VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998 Reorientation of Spin Density Waves in Cr(001) Films Induced by Fe(001) Cap Layers P. Bödeker,1 A. Hucht,2 A. Schreyer,1,3 J. Borchers,3 F. Güthoff,4 and H. Zabel1 1Institut für Experimentalphysik/Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum, Germany 2Theoretische Physik, Gerhard-Mercator-Universität Duisburg, D-47048 Duisburg, Germany 3National Institute of Standards and Technology, Gaithersburg, Maryland 20899 4Forschungszentrum Jülich, D-52425 Jülich, Germany (Received 17 November 1997) Proximity effects of 20 Å Fe layers on the spin density waves (SDWs) in epitaxial Cr(001) films are revealed by neutron scattering. Unlike in bulk Cr we observe a SDW with its wave vector Q pointing along only one 100 direction which depends dramatically on the film thickness tCr. For tCr , 250 Å the SDW propagates out of plane with the spins in the film plane. For tCr . 1000 Å the SDW propagates in the film plane with the spins out of plane perpendicular to the in-plane Fe moments. This reorientation transition is explained by frustration effects in the antiferromagnetic interaction between Fe and Cr across the Fe Cr interface due to steps at the interface. [S0031-9007(98)06723-4] PACS numbers: 75.70.­i, 75.25.+z, 75.30.Fv While the incommensurate spin density wave (SDW) mentary experiments with synchrotron radiation will be antiferromagnetism is well established for bulk Cr [1], it discussed elsewhere. is presently of high interest to analyze how the magnetic We have grown epitaxial Fe Cr(001) bilayers by molec- properties of Cr are altered either by reduced dimension- ular beam epitaxy on Al2O3 (1102) substrates with a 500 Å ality in thin films or by proximity effects to ferromagnetic thick Nb(001) buffer layer, following well established (FM) layers. The magnetic state of Cr is particularly in- growth recipes [11,12]. Cr(001) films with thicknesses teresting since ultrathin Cr films play an important role from 200­3000 Å were grown on the Nb buffer layer at in exchange coupled Fe Cr superlattices exhibiting giant 450 ±C with a growth rate of 0.1 Å s. As evidenced by re- magnetoresistance effects [2,3]. Also for theoretical treat- flection high energy electron diffraction (RHEED) during ments of the exchange coupling it is uncertain whether the growth, the crystalline quality of the Cr near the Cr Nb Cr spacer layer should be treated as a paramagnet, an anti- interface is not very high due to the 14% lattice mismatch ferromagnet, or as a proximity induced antiferromagnet between Nb and Cr. However, with growing Cr thick- [4]. In this context, the role of the Fe Cr interface is a ness the film quality improves dramatically [12]. After matter of intense study [5,6]. Magnetic domain imaging annealing for 30 min at 750± the Fe cap layer was grown of an Fe layer deposited on a wedge shaped Cr layer on at 300± at a rate of 0.1 Å s. For the scattering experi- an Fe whisker shows a domain pattern switching between ments it was necessary to keep the absolute amount of Cr parallel and antiparallel alignments having a periodicity of in the samples roughly constant. Therefore, for samples two Cr(001) monolayers and a phase shift consistent with with tCr , 1000 Å the Fe Cr structure was repeated sev- a SDW state [7]. More recently, neutron scattering and eral times up to a minimum total tCr of 2000 Å. All addi- perturbed angular correlation spectroscopy (PACS) have tional Fe Cr layers were grown at 300 ±C. For protection been used on Fe Cr(001) superlattices to investigate the against oxidation all samples were covered with a 20 Å magnetic structure of Cr directly for Cr film thicknesses Cr layer [13]. X-ray scattering shows that all samples are tCr of about 30­400 Å [8­10]. Although some inconsis- of high crystalline quality, with an out-of-plane crystalline tencies still remain, these experiments show that the SDW coherence length of 60%­80% of the total film thickness state collapses for Cr films well below the period L of and a mosaic spread of about 0.2± FWHM measured at the the SDW. (002) peak. The aim of the present work is to gain a basic under- To determine the magnetic structure, neutron scattering standing of the effect of FM proximity layers on the mag- experiments were performed on the triple-axis spec- netic properties of thin Cr(001) films in the SDW phase. trometers BT-2 of the National Institute of Standards and The thickness range of the Cr films (200­3000 Å) is cho- Technology and UNIDAS at the KFA Jülich, Germany. In sen such that the question of the presence of a SDW state both cases we used pyrolytic Graphite PG(002) monochro- is not an issue. Using neutron scattering we find that the mator and analyzer crystals to select a wavelength of propagation direction of the SDW depends dramatically l 2.351 Å. Graphite filters suppressed any l 2 on the Cr film thickness. Our experimental results are contamination. rationalized by computer simulations using a Heisenberg Bulk Cr exhibits an incommensurate SDW, i.e., the model which takes realistic Fe Cr interfaces with interfa- magnitude of the antiferromagnetically aligned Cr mag- cial roughness and interdiffusion into account. Comple- netic moments m varies sinusoidally with a temperature 914 0031-9007 98 81(4) 914(4)$15.00 © 1998 The American Physical Society VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998 dependent period L of about 21 lattice constants at T 0 [1]. The incommensurability is ascribed to a nesting vec- tor along the 100 directions of the Cr Fermi surface. The wave vector Q defines the direction of propagation of the SDW. At lowest temperatures a longitudinal SDW (LSDW) forms, i.e., m is parallel to Q. Above the spin- flip transition temperature, TSF 123 K, m is perpendic- ular to Q, forming a transverse SDW (TSDW). Above TN 311 K bulk Cr is paramagnetic. The incommensurate modulation of the antiferromag- netic (AF) spin structure by the SDW causes two satel- lite peaks to occur around the {1,0,0} positions [1], e.g., at (0,0,16d), (16d,0,0), and (0,16d,0) which can be in- vestigated by neutron scattering. Here d 1 2 jQj with jQj in reciprocal lattice units, d a L, and the Cr lattice constant a. In the first case, the position of the satellites indicates Q being oriented out of the film plane, the two latter cases occur for either direction of in-plane propaga- tion. In addition, the polarization of the SDW (i.e., TSDW or LSDW) can be obtained by making use of the selection rule for magnetic neutron scattering. It requires a com- ponent of the magnetization vector m to be perpendicular to the scattering vector jqj 4p l sin u where u is the scattering angle. Thus, a longitudinal SDW propagating along L, i.e., out of plane, will generate no intensity at (0,0,16d). However, satellites will occur at (1,0,06d). A commensurate AF (AF0) phase, on the other hand, will yield a single peak of purely magnetic origin at the Cr 001 FIG. 1. Neutron scans through the possible satellite positions positions. Thus, with neutron scattering we can uniquely around the (001) (top) and (010) (bottom) position for a determine AF0 and SDW magnetic order as well as SDW 3000 Å thick Cr(001) film capped with a 20 Å Fe layer for propagation and polarization. For a more detailed discus- 30 # T # 500 K. For each scan direction a schematic picture sion, see, e.g., Ref. [14]. of the reciprocal lattice with the open and solid circles as a Figure 1 reproduces neutron scans taken at possible representation of the possible and observed satellites at 100 K is shown. satellite positions around the Cr(001) and Cr(010) po- sitions of a 3000 Å Cr(001) film capped with a 20 Å Fe layer for temperatures of 30­500 K. To make the 311 K the SDW satellites disappear consistent with the spectra comparable, all intensities have been normalized bulk Néel temperature. with respect to the structural reflections. For all tempera- Another feature of the data of Fig. 1 is the presence tures only satellites in scans along the in-plane K direc- of intensity commensurate with the Cr(001) and Cr(010) tion occur, whereas in scans along L no satellites are positions indicating an additional AF0 phase. From the found. Thus, only SDWs propagating in the film plane temperature dependence the Néel temperature is found to are present. For T 30 K satellites appear around the be Tcom 450 K. Using the selection rule we again (001) position. From the selection rule described above observe a flipping of the spins from in plane below Tfilm SF we conclude that at T 30 K a LSDW propagates in the 40 6 10 K to out of plane above Tfilm SF . The origin of the plane with the spins dominantly oriented in plane. For AF0 phase will be discussed below. temperatures T $ 50 K, however, we find the reversed In summary, we find an in-plane LSDW and an AF0 situation. The satellites occur only around the (010) po- phase coexisting below 40 K, both with spins in plane. sition. Thus, we conclude that the SDW still propagates Above 40 K an in-plane TSDW and an AF0 phase coexist, in plane but that the polarization has changed to trans- both with spins out of plane. Thus, our measurements verse. Moreover, the absence of any satellites in the K- imply that the Cr moments are oriented perpendicular scan around (001) tells us that for temperatures T $ 50 K to the Fe moments since magnetization measurements we observe a TSDW with the spins pointing out of the confirmed that the Fe is magnetized in plane. film plane, i.e., perpendicular to the Fe Cr interface. The In Fig. 2 results of equivalent measurements on a series observed spin flip transition from the LSDW to the TSDW of samples with 250 # tCr # 3000 Å are summarized in at approximately Tfilm SF 40 6 10 K occurs at a much a qualitative phase diagram for T 100 K. Two points lower temperature than in bulk (Tbulk SF 123 K). Around at 42 and 80 Å from earlier experiments by Schreyer et al. 915 VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998 [10] have been added. The diagram can be divided into This phenomenological description is confirmed by four parts. For tCr # 45 Å only an AF0 phase with in- computer simulations of a classical Heisenberg model plane Cr spins exists. With increasing tCr up to 250 Å with the following Hamiltonian: we observe an out-of-plane TSDW with the Cr spins in 1 X X plane, consistent with results of Fullerton et al. [9]. For H 2 Je s D sz i ej i ? sj 2 ei i 2, (1) 250 Å # t 2 Cr # 1000 Å in- and out-of-plane TSDWs ij i coexist. Finally, for the thickest films, the reorientation where s to a TSDW propagating in the film plane with spins out i sxi, syi, szi are spin vectors of unit length at site i on a bcc(001) lattice, and e of plane is complete. Interestingly, this reorientation is i Fe, Cr is the element at this site. J is the nearest-neighbor exchange correlated with the occurrence of a coexisting AF eiej 0 phase coupling constant between elements e is with the same out-of-plane spin orientation. i and ej, and Dei the uniaxial anisotropy of element e The observed reorientation effect can be explained by i which, if positive, favors the z direction perpendicular to the film. We considering a realistic Fe Cr interface structure. In the assume that this anisotropy does not depend on the Fe Cr system three different interactions are present: a position of the atoms. We choose J FM Fe-Fe and an AF Cr-Cr intralayer interaction within FeFe kB 375 K and J each Fe or Cr layer, and in addition an AF [15] interlayer CrCr kB 2170 K, consistent with the critical temperatures Tcom 450 K for Cr and T interaction between the Fe and the Cr. At an ideally c 1000 K for Fe in mean field solution of this model. The interaction flat interface all three interactions can coexist without between Fe and Cr is chosen as J any frustration as long as all moments are oriented in FeCr kB 240 K [17]. The shape anisotropy of Fe induced by the dipole the film plane. However, at real interfaces steps and interaction is modeled by a negative uniaxial anisotropy interdiffusion may occur. Any step height of an uneven of D number of Cr layers along the Fe Cr interface introduces Fe kB 21.5 K. Finally, we introduce a very small uniaxial anisotropy D frustrations between the Fe and Cr intralayer interaction Cr kB 50 mK at the Cr sites induced by epitaxial strain, consistent with our results on on one hand, and the interlayer interaction on the other uncovered Cr films [14]. Using a combination of over- hand [16]. It is not possible to minimize all three relaxation dynamic and conjugate gradient method, we coupling energies independently. Thus, the resulting spin determine the ground state of this system for various structure depends on the values of the respective coupling configurations of the Fe Cr interface. This method is constants. The following four limiting cases can be much faster than the tight binding method used by distinguished assuming a single monoatomic step at the Freyss et al. [18], while the magnetic structure obtained interface. If the interface coupling is large compared to is qualitatively the same. To make our model even more the Fe or Cr coupling constant, a domain wall forms in realistic we have included interdiffusion at the Fe Cr the Fe (case 1) or in the Cr (case 2). For a very small interface [5] in addition to well defined steps [19]. In interface coupling the ideal FM and AF order in the Fe Fig. 3 the resulting ground state spin configuration is and Cr layers can be preserved by a domain wall forming shown. Clearly, the frustration induces an effective 90± along the interface (case 3). If, however, the AF interface coupling between the Fe and the Cr order parameter coupling is of intermediate magnitude, the system can (case 4). Together with the small uniaxial anisotropy react by reorienting the Cr moments perpendicular to the of the Cr atoms this leads to an orientation of the Cr Fe (case 4). FIG. 2. Qualitative magnetic phase diagram of Cr films capped with 20 Å thin Fe layers as a function of the Cr thickness. The superscripts describe the orientation of the Q FIG. 3. Ground state spin structure near an Fe Cr interface vector, the arrows the orientation of the Cr spins. The solid with monoatomic steps from computer simulations assuming and open circles represent the relative intensities of the TSDW interdiffusion over two layers. Note that the Fe moments are and the AF0 peaks, respectively. also affected. 916 VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998 spins perpendicular to the surface, consistent with the tCr. Compared to bulk, the spin flip temperature is re- experiment. duced to about 40 K. The occurrence of commensurate In our model we find this 90± orientation independent AF0 structures can be attributed to finite size effects. Us- of the presence of interdiffusion as long as there are steps. ing ground state calculations of a classical Heisenberg Two length scales are important, the thickness of the Cr Hamiltonian the observed reorientation transition is ex- layer and the separation of the steps at the interfaces. plained by a realistic Fe Cr interface with steps causing When tCr is reduced below the distance between steps, frustration of the system. more energy can be gained by the exchange interaction at We thank Professor Usadel for valuable discussions and the interface than is lost by roughness induced domain J. Podschwadek and W. Oswald for technical assistance. wall formation within the Cr. Consequently, for thin The work in Bochum and Duisburg was supported by the Cr films the Cr moments are predicted to be oriented Deutsche Forschungsgemeinschaft through SFB 166. in the film plane with domain walls in the Cr layer connecting the interfacial steps. Thus, our model also explains the observed reorientation transition with tCr (Fig. 2) [20]. For the thinnest Cr films the simulation yields a frustrated spiral structure in the Cr, which induces [1] E. Fawcett, Rev. Mod. Phys. 60, 209 (1988), and strong noncollinear coupling between the Fe layers in references therein. superlattices as predicted theoretically by Slonczewski [2] G. Binasch et al., Phys. Rev. B 39, 4828 (1989). [3] M. N. Baibich et al., Phys. Rev. Lett. 61, 2472 (1988). [21] and confirmed experimentally by Schreyer et al. [10]. [4] M. D. Stiles, Phys. Rev. B 54, 14 679 (1996). Interestingly, AF0 Cr induces such coupling between the [5] D. Venus and B. Heinrich, Phys. Rev. B 53, R1733 Fe layers whereas SDW Cr does not [10,22]. (1996); A. Davies et al., Phys. Rev. Lett. 76, 4175 (1996). Finally, we discuss the origin of the AF0 phase. For [6] D. Stoeffler and F. Gautier, J. Magn. Magn. Mater. 147, the smallest tCr well below the SDW period no SDW 260 (1995); A. Vega et al., Europhys. Lett. 31, 561 can form (see Fig. 2). Instead, the system becomes AF0 (1995); M. Freyss, D. Stoeffler, and H. Dreyssee, Phys. [9,10] consistent with theory [23]. Thus, the AF0 order Rev. B 56, 6047 (1997). is induced by a finite size effect. However, for thick [7] J. Unguris et al., Phys. Rev. Lett. 69, 1125 (1992). films and in-plane propagation of the SDW, AF [8] J. Meersschaut et al., Phys. Rev. Lett. 75, 1638 (1995). 0 order also occurs (see Figs. 1 and 2). Grazing incidence x-ray [9] E. E. Fullerton, S. D. Bader, and J. L. Robertson, Phys. and neutron experiments with depth resolved information Rev. Lett. 77, 1382 (1996). [10] A. Schreyer et al., Phys. Rev. Lett. 79, 4914 (1997). have revealed that the in-plane SDW phase is located [11] S. M. Durbin et al., J. Phys. F 11, L223 (1981); 12, L75 close to the top Fe Cr interface [24]. The AF0 phase (1982). seems to be limited to the lower Nb Cr interface of the [12] K. Theis-Bröhl et al., Phys. Rev. B 57, 4747 (1998). Fe Cr Nb sapphire structure. The lower quality RHEED [13] A. Stierle and H. Zabel, Europhys. Lett. 37, 365 (1997). data of the Cr near the Nb interface mentioned above [14] P. Sonntag et al., J. Magn. Magn. Mater. 183, 5 (1998). indicates small in-plane crystalline grain dimensions near [15] See, e.g., R. Jungblut et al., J. Appl. Phys. 70, 5923 the interface due to strain relaxation effects. This can (1991). induce AF [16] A. Berger and Eric E. Fullerton, J. Magn. Magn. Mater. 0 order due to a finite size effect for the in- plane SDW near the Cr Nb interface. With increasing 165, 471 (1997). t [17] This value was determined from a preliminary high field Cr the in-plane crystalline quality improves according to RHEED, allowing the formation of an in-plane SDW magnetization measurement on an Fe Cr superlattice. [18] M. Freyss, D. Stoeffler, and H. Dreysse, in MRS Sym- far away from the Cr Nb interface. On the other hand, posia Proceedings, Symposium M, Spring Meeting, San for out-of-plane SDW propagation (Fig. 2) no AF0 phase Francisco, 1997 (Materials Research Society, Pittsburgh, occurs near the Nb Cr interface, since in this case the 1997). limiting factor is the out-of-plane crystalline grain size. [19] We use the same Je and D for the interdiffused region i ej ei Using x-ray scattering we measure a much larger out-of- since deviations make no qualitative difference. plane coherence length than in the plane. [20] Certain interdiffusion profiles can also cause a 90± Consequently, a pure SDW propagating out of plane orientation between Cr and Fe spins for thick Cr films. can form without any AF0 contribution in the tCr range However, only steps explain the observed reorientation as between 45 and 250 Å. Thus, we can consistently explain a function of Cr thickness. Thus the steps explain all the occurrence of the AF observations, interdiffusion without steps does not. 0 phase by finite size effects. In conclusion, we have studied proximity effects be- [21] J. C. Slonczewski, J. Magn. Magn. Mater. 150, 13 (1995). tween Fe and Cr in the Fe Cr system with neutron scat- [22] E. E. Fullerton, C. H. Sowers, and S. D. Bader, Phys. Rev. B 56, 5468 (1997). tering. We have focused on the regime of large tCr about [23] Z. P. Shi and R. S. Fishman, Phys. Rev. Lett. 78, 1351 which no studies exist so far. As opposed to bulk Cr we (1997). find a single Q state SDW whose direction of propagation [24] P. Bödeker et al., Physica (Amsterdam) B (to be pub- is reoriented from in plane to out of plane upon reducing lished). 917