L.P. Akinshina et al.: FMR Line Splitting in Fe/Cr Multilayers 153 phys. stat. sol. (b) 214, 153 (1999) Subject classification: 75.70.Cn; 76.50.+g; S1; S1.1 FMR Line Splitting in Fe/Cr Multilayers L.P. Akinshina, A.V. Kobelev1†, A.A. Koshta, M.A. Milyaev, V.I. Minin, and A.A. Romanyukha Institute for Metal Physics, Russian Academy of Sciences, Urals Division, 620219 Yekaterinburg, Russia (Received January 8, 1999; in revised form March 9, 1999) Measurements of the magnetization curves and ferromagnetic resonance (FMR) were made on a series of samples of multilayers [Fe(13  A)/Cr(tCr)]12, with 7  A < tCr < 40  A, deposited by the meth- od of molecular-beam epitaxy on a sapphire substrate with the Fe buffer layer of 40  A thickness. The effective demagnetizing field 4pMs ±± H0u was estimated for all samples from the angular de- pendence of an FMR resonant field and linewidth for the uniform mode at the transverse excita- tion, where Ms is the saturation magnetization of the Fe layer, H0u is the uniaxial anisotropy field. An additional FMR line was observed for samples with small spacer thickness (tCr < 16  A). Its intensity was equal to that of a main line under the condition of tCr  tFe  12  A, decreasing down to zero both at reduction, and at the increase of tCr. The FMR lineshape in a field parallel to the surface was simulated by a superposition of two curves, possessing in view of the magnetization curve approximately Lorentzian shape with different effective field values H0u. The possible reason of the features observed can be the formation of regions with different effective anisotropy field values in a sample plane during the deposition. For all samples investigated at longitudinal excita- tion, an FMR signal which corresponds to an optical mode was not observed. 1. Introduction Multilayer metal structures are intensively investigated in connection with the phenom- enon of giant magnetoconductivity. This causes the interest in the magnetic properties and structure of multilayers. In superlattices consisting of magnetic (Fe) and non-mag- netic (Cr) layers of metals, in the absence of an external field, ferromagnetic, antiferro- magnetic or non-collinear magnetic ordering of magnetic layers has been found [1, 2]. The magnetic ordering depends on the thickness of the non-magnetic spacer, because, as had been shown by various experiments, the exchange parameter oscillates as a func- tion of spatial coordinate in these systems. On the other hand, the investigations of a thin structure of the multilayers revealed their columnar crystal morphology, that is connected coherently with the structure of the substrate. This structure changes with the increase of Cr layer thickness [3]. The interlayer boundary also has a complex structure, due to the formation of various mag- netic phases [4, 5]. The type of magnetic order in these systems can be determined by static magnetic measurements of the magnetization curve in a field parallel to the surface, and in some cases it gives the quantitative information on interlayer exchange parameters. Ferro- magnetic resonance (FMR) is more sensitive to the details of a magnetic structure. 1† Corresponding author: e-mail: Kobelev@ifm.ural.ru 154 L.P. Akinshina et al. However, this method does not determine the magnetic parameters directly. Moreover, the interpretation of the shapes of the FMR spectra is a separate task which requires the respective model. The research on the same multilayers by other methods is also useful. For the study of antiferromagnetic and non-collinear magnetic structure in multi- layers the excitation of an optical mode at longitudinal pumping [7] has special signifi- cance. The observation of an optical mode may confirm the existence of two magnetic sublattices and may help to define the parameters of exchange coupling. Some particu- lar peculiarities of an optical mode excitation in the model of biquadratic exchange were predicted in [8], and this should be verified experimentally. The purpose of the present work is to consider the mentioned problems by studying a series of Fe/Cr multilayers with the variable thickness of a Cr layer. We have worked out an approach described further to obtain information about the magnetic structure of the multilayers from the FMR and magnetization curve measurements. The results of structural research [3] and MoÈssbauer effect [4] for the same samples were invoked to interpret the FMR data. 2. Samples The method of molecular-beam epitaxy was used to obtain the Fe/Cr multilayers. The single crystal sapphire Al2O3 substrate with orientation [2110] was used. The substrate, however, does not play the main role in the process of epitaxial growth of the multi- layer. The buffer layer of Fe with a thickness of about 40  A was put on the substrate. Such a thickness was chosen to provide the transition from the hexagonal crystal struc- ture of the substrate surface to the cubic structure of the multilayer Fe/Cr film, which has orientation f100g. We have used the Fe buffer layer for the reason that it grows better than, for instance, the Cr one, although the latter grows smoother and does not add to the magnetic parameters of the sample. Later we have realized that the Cr buffers have some advantages, and the results of the studies on these samples, being not completed as yet, have to be published elsewhere. The multilayer Fe/Cr structure was deposited on the buffer layer, with the number of layers hold constant (both 12 layers of Fe and Cr). The thickness of the Fe layer is kept constant (13  A), whereas the thickness of Cr layers changes from 7.7 up to 40  A. These values of the spacer thickness were chosen to ensure magnetic ordering over the Ta b l e 1 List of the samples investigated sample buffer layer tFe tCr ( A) ( A) ( A) 1 42 14.6 7.7 2 40 13.0 9.0 3 42 12.3 11.1 4 36 11.2 14.5 5 40 12.2 18.8 6 36 10.8 22.0 7 42 12.9 29.6 8 40 11.1 35.1 FMR Line Splitting in Fe/Cr Multilayers 155 whole range starting with ferromagnetic order at small tCr < 7  A, through non-collinear, and to antiferromagnetic order at tCr > 30  A. At the last stage, the multilayer structure was covered by an additional layer of Cr for stabilization. The nominal values of layer thickness were estimated from the time and speed of deposition. The optimal deposi- tion parameters were defined from the preliminary deposition of thick layers of Cr and Fe. The values of thickness of the layers tCr and tFe were determined by X-ray diffrac- tion and micro-structural X-ray analyses of the samples (Table 1). 3. Experimental The FMR spectra were recorded at room temperature with an ERS-231 spectrometer (produced in the former GDR) operating in the X-band. For the computer treatment of spectral files this spectrometer was connected with an IBM-PC. The experimental param- eters of the spectra recording were the following: 100 kHz modulation frequency, 10±±4 T modulation amplitude, 5 T field sweep. The magnetic system allowed to vary the magnetic field strength in the range from 0.01 up to 1.0 T. The cylindrical microwave cavity TE102 has been used, which allows to carry out measurements of the FMR signal at the transverse excitation (direction of the static magnetic field being perpendicular to the magnetic vector of the microwave field). The angular dependences of FMR signal parameters were measured by a rotation of the electromagnet relative to a fixed microwave cavity (Fig. 1a). The rotation of a magnetic field over an angle q from 0 to 360, with respect to the sample plane, was executed with an accuracy of 0.1. The rectangular cavity TE102 has been used to detect an optical mode, in which the type of FMR excitation varies from longitudinal to transverse by the rotation of the magnet, at fixed position of the sample in the cavity (Fig. 1b). The magnetization curves and hysteresis loops were measured for all investigated samples by a standard Faraday method on a vibrating sample magnetometer in a range of field 0 kOe < H < 18 kOe. The samples of size 5 5 mm2 were oriented by their surface parallel to the magnetic field direction. The normalized magnetization curves Fig. 1. Microwave cavities used for the FMR investigations at a) transverse and b) longtitudinal excitation 156 L.P. Akinshina et al. Fig. 2. Relative magnetization curves m(H) for the sample with spacer thickness tCr = 11.1  A (^) and 14.5  A (&). Solid lines are approximations (eq. (5) with m0 = 0.65, Hb = 5 kOe and m0 = 0.4, Hb = 1.2 kOe, respectively) m(H) were obtained (Fig. 2) using high fields, approaching approximately saturation magnetization. 4. Assumptions According to our experimental conditions, we assume that only magnetically uniform modes are excited, and that the sample can be treated as an infinitely-layered one. In general, it is sufficient to consider an infinite antiferromagnet with two sublattices com- posed of Fe layers with different magnetization directions [8]. The Cr layer is treated as a non-magnetic spacer. Non-collinear ordering can be described by a combination of bilinear and biquadratic interlayer exchange interaction. The acoustic mode in this mod- el, contrary to an optical one, does practically not depend on the interlayer exchange. Therefore, we assume further that the processing of the angular dependence of the FMR field and the linewidth can be done in the usual way [16, 18]. A possible error may be caused in this case by the factor m(H), so that estimated values of the effective anisotropy field received from angular dependences are rather uncertain. 5. Modeling The calculations of the resonant field and linewidth as functions of the angle q were made in the model, taking into account the difference in the directions of magnetiza- tion and magnetic field vectors. In the samples investigated the values of demagnetizing fields exceed the fields of anisotropy, so it is possible to speak in general about an ``easy planeº type of anisotropy. In the absence of an external static field the magneti- zation vector lies in the sample plane. At an increase of the field, directed normally to the surface, magnetization leaves the plane. At the turn of the external field off a sam- ple plane up to the normal the directions of magnetization and external field vectors do not coincide. This effect results in a slower increase of the resonant field Hr when q FMR Line Splitting in Fe/Cr Multilayers 157 increases from zero (H0 is in the film plane) up to 90. The size of this backlog is proportional to an effective anisotropy constant and, consequently, by fitting of the angular dependence Hr(q) to experimental data it is possible to evaluate it. From the standard equation describing uniform FMR [16] we have (w/g)2 = [Hr(q) cos (q ±± qm) ±± Hu sin2 q] [Hr(q) cos (q ±± qm) + Hu cos 2q] , (1) where q is the angle of the magnetic field vector, qm is the angle of the magnetization vector relative to a surface normal, Hu = 4pMs ±± H0u where H0u is the effective field of uniaxial anisotropy, Ms the saturation magnetization of an iron layer and g the gyro- magnetic ratio. The equation relating q and qm is [17] 2Hr(q) sin (qm ±± q) = ±±Hu sin 2qm . (2) The parameters g and Hu were estimated by fitting of experimental data with theoreti- cal dependences following from (1) and (2). Good agreement was achieved generally. The values of g were found close to the free electron value. The angular dependence of FMR linewidth dH(q) was described by the expression [18] dH(q) = Hr(w(1 + a)) ±± Hr(w(1 ±± a)) , (3) where Hr(w) denotes the FMR resonance field as a function of frequency, a is the Gilbert relaxation parameter, ranking as the fitting parameter and related with the FMR linewidth by the expression dH(0) = 2aw/g . The modeling of the FMR lineshape was carried out for the case of a static field, lying in the sample plane. It was assumed, that two values of anisotropy fields Hu1 and Hu2 are present. Thus, a signal is excited with a lineshape, characteristic of a multilayer (transverse acoustic mode), which is a superposition of signals from two subsystems with the weight factors k1 and k2, P(H) = k1P(H, Hu1) + k2P(H, Hu2) , (4) P…H; Hu† ˆ …@=@H† Im ca…H; Hu† ; ‰H H Im c um…H†Š2 ‡ m2…H† …w=g†2 …1 ‡ a2† a…H; Hu† ˆ ; f‰H…H Hum…H†Š …w=g†2 …1 ‡ a2†g2 ‡ a2…w=g†2A2…H; Hu† A(H, Hu) = H[m(H) + 1/m(H)] ±±Hu . Expression (4) differs from the expression valid in the ordinary ferromagnet by the function m(H), describing the relative magnetization of a multilayer structure, formed by alternating layers of magnetic and non-magnetic metals. Expression (4) is adequate for the joint movement of the total moment of sublattices. This formula is sufficient by general and it is suitable for the description of a similar mode in a magnet with arbi- trary magnetic structure, characterized by the magnetization m(H). As a convenient trial function, approximating the experimentally received magnetization, the function depen- 158 L.P. Akinshina et al. Fig. 3. Evolution of the FMR spectra at the transverse excitation in the static field paral- lel to the film surface for a series of samples with varying spacer thickness tCr dent on the two following parameters m0 and Hb has been used: m m…H† ˆ 0 ‡ H=Hb : …5† 1 ‡ H=Hb The parameter Hb can be treated as the saturation field, and m0 is the zero- field relative magnetization. 6. Results None of the investigated samples has an FMR signal at parallel excitation. However, at transition to mixed excita- tion by the turn of the magnetic field relative to the sample, when the trans- verse component of the high-frequency field being present, the resonance sig- nal was observed. At completely transverse excitation all samples have an intense and well resolved single, or a splitted FMR line shape. The evolution of the FMR spectrum for the samples with increasing spacer thickness tCr is presented in Fig. 3. At small spacer Fig. 4. Angular dependence of the resonance field Hr(q) for the sample with tCr = 11.1  A (right peak). The curve is obtained according to (1) and (2) with the value of the demagnetizing field Hu = 13.1 kOe. The upper part of the curve is omitted FMR Line Splitting in Fe/Cr Multilayers 159 Fig. 5. Angular dependence of the linewidth dH(q) for the sample with tCr = 11.1  A (right peak). The curve is obtained according to (3) with the value of the demagnetizing field Hu = 13.6 kOe and dH0 = 390 Oe thickness (tCr < tFe) a narrow single line was registered. The additional FMR line arises at the left wing of the main one. The intensity of the additional line grows, becomes equal to the intensity of the main line at tCr  tFe  12  A, and then decreases again. For the samples with tCr > 16  A the FMR line becomes a broad single line with asymmetric shape. The results of the determination of the effective demagnetizing field (uniaxial anisotropy Hu) from the angular dependence of Hr (Fig. 4) and dH (Fig. 5) of the main line are presented in Table 2. The tendency of growth of Hu (in the assumption of constant Ms) was demonstrated for increasing tCr up to tCr = 16  A (Fig. 6), when the stabilization of the effective demagnetizing field (Hu) occurred. In the same region (Fig. 7) the linewidth remarkably grows, remaining constant at large tCr. The determination of the effective demagnetizing field was done once again indepen- dently by the modeling of the lineshape in a field parallel to the multilayer plane for those samples, where a splitted FMR signal has been observed. Thus, the fitting param- Ta b l e 2 Results of modeling modeling of the angular dependence of Hr and dH modeling of the FMR line shape sample Hu(Hr) Hu(dH) dH Hu1 Hu2 k1/k2 m0 Hb dH (kOe) (kOe) (Oe) (kOe) (kOe) (kOe) (Oe) 1 15.4 15.8 280 28.0 15.0 0.04 0.8 0.19 202 2 11.2 11.2 240 26.0 13.0 0.04 0.75 4.5 182 3 13.1 13.6 390 19.5 10.7 1 0.65 5.0 270 4 9.0 9.0 450 20.5 11.5 0.4 0.4 1.2 404 5 15.0 13.0 650 16.2 0.55 0.4 471 6 14.0 14.0 650 17.5 0.75 0.8 471 7 13.0 13.0 550 16.5 0.1 0.13 471 8 12.0 12.0 700 16.5 0.6 0.6 679 160 L.P. Akinshina et al. Fig. 6. Dependence of the effective demagnetizing field on tCr for the series of the samples. * obtained by processing of angular dependence of Hr and dH data, & obtained by modeling of the FMR lineshape in the field parallel to the surface. The dotted lines may guide the eyes eters m0 and Hb for these samples are essentially different (see Table 2). The curve representing the formula (4) in view of the chosen approximation for m(H), for four samples with tCr = 7.7 to 14.5  A agrees rather well with the experimental data (see, for example, Fig. 8). The values of the anisotropy fields Hu1 and Hu2 (Table 2) differ for Fig. 7. Dependence of the FMR line width on tCr for the series of samples. & obtained by proces- sing of angular dependence of Hr and dH data, * obtained by modeling of the FMR lineshape in the field parallel to the surface. The dotted line may guide the eyes FMR Line Splitting in Fe/Cr Multilayers 161 Fig. 8. FMR spectra in the field parallel to the surface for the sample with tCr = 14.5  A (^). The curve is obtained by modeling according to (4) with the parameter values dH0 = 404 Oe, Hu1 = 20.5 kOe and Hu2 = 11.5 kOe each sample by about a factor of two. The value of Hu2 approaches the value of Hu, obtained by the simulation of the angular dependences of Hr and dH. The dependence of the intensity of the peaks ratio k1/k2 on the spacer thickness tCr is depicted in Fig. 9. For the sample with tCr = 11.1  A the intensities of both peaks become equal. 7. Discussion One of the results received is the silence of an optical mode in the studied samples at the experimental conditions used. Different reasons for this should be considered. Esti- mates of the parameters of interlayer exchange interaction extracted from the values of Fig. 9. Relative intensity of the low-field and high-field peaks of the FMR signal for the series of samples with different tCr 162 L.P. Akinshina et al. m0 and Hs of the magnetization curves are rough because of the contribution of the relatively thick buffer layer (1/3 of the whole volume of the iron). Nevertheless, the calculations based on the theory of biquadratic exchange [8], in the assumption of an ideal structure of Fe/Cr layers, have shown that the values of characteristic resonant fields received for an optical mode are different for the investigated samples. These fields (30 kOe) for a part of the samples are inaccessible in our experimental condi- tions, but for others optical mode should be observed at longitudinal excitation. The absence of an FMR signal at longitudinal excitation for all samples can also mean that the uniform model used for the estimation of the resonance fields [8] is not adequate. Instead, a more complicated, non-uniform magnetic structure of a multilayer may exist. According to the results of MoÈssbauer effect investigations of the same sam- ples [4], mass transfer of Fe and Cr atoms on the boundaries between the layers par- tially washes out the interface. The latter process can lead to the formation of various solid solutions with different magnetic properties [4]. Therefore, the excitation of the uniform FMR mode corresponding to a simple two-sublattice magnetic structure can hardly be expected. Judging from the magnetization curves of the investigated samples at the spacer thickness 6 to 7  A, the saturation fields are not high (some hundreds of Oe), and the shape of the curve is close to the observed one on a thin single layer of iron [9 to 13]. For comparison, the single iron layers of thicknesses 30, 60 and 300  A were investi- gated. For all of them a sharp saturation effect in the fields of 10 to 1000 Oe was observed. Processing of the FMR spectra having single narrow lines gave the values of 4pMs ±± H0u close to the value for bulk iron. Thus, the samples with small spacer thick- ness are magnetically weakly coupled and, in their magnetic properties, they are similar to thin single Fe layers. For the samples with thicker spacer tCr (starting from the sample 2), there is a sec- tion of the magnetization curve with almost linear change of magnetization. For these samples the m0 values (see Table 2) are still close to unity. At the thickness of 10 to 12  A (samples 3, 4) the saturation field Hs increased up to 12 kOe. At further increase of the spacer thickness up to 20  A the reduction of Hs, together with a more sharp magnetization curve, is observed again. Then Hs grows a little at tCr  40  A (sample 8). Hence, in the interval of spacer thickness 12 to 40  A the change of the magnetic struc- ture, connected with the growth of the parameters of interlayer exchange occurs. Thus, the tendency to the formation of antiferromagnetic or non-collinear magnetic order may be assumed. The influence of the buffer layer on the FMR signal may be evaluated from the comparison with the results of FMR measurements on single Fe layers of similar thick- nesses (30 and 60  A). It appears that the buffer layer contributes a narrow single line to the main FMR line, with small effect on its position and intensity. The role of the mag- netic interaction of the Fe buffer layer with the principal body of the Fe/Cr multilayer is minimal due to the short range of the interaction involving the nearest Fe layer sepa- rated by a Cr spacer. The above conclusion is also supported by the evolution of the FMR spectra found (Fig. 3) at increasing spacer thickness. The additional signal re- vealed for some of the samples studied is not connected with the buffer layer because all samples have the same buffer. Generally, the additional line found in the FMR spectrum at the transverse excitation (Fig. 3) can be attributed to the surface mode [6] or a spin wave harmonic [14]. How- FMR Line Splitting in Fe/Cr Multilayers 163 ever, such interpretation contradicts to the observed spectra evolution with the sample rotation in a magnetic field. The more realistic reason for the observation of the above mentioned line is the existence of an additional phase, having different magnetic aniso- tropy. A similar phase spreading through the whole depth of the multilayer has been already observed by electron microscope [3]. Different values of the anisotropy field can be caused, for example, by magnetostriction effects. The latter assumption is in agreement with the results of FMR measurements on single iron layers and Fe/Cr mul- tilayers [15]. The characteristic FMR lineshape with a bent part in the center was ob- served for the sample (Fe/Cr)30. The modeling of this lineshape gave two values of an effective field, i.e. 17.6 and 28 kOe, respectively. The relative volume of participating phases (main and additional) may be related to the relative intensity of the peaks ob- served (Fig. 9). 8. Conclusions The performed investigations have shown the possibilities of FMR to study the mag- netic structure of the multilayers in combination with the magnetization and crystalline structure data. The approach, developed by computer simulation of the angular depend- ences of the resonance field and linewidth together with FMR lineshape modelling, allows to get reliable values of magnetic anisotropy. The most interesting result ob- tained is the evolution of the FMR spectrum in dependence on the spacer thickness. The splitting of the FMR spectrum observed in Fe/Cr multilayers can be explained by inhomogeneities of its structure in the form of their columnar texture [3]. This leads to the existence of two phases with different values of anisotropy fields, giving two contributions to the total FMR signal. Evaluations of the effective demagnetizing fields of these phases show that their values differ by a factor of two. The value of one of them, attributed to a low-field peak, coincides with that of bulk iron. This means, in the assumption of constant Ms, that in the latter phase the anisotropy field is close to zero. The FMR measurements have specified the range of Cr spacer thickness, smaller or equal to the thickness of Fe layer (<15  A), where magnetic inhomogeneities of a multi- layer are essential. Such a feature has not been detected for larger spacer thickness. This conclusion is supported by the observation of the complex structure of the inter- faces, stipulated by alloying in the same samples at small spacer thickness [4]. A possi- ble explanation of the FMR spectra evolution in dependence of the spacer thickness may be associated with an effect of percolation between the iron layers. Thus, one could argue that at small spacer thickness values (<15  A) there are no permanent inter- layer boundaries, whereas they exist at thicker spacers. 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