.34 1.73 x 10 .2 4.96 x 10 ~" 20 S 2.98 17.64 0.7534 A 2.96 17.75 2.29x10 -' 6.09x10 z 25 S 2.89 18.80 0.7520 A 2.95 18.36 2.85x 10 -2 6.51 x 10 2 30 S 3.02 17.52 0.7506 A 3.02 16.67 3.45 × 10 ~' 8.95 x 1(1 2 35 S 3.08 17.03 0.7492 A 3.08 15.74 3.94x10 2 1.06×10 2 J.A. Cowen et al. / Journal of Magnetism and Magnetic Materials 196-197 (1999) 67-69 69 samples were crystalline showing no texture and it was H ~ k O e therefore expected that the anisotropy would be small. 4 5 The fact that no variation of spin-wave frequency was N -r found at different orientations verified this assumption. 25 + - - - - ' + ~ - ~ _ _ + - - _ - + - - --+- - - ÷ 3 0 In conclusion, the effect of exchange coupling is small a _ - - - - ~ - ~ ~ ~ ~ - ~ 2 . 5 and films of intermediate thicknesses and below l i t - - - - " ' " -no- _ - - * . . . . - * . . . . t - - * 2 . 0 do(Cr) = 10 A in particular are needed to quantify such effects. The dipolar approach is a useful starting point for the analysis of the spin-wave frequencies in these films v - - - ~ - ~ " - - - ~ . w _ _ _ _ _ v - - ~ - ~ --- ~ v ~ - - - ~ l.O and the values of 47tMs deduced are consistent with bulk 0 5 values. 10 20 30 40 The authors would like to acknowledge EPSRC and C r s p a c e r t h i c k n e s s / A the EC HCM Network, contract number: CHRX-CT93- Fig. 3. Spin-wave frequency versus Cr thickness do for applied 0320. fields 0.1-4.5 kOe. References applied fields are shown in Fig. 3 for the A mode and a similar plot was obtained for the S mode. Only small [1] P. Griinberg, R. Schreiber, Y. Pang, M.B. Brodsky, H. changes in the frequencies were observed with the pos- Sowers, Phys. Rev. B 57 (1986) 2442. sible exception of the A mode at do = 10/~ which shows I-2] S.S.P. Parkin, N. More, K.P. Roche, Phys. Rev. Lett. 64 the largest variation. The variation was consistent at all (1990) 2304. fields. [3] H. Niedoba, B. Mirecki, M. Jackson, S. Jordan, S.M. Thomp- For exchange coupled layers one expects larger vari- son, J.S.S. Whiting, P. Djemia, F. Ganot, P. Moch, T.P. ations at small spacer thicknesses, and variations with Hase, I. Pape, B.K. Tanner, Phys. Stat. Sol. A 158 (1996) 259. larger magnitudes than those observed here. For example [4] P. Griinberg, J. Appl. Phys. 51 (1980) 4338. a 2 GHz spin-wave frequency variation was observed by [5] P. Griinberg, J. Appl. Phys. 57 (1985) 3673. BLS in Co/Ru multilayers for spacer layer thicknesses in [6] J. Fassbender, F.C. Nortemann, R.L. Stamps, R.E. Camley, a similar range [6]. On the basis of the current observa- B. Hillebrands, G. Guntherodt, S.S.P. Parkin, J. Magn. tions the neglect of exchange coupling is justified. The Magn. Mater. 121 (1993) 270.