Journal of Magnetism and Magnetic Materials 226}230 (2001) 1779}1781 Temperature dependence of interlayer coupling in Fe/Cr superlattices * FMR studies A.B. Drovosekov , D.I. Kholin , N.M. Kreines *, O.V. Zhotikova , S.O. Demokritov P.L. Kapitsa Institute for Physical Problems, Russian Academy of Sciences, Kosygina Str. 2, 117334 Moscow, GSP-1, Russia Fachbereich Physik, Universitaet Kaiserslautern, 67663Kaiserslautern, Germany Abstract The ferromagnetic resonance in a [Fe(30 As)/Cr(10 As)] superlattice with a relatively large value of biquadratic coupling constant was studied in a temperature range from 400 K down to liquid-nitrogen temperature. The monocrys- talline sample was grown by means of the MBE technique on a MgO [1 0 0] substrate. Measurements were performed in magnetic "elds up to 10 kOe at frequencies ranging from 17 to 37 GHz under both transversal and longitudinal FMR excitations. Resonance spectra with several modes including the acoustic and the optical branches were observed in the whole temperature range. Temperature dependence of both bilinear and biquadratic coupling constants was derived from the experimental spectra. 2001 Elsevier Science B.V. All rights reserved. Keywords: Multilayers*metallic; Exchange coupling*biquadratic; Ferromagnetic resonance Among all magnetic multilayers the Fe/Cr/Fe system lattice itself was deposited at 1503C and, according to the is one of the most extensively investigated [1]. The bi- results of low-energy electron di!raction, demonstrated quadratic interlayer coupling, "rst observed in Refs. a well-de"ned monocrystalline structure with [1 0 0] axis [2,3], also increased the common interest to the problem perpendicular to the sample plane. of magnetic interaction of two ferromagnetic layers FMR measurements were performed using a home- through a chromium spacer. Nevertheless, the origin of made spectrometer at frequencies ranging from 17 to the biquadratic and even the bilinear coupling in 37 GHz in magnetic "elds up to 10 kOe applied in the Fe/Cr/Fe structures is still not clear. The temperature sample plane. Due to a radial direction of microwave dependence of interlayer interaction is investigated magnetic "eld on the bottom of a cylindrical resonator, mostly for relatively large ('30 As) spacer thickness, both the transversal and the longitudinal FMR pumping where the coupling mechanism can be di!erent from that was imposed on the sample during our measurements. through a thin Cr layer and is known to be due to the The experimental setup allowed us to vary the sample spin density wave in chromium [1,4]. temperature from 80 to 400 K. We observed multiple The [Fe(30 As)/Cr(10 As)] superlattice used in our ex- absorption lines including the optical and the acoustic periments was prepared by means of the MBE technique resonance branches at all investigated temperatures (for on a MgO [1 0 0] substrate. A 10 As iron seed layer and detailed discussion of these modes see Refs. [5,6]). Two 1000 As silver bu!er layer were deposited at 1303C onto experimental spectra obtained at room and at liquid- the substrate before growing the superlattice. The super- nitrogen temperature are shown in Fig. 1. The observed spectra, especially the optical branch, show a strong temperature dependence. At nitrogen temperature the resonance "elds for two FMR branches in the strong * Corresponding author. Tel.: #7-095-9382029; fax: #7- magnetic "eld part of the plot (shown by dark squares 095-9382030. and dark triangles) increased by almost 2 kOe with re- E-mail address: kreines@kapitza.ras.ru (N.M. Kreines). spect to their room temperature position. To derive the 0304-8853/01/$- see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 1 0 1 3 - 1 1780 A.B. Drovosekov et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1779}1781 interlayer coupling parameters from the measured spectra, we performed computer simulations of the su- perlattice resonance spectrum on the basis of the biquad- ratic coupling model, taking into account the fourfold in-plane magnetic anisotropy of iron and the real number of magnetic layers in the system. The following energy expression was used to describe the magnetic properties of the multilayer: L J L\ E"!d (H ) M H)! (MH )MH> ) H M 1H J L\ K L ! (M (M M H ) MH> ) #d H ) z) (1) 1 H 2 H H L !d [(M 4M H ) x) #(MH ) y) #(MH ) z) ], 1 H where J and J are the bilinear and biquadratic coup- ling constants, MH is the magnetization vector of the jth iron layer, d is the thickness of each iron layer, K is the e!ective surface anisotropy coe$cient, which includes the demagnetization "eld and the surface anisotropy, H is the e!ective fourfold anisotropy "eld with easy axes x, y and z, where the z-axis is normal to the sample plane, and n is the number of ferromagnetic layers in the struc- Fig. 1. FMR spectra for a [Fe(30 As)/Cr(10 As)] superlattice at ture. The detailed description of these calculations can be two di!erent temperatures with magnetic "eld applied along the found in Ref. [6]. hard magnetization axis of iron in the "lm plane. Points * ex- The calculated spectra are shown in Fig. 1 by solid perimental data, solid curves * results of numerical simulation lines. The J (see in text). Error bars represent the observed line width when it and J values were chosen to provide the best "t to the acoustic (dark circles) and optical (dark exceeds the point size. squares) branches of the experimental spectra. M1 value was taken to be equal to that in bulk iron. The fourfold anisotropy "eld H was chosen to describe the di!erence in experimental spectra with magnetic "eld applied along the hard and easy anisotropy axes in the sample plane. It was proved to be equal to 500 Oe, which coincided with the bulk value, and did not exhibit any change in temper- ature. The temperature dependencies of J , J and satu- ration "eld H1 are shown in Fig. 2. The con"dence bands presented in the "gure correspond to parameter values that give a one linewidth deviation of calculated curves from the experimental data. Taking into account this uncertainty in parameter de"nition, we can a$rm that both the bilinear J and the biquadratic J coupling constants increase signi"cantly with cooling the sample Fig. 2. Temperature dependence of saturation "eld H down to 80 K. The observed J 1 and , J and H1 temperature coupling constants J dependencies can be treated as linear within our pre- and J . The lines are guides to the eye. cision. The presented results for J are in quantitative agreement with the data from Ref. [7], where temper- larger chromium thickness (80 and 102 As). It shows that ature dependencies of J and J were derived from FRM di!erent coupling mechanisms can be responsible for measurements for a Fe(40 As)/Cr(11 As)/Fe(40 As) sand- interlayer exchange in the cases of thick and thin chro- wich. Our J values are about 3 times larger, than that mium spacers. reported in Ref. [7], which can be easily ascribed to the di!erence in the interfaces morphology. It is worth not- This work was partially supported by the Russian ing that an absolutely di!erent H1 on temperature de- Foundation for Basic Research (Grant No. 98-02-16797). pendence was reported in Ref. [8] for a signi"cantly The authors wish to thank Prof. B. Hillibrands for the A.B. Drovosekov et al. / Journal of Magnetism and Magnetic Materials 226}230 (2001) 1779}1781 1781 possibility to use the equipment of his laboratory for [4] P. BoKdeker, A. Schreyer, H. Zabel, Phys. Rev. B 59 (1999) preparing the samples. 9408. [5] A.B. Drovosekov, D.I. Kholin, N.M. Kreines, V.F. Mesh- cheriakov, M.A. Miliayev, L.N. Romashev, V.V. Ustinov, JETP Lett. 67 (1998) 727. References [6] A.B. Drovosekov, O.V. Zhotikova, N.M. Kreines, D.I. Kholin, V.F. Meshcheryakov, M.A. Milyaev, L.N. [1] D.T. Pierce, J. Unguris, R.J. Celotta, M.D. Stiles, J. Magn. Romashev, V.V. Ustinov, JETP 89 (1999) 986. Magn. Mater. 200 (1999) 290. [7] A. Azevedo, C. Chesman, M. Lucena, F.M. de Aguiar, S.M. [2] M. Ruhrig, R. Schafer, A. Hubert, R. Mosler, J.A. Wolf, S.O. Rezende, S.S.P. Parkin, J. Magn. Magn. Mater. 177}181 Demokritov, P. Grunberg, Phys. Stat. Sol. A 125 (1991) 635. (1998) 1177. [3] B. Heinrich, J.F. Cochran, M. Kovalevski, J. Kirschner, [8] J. Dekoster, J. Meersschaut, S. Hogg, S. Mangin, E. Z. Celinski, A.S. Arrott, K. Myrtle, Phys. Rev. B 44 (1991) NordstroKm, A. Vantomme, G. Langouche, J. Magn. Magn. 9348. Mater. 198}199 (1999) 303.