ARTICLE IN PRESS Physica B 357 (2005) 22­26 www.elsevier.com/locate/physb X-ray resonant magnetic scattering on noncollinearly coupled Fe/Cr superlattices A. Nefedov , J. Grabis, H. Zabel Institut fu¨r Experimentalphysik/Festko¨rperphysik, Ruhr-Universita¨t Bochum, Universittstr. 150, 44780 Bochum, Germany Abstract We have studied in detail the structural and magnetic properties of an antiferromagnetically (AF) coupled Cr(25.6 A )/Fe(15.2 A ) superlattice by soft X-ray resonant magnetic scattering. Using the resonance condition close to the Fe L3 edge, magnetic peaks are observed at the half-orders Bragg peaks positions. The magnetic hysteresis loops measured at the even-order and at the half-order Bragg peaks demonstrate the biquadratic type of AF coupling for Fe/ Cr multilayer. Experimental data were simulated using the matrix formalizm in order to go away from macroscopic magnetic properties of such superlattices and to understand their layer-by-layer magnetic structure. r 2004 Elsevier B.V. All rights reserved. PACS: 75.25.+z; 75.70.Cn; 61.10.Kw Keywords: Soft X-ray resonant magnetic scattering; Noncollinearly coupled superlattice Magnetic heterostructures consisting of two or Moreover, Ru¨hring et al. reported that in the more ferromagnetic (F) layers separated by non- transition regions of the coupling constants J magnetic or antiferromagnetic (AF) spacer layers between collinear 180ðAFÞ and 0ðFÞ spin align- have received much attention due to their im- ment, a noncolinear 90 coupled magnetization portance in fundamental science and technology. profile exists [2]. It has been shown that, depending on the thickness It is well known that X-ray resonant magnetic of the spacer layer, ferromagnetic layers may be scattering (XRMS) provides direct information on coupled ferromagnetically or antiferromagneti- the magnetic structure of materials. During the cally via the interlayer exchange interaction [1]. last decade, a growing number of experiments have been carried out and it has been shown that in case of antiferromagnetically ordered multi- Corresponding author. Tel.: +0049 234 3223 620; fax: layers, the periodicity of the magnetization ampli- +00 4923 432 14173. E-mail address: alexei.nefedov@ruhr-uni-bochum.de tude leads to a magnetic contribution at the half- (A. Nefedov). order low-angle Bragg peak. Furthermore, varying 0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.11.014 ARTICLE IN PRESS A. Nefedov et al. / Physica B 357 (2005) 22­26 23 the external magnetic field during the XRMS transition metals, the L absorption edges must be measurements, a hysteresis loop can be measured. utilized, which are located in the soft X-ray range. Up to now for most of the XRMS experimental Since for this energy range special vacuum data, especially in the soft X-ray range, a detailed conditions are required, a UHV-diffractometer analysis of magnetization and magnetization ALICE containing a two-circle goniometer [8] was reversal is absent or has been made for collinear used for the scattering experiments to be described magnetic configuration only. For the hard X-ray below. The magnetic field was applied in the range, progress in the data analysis had taken scattering plane parallel to the in-plane hard axis place during the last years (see, for example, of the sample ðj ¼ 90Þ: In our geometry, the Ref. [3] and refererences therein). However, for magnetization vector corresponding to j ¼ 0 is soft X-rays and in the case of antiferomagnetically normal to the scattering plane and the positive coupled multilayers the situation is more complex. direction of j rotation is clockwise (Fig. 1a). The It has been shown earlier, that in remanence such multilayers can be in multidomain state [4,5] and/ or with noncollinear coupling in adjacent magnetic layers [6,7]. For noncollinearly coupled multilayers we cannot use the asymmetry ratio R ¼ ðIþ I Þ= M =0° Iþ þ I ; where I is the intensity of right/left- circular polarized radiation, because this ratio is M =-90° =90° sensitive to the magnetization in the scattering || plane only ðM =+/-180° kÞ: But utilizing the direct intensity of circularly polarized or p-linearly polarized radiation, we can extract information about both in-plane magnetization components ðM k and M?). In order to understand the magnetic structure a simulation of the structural factor is necessary, using possible magnetic configurations. In our H previous paper [5], we presented results on Fe/Cr (a) multilayer demonstrating the collinear coupling. In this study, we would like to focus our attention 10-1 experimental on magnetic configurations of noncollinearly simulation coupled Fe/Cr superlattices. 10-2 We have grown Fe/Cr superlattices by molecu- 10-3 lar beam epitaxy with Cr thickness close to the [a. u.] second maxima (25 (A) in the AF interlayer ex- 10-4 change coupling. The Fe layer thickness ð 15 (AÞ 10-5 and the number of repeats ðN ¼ 10Þ was chosen to Intensity not exceed the total penetration depth of the soft 10-6 polarization X-rays. The detailed procedure of the sample 10-7 preparation is described in Ref. [5]. SQUID 10 20 30 40 50 60 70 80 90 100 110 magnetometry indicated noncollinear coupling (b) with H 2 [deg] S ¼ 2:5 kOe: The four-fold in-plane crystal anisotropy of the magnetization has been observed Fig. 1. (a) The scattering geometry of the experiment; (b) by magneto-optical Kerr effect measurements. Reflectivity taken at the Fe L3 edge with p-linearly polarized The XRMS experiments were carried out at radiation for AF-coupled superlattice with 10 repeats of the undulator beamlines UE56/1 and UE56/2 [Fe(15.2 A )/Cr(25.6 A )] deposited on Cr(240 A )/MgO(0 0 1) buffer-substrate system: open circles-the experimental data, of the Berlin storage ring for synchrotron radia- solid line-the simulation using a model, corresponding to tion (BESSY). In order to study XRMS on 3d biquadratic coupling. ARTICLE IN PRESS 24 A. Nefedov et al. / Physica B 357 (2005) 22­26 Fe/Cr multilayer was characterized with both to the easy axis of the in-plane magnetic aniso- circularly and linearly polarized radiation. tropy (j1 ¼ 135 and j2 ¼ 45 to the scatter- By tuning the incident energy to just below the ing plane for the odd and even iron layers, Fe L3 edge, we observe structural Bragg peaks at respectively). This results were confirmed by the the even positions and magnetic Bragg peaks at simulation of the hysteresis loops described below. the half-order positions in units of the reciprocal Hysteresis loops measured with linearly (p) and pffiffiffi lattice vector associated with the superlattice left-circularly ðe ¼ ðs ipÞ= 2Þ polarized radia- periodicity (Fig. 1b). The fact that we can observe tion at the position of the structural (the 3rd order, a few orders of Bragg reflections reflects on 2y ¼ 80:4) Bragg peak and the half-order (the 7/2 the high structural quality of the sample. The line order, 2y ¼ 97:2) magnetic peak are reproduced represents a simulation procedure based on the in Figs. 2 and 3, correspondingly. For a simulation matrix formalism [9] with the optical constants of these data we calculated the dependence of the taken from [10]. All structural parameters (layer magnetization directions for the odd and even Fe thicknesses and interface roughnesses) were taken layers on the external field by minimizing the from the fit of the hard X-ray data using standard energy density for each field value in a Stoner­ Parratt formalism. The magnetic interface rough- Wohlfarth-like model [12]. Contributions of the nesses were introduced in the model using slicing Zeeman energy, the four-fold crystal anisotropy, method. More details of the simulation procedure the bilinear, and biquadratic exchange coupling will be published elsewhere [11]. It has been found have been taken into account. It has been that the magnetic roughness in the present multi- established that magnetic roughnesses do not layer amounts to about 65% of the value of the affect the shape of the hysteresis loops (there is structural roughnesses (2.6 A and 4 A , respec- an intensity scaling effect only). Therefore in order tively). The best agreement between the experi- to simplify the simulation procedure, we used one mental data and the calculated values is achieved AF domain configuration and calculated the for the magnetic structure corresponding to hysteresis loops without taking into account biquadratic (90) coupling in the multilayer with magnetic roughness, but using some scaling of the magnetization vector in the iron layer parallel the intensity. According to this model, the 340 7000 320 6000 [a.u.] 300 Intensity 280 5000 260 pol. - pol. -2 -1 0 1 2 -2 -1 0 1 2 (a) H[kOe] (b) H[kOe] Fig. 2. Hysteresis loop measured at the position of the structural 3rd order, ð2y ¼ 80:4Þ Bragg peak for p linearly (a) and left- circularly polarized radiation (b). Open circles-the experimental data, solid lines-simulation with the model presented in Fig. 4. ARTICLE IN PRESS A. Nefedov et al. / Physica B 357 (2005) 22­26 25 40 20 35 15 30 [a.u.] 25 10 Intensity 20 5 15 -pol. pol. -2 -1 0 1 2 -2 -1 0 1 2 (a) H[kOe] (b) H[kOe] Fig. 3. Hysteresis loop measured at the position of the half-order (7/2 order, 2y ¼ 97:2) magnetic peak for p-linearly (a) and left- circularly polarized radiation (b). Open circles-the experimental data, solid lines-simulation with the model presented in Fig. 4. coherent rotation of the magnetization from j ¼ 90 90 at saturation to the corresponding easy axis 45 1 (j1 ¼ 135 for odd and j2 ¼ 45 for even iron 1 layer) close to the remanent state takes place. At 0 2 remanence the domain wall propagates fast -45 2 1 through the iron layers changing, the angles of [deg] -90 2 the magnetization by 180: By increasing the 1,2 -135 1 1 magnetic field, the coherent rotation to the -180 saturation takes place again (Fig. 4). Finally it 2 has been found that for the best agreement -225 2 between data and simulation it is necessary to -270 add some ferromagnetic background, resulting -2 -1 0 1 2 from the presence of  5­10% ferromagnetically H [kOe] coupled domains. The results of these calculations Fig. 4. The model used in the simulation of the hysteresis loops: are presented by solid lines in Figs. 2 and 3. the solid and dashed lines-the dependence of the angles j In conclusion, we have shown that XRMS allows 1;2 of the magnetization vector of the odd and even Fe layers, to study in detail the magnetic structure of correspondingly. noncollinearly coupled Fe/Cr superlattices. Using the resonance condition close to the Fe L3 edge, magnetic peaks are observed at the half-order Bragg We would like to thank K. Westerholt for peaks positions. The experimental data of the useful discussions, J. Podschwadek for technical reflectivity and hysteresis loops and their simulation assistance during sample preparation, B. Zada reflect biquadratic AF coupling with the in-plane and W. Mahler (BESSY) for their help with the easy-axis orientation of Fe magnetization in adja- beamline operation. This work was supported cent layers at remanence. With increasing magnetic by the German Federal Ministry of Education field coherent rotation of the magnetization vectors and Research (BMBF) under Contract no. takes place to the total saturation. 03ZA6BC2. ARTICLE IN PRESS 26 A. Nefedov et al. / Physica B 357 (2005) 22­26 References [6] T.P. Hase, et al., Phys. Rev. B 61 (2000) 15331. [7] A. Schreyer, et al., Phys. Rev. B 52 (1995) 16066. [1] P. Gru¨nberg, R. Schreiber, Y. 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