Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 Study of the magnetic order in a Co/Cr multilayer by magnetic Bragg di!raction at the Co 2p resonance Alessandro Mirone *, Maurizio Sacchi , Esther Dudzik , Hermann DuKrr , Gerrit van der Laan , Annie Vaure s , FreHdeHric Petro! LURE, Universite& Paris-Sud, BP 34, 91898 Orsay, France Daresbury Laboratory, Warrington, WA4 4AD, UK Unite& mixte CNRS/Thomson-LCR, Domaine de Corbeville, 91404 Orsay, France Received 26 January 2000; received in revised form 27 April 2000 Abstract We have measured the resonant scattering from an antiferromagnetic Co/Cr multilayer at photon energies close to the cobalt 2pP3d transitions. The cobalt dielectric tensor has an anisotropic component, enhanced by resonance, which depends on the magnetic order and follows its modulation inside the sample. We have studied the vertical distribution of this component through the dependence of the re#ectivity on the scattering angle. Using s-polarized light, we have observed the signature of the cobalt}cobalt antiferromagnetic coupling as an half-integer-order Bragg peak. Experi- mental results have been analyzed by numerical simulation. 2000 Elsevier Science B.V. All rights reserved. PACS: 75.70.i; 78.20.Ls; 78.66.Bz; 78.70.Ck; 75.30.P6 Keywords: Magnetic multilayers; Magnetic X-ray scattering 1. Introduction observed in the resonant re#ectivity from Fe [3,4], Co [5] and Ni [6] in the soft X-rays range at the The measurement of the resonant scattering of L polarized X-rays is a valuable tool to investigate edges. The wavelengths required to excite these resonances and in general those of the 3d the magnetic order of matter. First experiments, transition metals (TM) L performed in the hard X-ray energy region measur- edges, are in the order of tens of As, preventing experiments under Bragg ing the Bragg di!raction at the 3d edges of actinide di!raction conditions for most crystalline mater- compounds [1] and at the 2p edges of rare earths ials. Enhanced magnetic signals can be recovered [2], had a strong impact on the study of these for arti"cially layered structures, where the Bragg systems. Soon after, large magnetic e!ects were condition depends on the chemical and magnetic modulation periods [7}10]. In these samples, the distribution of the magnetic moments can be * Corresponding author. Tel.: #33-1-64468814; fax: #33-1- highlighted by studying the behavior of the Bragg 64464148. peaks in /2 scans. This has opened an entirely E-mail address: mirone@lure.u-psud.fr (A. Mirone). new experimental "eld of investigation which can 0304-8853/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 0 ) 0 0 4 0 6 - 6 138 A. Mirone et al. / Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 address phenomena like oscillatory exchange- coupling, perpendicular anisotropy and enhanced interfacial magnetic moments. Recent studies on a Ce/Fe multilayer, for instance, have measured the pro"le of Fe-induced magnetization inside the Ce layers [11] by observation of high-order Bragg peaks. In this work we discuss the resonant magnetic re#ectivity at the cobalt 2pP3d resonance for a cobalt}chromium multilayer. This system is known to exhibit an oscillatory exchange coupling between cobalt layers as a function of the Cr thick- ness [12]. For the sample that we considered (10 As Fig. 1. Magnetization loop at room temperature for the Co/Cr Cr and 17 As Co), cobalt layers are antiferromag- multilayer, measured by SQUID magnetometry. netically coupled. We have analyzed this antifer- romagnetic ordering by resonant magnetic scattering at the L edges of cobalt. 2. Experimental method A (Co17 As/Cr10 As);30 multilayer was grown by DC magnetron sputtering in a UHV compatible sputtering system [13]. The multilayer was depos- ited on a 50 As Cr bu!er layer grown on a chemic- ally etched Si(0 0 1) substrate. A 50 As Cu overlayer was deposited to protect the sample. The Ar pres- Fig. 2. Sketch of the experimental setup. sure was set to 3 mTorr and the deposition rates for Co, Cr and Cu were 3 As/s. The multilayer was "rst characterized by conventional X-ray re#ectometry polarized photons over the 60}1000 eV range. In and the multilayer period deduced from the low- our experimental conditions, the plane grating angle Bragg peaks, was found in good agreement monochromator gave a resolving power of about with the nominal value. 3000 at the Co L-edges. The endstation was a ver- The in-plane magnetization loop at room tem- tical scattering /2 re#ectometer working in perature was measured with a Quantum Design vacuum (&10\ mbar), separated from the beam- MPMS Squid magnetometer. As shown in Fig. 1, line by a highly transparent window. In this scatter- the loop displays the signature of an antiferromag- ing geometry, sketched in Fig. 2, the polarization of netic (AF) coupling between the Co layers: a large the incoming light is along the y-direction in the saturation "eld H of about 1T is necessary to surface plane and normal to the scattering plane overcome the AF coupling, and remanent magne- (S-polarized light). Measurements were performed tization M is only 0.45% of the saturation value both in remanent conditions and in the presence of M . H can be related to the AF interlayer ex- a permanent magnet giving a "eld of about 1 kG at change coupling J by the well known formula [14], the sample surface. This weak "eld, well below the !4J"H M t$. For this multilayer we "nd value necessary to impose a parallel orientation of J"!0.41 erg s cm\ . all the Co layers, is su$cient to break the x}y plane X-ray scattering measurement were performed at symmetry of the antiferromagnetic domains. Ap- the 5U.1 undulator beam-line [15] of the SRS stor- plying the "eld along the x (or y) direction favors age ring (Daresbury laboratory), delivering linearly the orientation of the domains along the y (or x) A. Mirone et al. / Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 139 orthogonal axis. The monochromator energy cali- multilayer. Re#ectivity is obtained by imposing the bration was "xed by recording absorption spectra condition of outgoing waves in the substrate. at the Co 2pP3d resonances and by comparing For chromium, we used a scalar dielectric con- to cobalt absorption spectra from the literature stant obtained from tabulated values [19], since we [16]. are far from the chromium resonances. For cobalt, we started from the absorption spectra reported in the literature [16] of bulk magnetized metallic co- 3. Numerical method balt measured for positive and negative helicity of the circularly polarized photons. The absorption The calculation of re#ectivity from the magnetic data were rescaled to join the tabulated values [19] multilayers is done taking into account the ten- for cobalt on the two sides of the 2pP3d edges to sorial nature of the dielectric constant in magnetic obtain the imaginary part of the index, > and \. materials. The "rst step of the procedure is to "nd, The decrement to the real part of the optical index, for given values of photon energy and incidence !, was obtained by Kramers-Kronig transforma- angle, the electromagnetic (EM) eigenmodes inside tion of !. The dielectric tensor was constructed on a uniform tensorial medium. These eigenmodes the basis of the optical indexes n correspond to the solution of a second-order di!er- !"1! !!i !, neglecting linear dichroism [17]. In the (xyz) frame ential equation [17]. The four eigenmodes found of Fig. 2, and for a magnetization along the x-axis correspond to the two opposite propagation direc- (M"me( tions (ingoing and outgoing) and the two pho- V), the cobalt dielectric tensor is ton polarizations which are given by the solution + KC( " V of the eigenproblem may vary between linear and circular. To calculate a multilayer stack, the eigenmodes ( ># \)/2 0 0 0 ( ># \)/2 $i( >! \)/2 , for all the layers of the stack must be found "rst, 0 Gi( then Fresnel's equations have to be solved for the >! \)/2 ( ># \)/2 interfaces between layers. (1) Fresnel's equations impose four conditions of continuity on the parallel components of the EM where !"n !, the $ sign depends on the sign of "eld across the interfaces (two parallel components the magnetization (it alternates over the cobalt for E and two for B). When the EM "eld across the layers for antiferromagnetic coupling). The dielec- interface is decomposed in the eigenmodes basis, tric tensor for y magnetization is written similarly the resulting 4;4 matrix describes the linear de- as pendence between the eigenmode coe$cients on " both sides of the interface. The interface roughness + KC(W (which can be due to either interdi!usion or corru- gation) is taken into account by introducing De- bye}Waller-like factors [18]. ( ># \)/2 0 $i( >! \)/2 0 ( ># \)/2 0 The propagation of the modes across the thick- Gi( >! \)/2 0 ( ># \)/2 ness of a layer is described by a 4;4 diagonal matrix whose diagonal elements are the propaga- (2) tion factors for the eigenmodes (which are the ex- ponential of the eigenvalue times the layer thickness). 4. Results and discussion At the end of the procedure the whole stack is described by a 4;4 matrix, obtained by multiply- We show in Fig. 3 the re#ectivity versus grazing ing the interface and the propagation matrices angle for x and y magnetization (M) at a photon together from one side to the other side of the energy of 773.5 eV. This energy lies immediately 140 A. Mirone et al. / Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 peak of the product M(E ;E ), where E in- dicates the polarization of the ingoing (outgoing) wave, must be non-zero [15]. Assuming E along the y-direction (S-polarization), this implies that the scattering process induces a polarization rota- tion and E has a component in the scattering plane (SPP scattering channel). When the external "eld orients the magnetization along the y-axis, E is parallel to M and the product vanishes. For M along x, on the contrary, M(E ;E ) is non- zero and is proportional to the P component of E . Moreover each cobalt layer contributes to the SPP channel with a phase that is the sum of an Fig. 3. Experimental results of /2 scans at 773.5 eV photon optical-path-dependent term plus a$ term that energy. Open squares refer to measurements performed in an depends on the sign of the magnetization. As a con- external "eld H applied in the scattering plane (x-direction), sequence the SPP channel is sensitive to the mag- which orients the sample magnetization along y. Filled circles netization modulation. The magnetic signal refer to H#y and magnetization along x. The main peak at about 17.53 is due to "rst-order Bragg di!raction from the chemical appearing at an angle equal to half of the "rst modulation of the multilayer. The half-order Bragg peak due to Bragg order angle indicates that the magnetic antiferromagnetic order is around "8.53. The inset shows the modulation has a period double than the chemical detail of the magnetic peak, with in the addition the spectrum is modulation (see Fig. 2) and is a clear signature of measured in remanent conditions with an isotropic distribution antiferromagnetic coupling between cobalt layers. of the magnetic domain directions in the sample (no external "eld). When the magnetization is turned from x to y the S to P channel is closed because + KC( , given by V Eq. (2), has no o!-diagonal element connected to before the cobalt 2pP3d transition so that the the y-direction. As a conseguence the M#y curve absorption is still low but the dichroism in the real has no magnetic peak around 8.53. part of the index is strong. The re#ectivity oscilla- The magnetic peak brings us information on tions of the period about 13 arise from interference both the magnetic polarization intensity and its between the signals from the top and the bottom of distribution inside the sample. Regarding the distri- the multilayer (the whole stack is probed at this bution, the width of the magnetic signal is sensitive energy). This phenomenon is well known in the to the coherence of antiferromagnetic coupling. In literature on X}UV multilayers [20] and the oscil- the case of perfect antiferromagnetic ordering of the lations are called Kiessig fringes. The number of cobalt layers the width is inversely proportional to fringes between two Bragg peaks is related to the the number of layers but it is expected to get larger multilayer total thickness. The curve of Fig. 3 in case of imperfect antiferromagnetic alignment. shows a peak at an angle of about 8.53 that is half The peak height is sensitive to magnetization inten- that of the "rst-order Bragg peak (about 17.53). sity and distribution inside the sample. This signal appears when the magnetic polarization We show in Figs. 4 and 5 the numerical "ts at is parallel to x and disappears completely when it is 773.5 and 787.5 eV for the x-polarized and y-polar- parallel to the y-axis. We show in the inset of Fig. 3 ized case, respectively. The simulation is done con- the details of the magnetic peak, together with the sidering a 16.7 and 10.4 A thicknesses for cobalt re#ectivity curve measured in remanent conditions and chromium, respectively, and perfect antifer- (H"0). This latter curve corresponds to dis- romagnetic ordering between all the cobalt layers. ordered magnetic domains and gives a lower mag- We consider a "6 As roughness for the cobalt- netic peak than for the x-polarized case. The origin crome interface. of the magnetic signal can be understood consider- We also considered a slight drift of the layer ing that in order to observe a magnetic di!raction thicknesses of about 0.1 A from top to the bottom A. Mirone et al. / Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 141 Fig. 4. Calculated and experimental scattered intensity at 773.5 Fig. 5. As in Fig. 4, for a magnetization oriented along y. and 787.5 eV photon energy for a magnetization orientation along x. The simulation is done considering a 16.7 and 10.4 A thicknesses for cobalt and chromium, respectively, and perfect antiferromagnetic ordering between all the cobalt layers. In order to "t the height of the half-order Bragg peak, the magnetic culated magnetic peak strongly depends on the part of the refractive index has been reduced by a factor 0.6 with magnetization distribution and we obtain the best respect to bulk values. agreement when the central layer has zero thick- ness, which corresponds to a 0.6 magnetic moment reduction factor, uniform over the entire cobalt of the multilayers. This drift has been chosen in layer. order to "t correctly the positions of the Kiessig The y-polarized case "ts well to the calculated fringes which are very sensitive to the thickness re#ectivity assuming complete y-polarization and drift, even when they are too small to a!ect the does not show any magnetic peak. An incomplete Bragg or the magnetic peaks. In order to "t the polarization could explain the height of the mag- height of the magnetic peak the asymmetry ratio netic peak without the need to scale the asymmetry between the two helicities has been rescaled with for cobalt, but then a magnetic peak should be respect to the bulk values [16] by a factor 0.6. This visible even in the y-polarized case. reduction might simulate an interface e!ect. In order to check the sensitivity of the magnetic We also simulated a non-uniform distribution of order we compare in Figs. 6 and 7 the experimental the magnetic-scattering amplitude within the Co re#ectivity to a simulation done assuming the same layer splitting it in to three layers: a central one structural parameters as those used in Figs. 4 and having bulk constants and two interface layers 5 and a &slip' in the antiferromagnetic alignment at characterized by a reduced magnetic moment. The a given point in the stack. reduction factor was taken as a function of the In particular, we considered two consecutive co- interface layers thickness in order to keep the total balt layers having parallel magnetization. Figs. 6 magnetization constant. We "nd that the cal- and 7 show the magnetic peak at 773.5 and 787.5 eV 142 A. Mirone et al. / Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 Fig. 6. Calculated and experimental re#ectivity at 773.5 eV Fig. 7. Same as Fig. 5, for a photon energy of 787.5 eV. photon energy for x-oriented magnetization. The simulation is done considering the same structural parameters as in Fig. 3 but imperfect antiferromagnetic ordering in the stack and using unscaled magneto}optical constants. In the simulation a slip in the antiferromagnetic alignment is introduced at the top (a), 5. Conclusion middle (b) and bottom (c) of the multilayer. The slip consists of two consecutive cobalt layers ferromagnetically coupled. We have studied the antiferromagnetic coupling between cobalt layers in a Co/Cr multilayer by re#ectivity measurements versus incidence angle at respectively for three di!erent positions of the slip, photon energies close to the cobalt 2pP3d using x-polarization. The three positions are at the transitions. The cobalt dielectric tensor has an an- bottom, in the middle and at the top of the multi- isotropic component, enhanced by resonance, layer. The simulation is done assuming bulk optical which depends on the magnetic order and follows constants for cobalt. its modulation inside the sample. We have studied The height of the simulated magnetic peak is the vertical distribution of this component through lowered by destructive interference in all three the dependence of the re#ectivity on the scattering cases. This reduction is large when the slip is at the angle. We have polarized the cobalt layers in the top, and lower when the slip is at the bottom tangential (sagittal) direction by a weak sagittal because of absorption in the sample. In the 787.5 eV (tangential) magnetic "eld and using S-polarized case the slip destroys completely the magnetic light, we have observed the signature of the co- peak. balt}cobalt antiferromagnetic coupling as an half- In the 773.5 eV case a slip in the antiferromag- integer-order Bragg peak. By numerical simulation netic alignment at the top of the multilayer could of the experimental results we have found that the explain the magnetic peak height without the need height of this peak cannot be explained assuming of the asymmetry reduction hypothesis but this bulk optical constants for cobalt. By introducing would give no magnetic peak at 787.5 eV. a reduction of 60% of the asymmetry ratio the A. Mirone et al. / Journal of Magnetism and Magnetic Materials 218 (2000) 137}143 143 magnetic peak can be reproduced with good agree- [2] D. Gibbs, D.R. Harshmann, E.D. Isaacs, D.B. McWhan, ment. On the other hand, the hypothesis of in- D. Mills, C. Vettier, Phys. Rev. Lett. 61 (1988) 1241. complete magnetic alignment, or imperfect anti- [3] C.-C. Kao, C.T. Chen, E.D. Johnson, D.P. Siddons, ferromagnetic coupling within the stack, could G.C. Smith, Phys. Rev. Lett. 65 (1990) 373. [4] V. Chakarian, Y.U. Idzerda, C.C. Kao, C.T. Chen, J. explain the lowering of the magnetic peak in certain Magn. Magn. Mater. 165 (1997) 52. cases but cannot give a good agreement with the [5] C.-C. Kao, C.T. Chen, E.D. Johnson, J.B. Hastings, whole set of experimental results. Within the limits H.J. Lin, G.H. Ho, G. Meigs, J.-M. Brot, S.L. Hulbert, imposed by available experimental data, the analy- Y.U. Idzerda, Ch. Vettier, Phys. Rev. B 50 (1994) 9599. sis of the peak height seems to indicate a reduction, [6] M. Sacchi, J. Vogel, S. Iacobucci, J. Magn. Magn. Mater. 147 (1995) L11. compared to the bulk value, of the magnetic depen- [7] L. Se ve, J.M. Tonnerre, D. Raoux, J.F. Bobo, M. Pieucuch, dent part of the cobalt dielectric tensor. In terms of M. De Santis, P. Troussel, J.M. Brot, V. Chakarian, Co magnetic moment, this reduction of about 60% C.C. Kao, C.T. Chen, J. Magn. Magn. Mater. 148 (1995) leads to an estimated magnetic moment per Co 68. atom of the order of 1 [8] J.M. Tonnerre, L. SeHve, D. Raoux, G. Soullie , B. Rodmacq, . From the SQUID P. Wolfers, Phys. Rev. Lett. 75 (1995) 740. measurements we "nd an average magnetic mo- [9] J.M. Tonnerre, L. Se ve, D. Raoux, B. Rodmacq, M. De ment of 1.16$0.06 @ per Co atom which is not far Santis, P. Troussel, J.M. Brot, V. Chakarian, C.C. Kao, from the estimated moment deduced from re#ectiv- E.D. Johnson, C.T. Chen, Nucl. Instr. and Meth. B 97 ity. The slight di!erence can be understood in terms (1995) 444. of sensitivity of the two methods to the interfacial [10] M. Sacchi, C.F. Hague, L. Pasquali, A. Mirone, J.M. Mariot, P. Isberg, E.M. Gullikson, J.M. Underwood, Phys. magnetism. It is highly probable that the magnetiz- Rev. Lett. 81 (1998) 1521. ation is more strongly reduced at the Co/Cr interfa- [11] L. Se ve, N. Jaouen, J.M. Tonnerre, D. Raoux, ces, due to chemical intermixing for example, than F. BartolomeH, M. Arend, W. Felsch, A. Rogalev, in the interior of the Co layers. J. Goulon, C. Gautier, J.F. BeHrar, Phys. Rev. B 60 (1999) 9662. [12] S.S.P. Parkin, R. Bhadra, K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. Acknowledgements [13] J.M. Slaughter, W.P. Pratt, P.A. Schroeder, Rev. Sci. Instr. 60 (1989) 127. We thank Dr. Gerard SoullieH for useful dis- [14] F. Nguyen Van Dau, A. Fert, M.N. Baibich, J.M. Broto, S. cussions and suggestions on data analysis. We are Hadjhoudj, H. Hurdequint, J.P. Redoules, P. Etienne, J. grateful to R. Loloee and Prof. P.A. Schroeder from Chazelas, G. Creuset, A. Friedrich, J. Massies, J. Phys. (Paris) 49 (1998) C8-1663. the Department of Physics and Astronomy of [15] G. van der Laan, H.A. Durr, E. Dudzik, M.D. Roper, S.P. Michigan State university for providing the Co/Cr Collins, T.P.A. Hase, I. Pape, Synchrotron Radiat. News sample. 12 (1999) 5. [16] C.T. Chen, Y.U. Idzderda, H.-J. Lin, N.V. Smith, G. Meigs, E. Chaban, G.H. Ho, E. Pellegrini, F. Sette, Phys. Rev. Lett. 75 (1995) 152. References [17] M. Sacchi, A. Mirone, Phys. Rev. B 57 (1998) 8408. [18] B. Vidal, P. Vincent, Appl. Opt. 23 (1984) 1794. [1] D.B. McWhan, C. Vettier, E.D. Isaacs, G.E. Ice, D.P. [19] B.L. Henke, E.M. Gullikson, J.C. Davis, At. Data Nucl. Siddons, J.B. Hastings, C. Petersand, O. Voigt, Phys. Rev. Data Tables 54 (1993) 181. B 42 (1990) 6007. [20] E. Spiller, Appl. Opt. 15 (1976) 2333.