ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e973–e974
Ferromagnetic resonance studies in Fe/Ti multilayers H. Lassria, H. Ouahmaneb, A. Berradac,*, A. Kaabouchia, A. Diniad, R. Krishnane b
a # LPMM, Facult!e des Sciences, Universit!e Hassan II Ain Chock, B.P. 5366 Maarif, Casablanca, Morocco Universit!e moulay Isma.ıl, Facult!e des Sciences et Technique d’Errachidia, D!epartement de Physique, Errachidia, Morocco c Laboratoire de Physique des Mat!eriaux, Facult!e des Sciences, avenue Ibn Batouta, B.P. 1014, Rabat 10000, Morocco d IPCMS-GEMM (7504, CNRS) ULP-ECPM, 23 rue Loess, Strasbourg 67037, France e Laboratoire de Magn!etisme et d’Optique, URA 1531, 45 Avenue des Etats Unis, Versailles, Cedex 78035, France
Abstract The magnetic properties of sputtered Fe/Ti multilayers are presented. The magnetization results reveal an interdiffusion at the Fe/Ti interfaces. The FMR spectra were obtained as a function of orientation of the applied magnetic ﬁeld from in-plane to out-of-plane and were ﬁtted theoretically to determine the magnetic anisotropy. We also observed one or two weak peaks at the high-ﬁeld-side of the uniform resonance mode, which we attributed to a surface ( and the effective mode. Spin-waves resonance modes were observed in the Fe/Ti multilayers (tFe ¼ 40 and 60 AÞ exchange constants were determined. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Et; 75.70.Cn; 76.50.þg Keywords: Fe/Ti multilayer; Ferromagnetic resonance; Anisotropy; Spin-wave
The interlayer coupling between ferromagnetic layers in multilayered and layered ﬁlms containing transition metals has been shown to have an important inﬂuence on the magnetic and the electronic properties in these systems [1,2]. Ferromagnetic resonance (FMR) and spin wave resonance (SWR) have been used to study the effective parameters of multilayers , such as the effective exchange constant (Aeff ), the effective magnetization (4pMeff ), etc. In this work, we used the FMR method to determine the interface anisotropy and the effective exchange constant. The multilayers have been prepared by DC triode sputtering. The chamber was ﬁrst evacuated to a pressure of 107 Torr: Argon of 5 N purity was used as the sputter gas and its pressure was kept constant at ( 7 104 Torr: The rates of deposition were 17 A=min ( for Ti and 20 A=min for Fe. The thickness of the Fe ( and that of Ti layer was varied in the range 20–60 A ( The number (N) of layer was in the range 10–20 A: bilayers were in the range 10–30. *Corresponding author. Tel./fax: +212-37671118. E-mail address: [email protected]
Low angle X-ray diffraction studies were made to check the periodic structure. The saturation magnetization (MS ) was measured using a vibrating sample magnetometer (VSM). The FMR spectra, at 9:8 GHz and room temperature, are obtained as a function of the orientation of the applied magnetic ﬁeld from in-plane to out-of-plane. Our results would indicate that the interface is diffuse due to the interdiffusion and the structural imperfection effects. In perpendicular geometry, the resonance spectra are composed of more than one mode and the more-intense central peak correspond to the principal mode, the lowerﬁeld one to a volume spin wave and the higher-ﬁeld one may be identiﬁed as a surface mode, as described theoretically by Puszkarski . A typical FMR spectrum in perpendicular conﬁguration for ðFe40 A( =Ti10 A( Þ30 multilayer is shown in Fig. 1. The angular dependence of the resonance ﬁeld (Fig. 2) ﬁtted well to the following expressions of uniform mode in a single-layer ﬁlm: H sinðy yH Þ ¼ 4pMeff siny cosy
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.1155
ARTICLE IN PRESS e974
H. Lassri et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e973–e974
16 (Fe60 Å / Ti20 Å)10 15 (Fe40 Å / Ti10 Å)30
Fig. 1. FMR spectrum for ðFe40 A( =Ti10 A( Þ30 multilayer for perpendicular geometry at 300 K:
Fig. 3. Resonance ﬁeld Hr in perpendicular orientation versus n2 :
If the multilayers were assumed to be coupled by interlayer exchange interaction into a single magnetic system and the spin-waves were sustained by the whole multilayer, the resonance ﬁeld of multiple peaks could be ﬁtted to the resonance conditions similar to the single-layer ﬁlms as follows: o=g ¼ Hr> 4pMeff þ 2Aeff kn2 =MS ;
Fig. 2. Angular dependence of uniform resonance ﬁeld for ðFe40 A( =Ti10 A( Þ30 multilayer.
and ðo=gÞ2 ¼ ½H cosðy yH Þ 4pMeff cosð2yÞ ½H cosðy yH Þ 4pMeff cos2 y;
where o is the microwave frequency, g the gyromagnetic ratio, yH and y are the angles of H and MS with respect to the ﬁlm normal. By ﬁtting the data from the angle-dependent FMR measurements, the information about the perpendicular anisotropy can be extracted. Then the interface anisotropy constant KS is deduced to be KS ¼ 0:9 erg=cm2 : Here KS is a positive value, which means that the interface anisotropy conﬁnes the magnetization along the ﬁlm normal. For the surface mode (k ¼ ikS ) observed in the Fe ( the ﬁeld splitting with respect to layer (with tFe ¼ 40 A), the uniform mode is described by Hsurf H0 ¼ 2AkS2 =MS :
If the presence of such a mode were to be interpreted solely in terms of a surface anisotropy, taking [5,6] kS E KS =A; one would deduce at 300 K AKS ¼ 0:9 erg=cm2 for the Fe/Ti interface, if we take for our Fe layer MS ¼ 1700 emu=cm3 and A ¼ 2 106 erg=cm; in agreement with that obtained from the FMR study.
where kn is the spin-wave number and kn ¼ np=L: n is the volume spin-wave mode number, Hr the corresponding ﬁeld, and L the total thickness of the ﬁlm. Spinwaves resonance modes were observed in some Fe/Ti multilayers and the relation of resonant ﬁeld Hr with the mode number n obeys the so-called n2 law (Fig. 3). Both odd- and even-numbered modes are observed and this fact indicates that the pinning in this ﬁlm is asymmetrical  at the two surfaces of the Fe layer. This is consistent with the presence of the surface mode. From the slope of the straight line, we obtained the effective exchange constants Aeff ¼ 0:97 106 and ( respectively. 0:48 106 erg=cm for tFe ¼ 40 and 60 A; These values are less than that of the Fe single-layer thin ﬁlm made under the same conditions as that of the Fe layers in multilayers, A ¼ 2 106 erg=cm; by more than one order of magnitude, which shows the weak interlayer coupling between Fe layers in Fe/Ti multilayers.
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