PHYSICAL REVIEW B VOLUME 59, NUMBER 14 1 APRIL 1999-II Spin-density waves and reorientation effects in thin epitaxial Cr films covered with ferromagnetic and paramagnetic layers P. Bo¨deker, A. Schreyer, and H. Zabel Institut fu¨r Experimentalphysik/Festko¨rperphysik, Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany Received 11 September 1998 We report about synchrotron and neutron-scattering studies investigating incommensurate spin-density waves I-SDW's in epitaxially grown thin Cr 001 films, including surface and interface effects. These studies show that thin ferromagnetic cap layers of Fe, Ni, and Co with a thickness of only 2­3 nm have a strong effect on the propagation and orientation of the I-SDW's in Cr. For thick Cr films there exist essentially only transverse I-SDW's propagating parallel to the film plane with the spins oriented normal to the plane and at right angles to the in-plane magnetization of the ferromagnetic cap layers. With decreasing Cr thickness a different transverse I-SDW grows at the expense of the in-plane ones, now propagating normal to the plane and with spins parallel or antiparallel to the film magnetization. At a Cr thickness of about 250 Å , the transverse out-of-plane I-SDW completely dominates the phase diagram of Cr. All other domains are suppressed and a spin-flip transition does not occur above 10 K in strong contrast to bulk. For in-plane propagation of the I-SDW we find a coexisting commensurate spin-density wave C-SDW which vanishes during the reorienta- tion to out-of-plane propagation with Cr thickness. Finally, for Cr thicknesses well below the period of the I-SDW, the Cr can only order as a C-SDW. The behavior of the SDW's in thin Cr films with ferromagnetic cap layers can be understood in terms of competing interactions at the rough interfaces inducing frustration and by finite-size and strain effects. We have also investigated the effect of Cu and Pd cap layers on the SDW. The Cu cover is similar to a Cr/vacuum interface, whereas the effect of the Pd cover is intermediate between the ferromagnetic layers and Cu. S0163-1829 99 11513-3 I. INTRODUCTION scattering. With this method either the Thomson or the mag- netic scattering cross section can be utilized. However, since The complex magnetic structure of Cr, comprising an in- no magnetic resonance enhancement occurs at the Cr K edge, commensurate antiferromagnetic spin-density wave I- the magnetic cross section is too weak for the investigation SDW , has been of continuing interest since its discovery in of thin films. The normal Thomson cross section yields in- 1959.1 Recent attention to the magnetic structure of Cr is in formation on the propagation of the charge-density CDW's part due to its use as spacer layer in giant magnetic resistance and strain waves SW's accompanying the spin-density materials, in particular in Fe/Cr Refs. 2 and 3 and Co/Cr waves, but not on the orientation of the Cr spins. Recently, superlatttices.4 Predictions of surface enhanced magnetic perturbed angular correlation spectroscopy PACS has been moments and topological ferromagnetic order on stepped Cr used for the analysis of SDW's in Cr films.7,8 This method is surfaces5 have spurred much experimental activity using sur- only sensitive to the spin orientation but not to the propaga- face science methods to characterize the magnetic surface tion of the SDW's. In contrast to synchrotron charge scatter- state of Cr.6 However, a characterization of the Cr magnetic ing, PACS experiments can distinguish between commensu- rate and incommensurate SDW's and can provide an state at surfaces and in thin films is not an easy task. Fre- estimate for the magnetic moments. Compared to the other quently used experimental techniques in the area of surface methods, neutron scattering remains the only experimental and thin-film magnetism, such as vibrating sample magne- technique which provides information on both spin orienta- tometry, superconducting quantum interference device mag- tion and propagation direction of the spin-density waves, on netometry, or magneto-optical Kerr effect are only applicable commensurate and incommensurate phases, as well as on the to ferromagnets. In the past, the most powerful method for magnetic moments. Examples of this will be shown further studying the magnetism of Cr has been neutron scattering below. due to its sensitivity to antiferromagnetism. On the other For an excellent and comprehensive review of the physi- hand, when studying thin films, the intensity of neutron cal properties of Cr we refer to the review paper by Fawcett.9 sources may not suffice. Nevertheless, we will show that Here, only the properties, which are of direct concern to this neutron scattering remains the most useful and direct method paper are briefly mentioned. Chromium has a bcc structure even for thin-film investigations. With elastic magnetic with a lattice parameter a 2.88 Å . As a 3d metal, Cr has neutron-diffraction the spin orientation and the propagation to be considered an itinerant antiferromagnet with an average direction of the spin-density waves can be analyzed. Further- magnetic moment of 0.46 B per atom at 4.2 K.10 If Cr had a more, commensurate and incommensurate SDW's can easily commensurate antiferromagnetic structure, the magnetic mo- be distinguished and the magnetic moments including their ment density at the corners would be opposite to the ones at orientation can be determined. Scattering with synchrotron the center of the bcc unit cell, as schematically indicated in x-ray radiation is a very important alternative to neutron Fig. 1 a , forming a commensurate spin-density wave C- 0163-1829/99/59 14 /9408 24 /$15.00 PRB 59 9408 ©1999 The American Physical Society PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9409 311 K, Cr is a paramagnet. Between 123 and 311 K the periodicity of the SDW depends markedly on the tempera- ture, increasing from 60 Å at 123 K to 78 Å at 311 K, as mentioned before. Under normal conditions, below the Ne´el temperature bulk Cr forms a polydomain state. A single domain state can, however, be achieved by cooling the sample through the Ne´el temperature either in a high external magnetic field or under tensile stress along one of the cube edges. As already pointed out, the spin-density-wave structure of Cr is usually incommensurate. However, elastic strains or chemical impu- rities may cause the SDW to be commensurate.11 For in- stance, alloying 3% Mn is sufficient for a complete transition to the commensurate phase. The commensurate antiferro- magnetic structure is designated as the AF0 phase. We have recently studied the spin-density-wave structure in thin epitaxial Cr 001 films as a function of film thickness FIG. 1. Schematic representation of the magnetic structure of Cr. The top shows the bcc unit cell of Cr with the arrows indicating and temperature12,13. Aside from a native oxide layer, these a commensurate antiferromagnetic spin structure. The lower panel films were not covered by another metallic film. The striking represents the incommensurate modulation of the antiferromagnetic features of these experiments include a single-Q longitudinal spin structure causing an incommensurate spin-density wave. Here I-SDW, propagating out-of-plane, an enhanced modulation a transverse I-SDW propagating in the 001 direction is shown period of the magnetic moments, an enhanced spin-flip tem- with the magnetic moments at right angles to the propagation direc- perature, and a commensurate antiferromagnetic phase with tion. SDW indicates the period of the I-SDW, which is about moments out of plane, which first appears close to the bulk 42­54 Cr monolayers depending on temperature. Ne´el temperature at 311 K and persists well above it. The SDW structure with a wave vector of Q 2 / 2 /a enhanced SDW can be attributed to strain effects. Possible explanations for the out-of-plane propagation of the ISDW 2.18 Å 1 commensurate with the lattice, where is the and the out-of-plane orientation of the Cr spins in our periodicity of the C-SDW. Furthermore, the magnetic mo- samples include surface pinning effects, hybridization with ments can be oriented parallel to any of the 100 crystallo- the buffer Nb layer, and interaction with the native Cr oxide graphic axes. Therefore, in thermal equilibrium three differ- layer at the surface. PACS experiments by Meerschaut et al. ent domains are expected to coexist for the different on one of the samples8 agree with the presence of an incom- orientations of the magnetic moments. Pure Cr exhibits, in mensurate and a commensurate phase with spins oriented fact, an incommensurate spin-density wave I-SDW struc- perpendicular to the surface. Unlike neutron scattering the ture, which consists of a sinusoidal modulation of the mag- PACS data also allows an independent determination of the netic moments, as shown schematically for a transverse relative volume fraction of both phases and the respective SDW in Fig. 1 b . Here the magnitude of the SDW wave magnetic moments of the Cr atoms in both phases. vector is Q (2 /a)(1 ) 2 /a 2 / SDW , where is Here we report on neutron and synchrotron scattering ex- a measure of the deviation from the commensurability and periments to study the effects that ferromagnetic and para- SDW is now the periodicty of the incommensurate SDW. magnetic cap layers have on the SDW's in epitaxial Cr 001 The I-SDW can be visualized by a spin lattice which is films. These investigations are important for a better under- slightly expanded as compared to the crystal lattice, yielding standing of interface effects between ferro- and antiferro- a beating effect between both, with a beat periodicity of magnetic layers with possible applications to exchange cou- SDW a/ . In bulk Cr SDW increases smoothly from 60 Å pling and interface bias effects. In particular for the Fe/Cr at 10 K to 78 Å at the Ne´el temperature of 311 K, corre- interface we know that the interlayer exchange integral is sponding to an increase from 42 to 54 Cr monolayers, re- negative, prefering an antiparallel alignment of the Fe and Cr spectively. magnetic moments at the interface.14 Thus, for a perfectly Next we need to distinguish between the propagation di- sharp interface we expect that a ferromagnetic Fe layer with rection and the orientation of the I-SDW. The propagation in-plane magnetization will project out a transverse SDW direction can be any of the three crystallographic 100 di- propagating perpendicular to the plane with spins in the rections. The orientation may, however, be either longitudi- plane, as depicted in Fig. 23. Almost ideal epitaxial growth nal or transverse. For longitudinal I-SDW's the spins are of Cr 001 on a Fe whisker appears to support this oriented parallel to the propagation direction Q ,(S Q ), notion.15,16 Domain images of a top Fe layer capping a Cr whereas for the transverse I-SDW's they are oriented perpen- wedge on a Fe whisker substrate show that the average mag- dicular to Q ,(S Q ). In bulk Cr one finds at low tempera- netization vector in the Fe domains rotates by 180°, when- tures a longitudinal I-SDW, refered to as the AF2 phase. ever the Cr layer thickness is incremented by one monolayer. Usually all three propagation directions occur with equal Additional phase slips are consistent with the incommensu- probability in three different domains. At 123 K a first-order rability induced by an I-SDW.16 However, interfacial rough- spin-flip transition occurs to a transverse I-SDW (AF1 ness may have a dramatic effect on the orientation of the phase , again coexisting in different domains. The transverse SDW's in the Cr films, on the domain formation of the I-SDW exhibits a first-order Ne´el transition at 311 K. Above SDW's, and possibly on the magnetic moments themselves. 9410 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 Computer simulations by Stoeffler and Gautier17 have shown that interfacial roughness may lead to a moment reduction. This appears to be supported by the Mo¨ssbauer experiments probing the hyperfine fields close to the Fe/Cr interface.18 In this paper we provide the first systematic study of spin- density waves in epitaxial Cr 001 films covered with ferro- magnetic and paramagnetic cap layers as a function of the Cr film thickness. Preliminary reports of these studies19,20 as well as a letter-style excerpt21 have been published else- where. This paper is organized as follows. In Sec. II we describe the scattering techniques used, including the selection rules for synchrotron and elastic magnetic neutron scattering, in Sec. III we provide information on the sample preparation FIG. 2. Overview of the satellite reflections as they occur for and sample characterizations, in Sec. IV we discuss the ex- different longitudinal and transverse incommensurate spin-density periments on SDW's in Cr films capped with Fe layers, in waves. Sec. V we report about equivalent measurements with ferro- magnetic cap layers of Co and Ni and with the paramagnetic components of the magnetization vector perpendicular to the layers of Cu and Pd. Finally in Sec. VI we discuss our results scattering vector. At least six scans along H, K, and L across and compare the effect of the different cap layers on the the satellite peak positions at two different orthogonal SDW in epitaxial Cr 001 films. In closing we want to em- reciprocal-lattice points are required for a unique character- phasize that this paper mainly deals with proximity effects ization of the SDW's in Cr. For thin films the z axis is de- between the SDW state in Cr films and ferromagnetic or fined to be perpendicular to the film plane, i.e., L is the paramagnetic cap layers. It does not discuss the interlayer out-of-plane direction whereas H and K are the two equiva- exchange coupling which results from this. For the latter lent in-plane directions. In practice, four scans across the properties we refer the interested reader to recent reviews22,23 010 and 001 positions in the K and L directions, respec- and to a number of recent publications.7,24­28 tively, have turned out to be most useful for thin films, since the two in-plane directions H and K can be regarded as equivalent. In this case the scan directions are always either II. SCATTERING EXPERIMENTS parallel or perpendicular to the scattering vector, which sim- The most powerful tool for the investigation of spin struc- plifies considerably the interpretation of the results. For ex- tures and phase transitions in Cr has been elastic neutron- ample, scanning along the K direction across the 010 posi- neutron scattering.29 More recently also x-ray and synchro- tion will detect an in-plane transverse SDW with spins either tron scattering experiments have been added.30­32,12,13 In parallel to H or L. Another K scan at the 001 position neutron-scattering experiments the magnetic moment of the reveals whether there are any in-plane components of the Cr neutrons couple to the magnetic moments of the magnetic magnetic moments. If satellite peaks exist in this scan, the material via dipolar interaction. Working out the elastic- spins lie in the plane, otherwise they are orientated in the scattering cross section, one obtains33,34 for the scattering perpendicular direction. Table I provides a summary of the cross section of an unpolarized neutron beam with a magne- four different scan directions and their interpretation accord- tization wave M (r ): ing to the selection rules. The magnetic spin-density-wave vector Q can also be d measured via nonresonant magnetic x-ray scattering, as has d n M q 2 sin2 q , 1 recently been shown by Hill et al.35 According to Bru¨ckel et al.,36,37 the nonresonant magnetic x-ray cross section for very high photon energies ( 100 keV) can be written as where q is the angle between M and q , and M q is the Fourier component of M (r ), corresponding to the scattering vector q k k . Equation 1 describes the scattering inten- d 2 C 2 S 2. 2 sity of a Bragg peak due to a magnetization wave M (r ), d x-ray r0 d which in the case of Cr represents the SDW with a polariza- tion vector S (r ) M (r ) and a spin-density-wave vector Q . Here, r2o is the classical electron radius, C is the Compton Figure 2 shows a partial reciprocal lattice of Cr. The wavelength, d is the interplanar lattice spacing, and S is the SDW satellite peaks are marked by open circles. They occur spin component perpendicular to the scattering plane. Thus, around the structurally forbidden bcc reflections. Any inten- nonresonant magnetic x-ray scattering with high-energy pho- sity in their vicinity has, therefore, to be of magnetic origin. tons is sensitive to the spin component perpendicular to the There are two selection rules to be obeyed for finding the scattering plane, and the selection rules are similar to those propagation direction and spin orientation of SDW's. First, for magnetic neutron scattering. However, this scattering the vector between any of the satellite peak positions and the contribution is rather weak and can only be applied to bulk next-nearest-allowed bcc reciprocal-lattice point determines samples.37 Resonant enhancement of the magnetic cross sec- the propagation direction of the SDW. Second, the magnetic tion does not occur in the vicinity of the Cr K edge. There- neutron-scattering cross section yields only intensity for fore, magnetic x-ray scattering on Cr films remains not prac- PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9411 TABLE I. List of four different neutron scans across the 001 and 010 reflections used in the present work and the information gained from these scans. The schematics indicate the positions of the satellites in reciprocal space observed for each of the I-SDW's listed. tical. The spin-density wave sets up a charge density and a nesses down to about 1000 Å . Investigation of thinner Cr strain wave in the Cr lattice. The amplitude of the charge- films requires the growth of multilayers, such that the signal density wave is only about 0.1 electrons and can hardly be can be added up from a stack of Cr layers. recognized in the presence of the normal charge scattering. We have carried out synchrotron experiments at the Na- The strain wave, on the other hand, is more easy to detect. tional Light Source in Brookhaven NSLS, beamline X22B The strain waves can be visualized as frozen phonons, yield- and at the HASYLAB in Hamburg beamline RO¨WI . ing the same selection rule for the scattering cross section as Neutron-scattering experiments were carried out at the re- a one-phonon cross section, i.e., the scattering vector and the search reactors of the National Institute of Standards and displacement amplitude form a scalar product (q * ), where Technology NIST, instrument BT2 , and of the Forschung- is the amplitude of the strain wave. Therefore, only sat- szentrum Ju¨lich instrument UNIDAS . In all cases we used a monochromater and analyzer. For the synchrotron experi- ellite reflections with a Q component parallel to the scatter- ments either two Si 111 crystals HASYLAB or two ing vector q will yield intensity, the others are silent. The Ge 111 crystals NSLS were used. For the neutron experi- charge-density wave and the strain wave are independent of ments we used highly oriented pyrolytic graphite as mono- the orientation of the magnetic moment. Therefore, the peri- chromator and analyzer. The /2 contamination was sup- odicity is only half that for the spin-density wave and the pressed with a stack of pyrolytic graphite filters. wave number is doubled. Thus, the satellite reflections due to the CDW or SW occur at the positions 2Q close to the bcc allowed charge peaks at 200 , 110 , etc., providing infor- III. SAMPLE DESIGN, GROWTH METHODS, mation on the propagation direction of the spin-density AND CHARACTERIZATIONS waves but not on their polarization see Fig. 2 . For informa- A. MBE growth tion on the spin direction and polarization, neutron scattering is required. Furthermore, with neutron scattering one can We have grown single crystalline bcc Cr 001 layers on easily distinguish between commensurate and incommensu- Al2O3 11¯02 substrates with a Nb 001 buffer layer using rate SDW's, since at the 100 position no scattering from molecular-beam epitaxial MBE methods. Using a well es- the chemical structure is allowed. In contrast, the huge al- tablished growth recipe already reported previously12 we lowed charge peak at the 200 position is prohibitive for achieved high-quality single-crystal growth of the Cr films detecting any commensurate phase with synchrotron experi- on the Nb buffer. The universal three-dimensional epitaxial ments. Therefore, neutron scattering has a distinct advantage relation between Nb and sapphire, which is essential for over synchrotron x-ray scattering as concerns the analysis of growing epitaxial metal films with single domains, has al- the polarization of the SDW and the detection of commen- ready been reported by Durbin et al.38 The Nb 111 direction surate contributions. The disadvantage of neutron scattering points along the c axis of the sapphire, whereas the 001 is the lower flux even at high flux neutron sources as com- direction of Nb is parallel to the Al2O3 11¯02 direction, pared to synchrotron sources. Therefore, elastic neutron scat- being the surface normal of the sapphire R plane. Since tering for the study of SDW's in Cr films is limited to thick- bcc-Cr grows parallel to bcc-Nb in spite of the large lattice 9412 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 3. RHEED and LEED pictures of the Cr 001 surface. a FIG. 4. Auger spectrum of the uncovered Cr surface of 2000 Å RHEED picture along the 100 azimuth, b along the 110 azi- thick Cr film. No lines other than from Cr are visible. muth; c and d show the corresponding LEED pictures of the Cr surface. B. RHEED, LEED, and Auger analysis mismatch of 13%, R plane orientated sapphire substrates are Figure 3 shows RHEED and LEED pictures of the Cr used for the growth of 001 oriented Cr films on Nb. We surface in two different orientations after completion of the have grown a series of Cr layers with thicknesses ranging growth and after annealing. In both azimuths along the 100 from 500 to 4000 Å as well as Fe/Cr 001 superlattices in and 110 direction, Laue zones of the zero and first-order this fashion. To maximize the amount of Cr in the beam, 5 reflections can be recognized. The LEED pictures are re- 5 cm2 large substrates were used for the samples intended corded with two different energies to probe the 100 a and for the neutron-scattering experiments. X-ray scattering and the 110 surface symmetry b . Figure 4 reproduces an Auger energy-dispersive x-ray spectra taken from the center and spectrum of the Cr surface after growth. Only the Cr LMM near the edges of the samples confirmed a perfect lateral lines at 447, 459, 489, 529, and 571 eV are visible. There are homogeneity obtained by continuous rotation of the samples no signs of any C, N, or O contaminations at the surface. during growth. Due to the 13% lattice mismatch, pseudomor- When depositing Fe on Cr, many RHEED oscillations can phic growth of Cr on Nb is excluded. As a result of the high be observed. This is shown in Fig. 5. lattice misfit the crystal quality of the first monolayers is not A more detailed RHEED study of the growth of Fe 001 very high according to reflection high-energy electron dif- on Cr 001 as a function of substrate temperature and growth fraction RHEED , but improves with increasing film thick- rate has been reported in Ref. 39. In Fig. 6 again RHEED ness. We find that a minimal thickness of the Cr buffer of and LEED pictures are reproduced after deposition of a 20 Å 200 Å is necessary for a sufficiently high film quality.39 The thick Fe cap layer on Cr. The sharp reflections seen in these Cr films are expanded in the film plane and relax with in- graphs are an indication for the high quality of our samples. creasing film thickness.40 The in-plane lattice relaxation fol- The Auger spectrum in Fig. 7 exhibits only Fe LMM lines at lows the usual strain relaxation model for metals.41 562, 596, 651, and 703 eV, but no lines from the Cr sublayer, The Cr 001 films were grown on Nb 001 at an opti- indicating that the Fe layer completely covers the Cr film. mized substrate temperature of 450 °C with a growth rate of Furthermore, the lack of any O, N, or C lines proves again 0.15 Å /s. At this temperature Cr 001 grows in a layer by the chemical purity of the sample. layer fashion and there is essentially no increase of the sur- face roughness noticeable with increasing film thickness. Af- ter growth, the Cr films were annealed at 750 °C for 30 min, which leeds to a considerable improvement of the surface roughness and crystal structural coherence, as shown by the RHEED and low-energy electron diffraction LEED pic- tures presented in the next section. After Cr growth and the annealing step, the samples were cooled to 300 °C and different 20 Å thick metal layers (M Fe,Co,Ni,Cu,Pd) were deposited on the Cr. The growth temperature for the M layer is a compromise between surface roughness and interdiffusion. Finally, as a protection against oxidation, the M films were covered with another 20 Å thick Cr film. This Cr layer passivates the other epitaxial films since at room temperature and under normal atmospheric conditions the Cr-oxide film thickness saturates at about FIG. 5. RHEED intensity oscillations observed during the 10­15 Å .42 growth of Fe 001 on Cr 001 . PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9413 FIG. 8. Small-angle x-ray reflectivity scan of a sample consist- ing from surface to substrate of a 20 Å thick protecting Cr-oxide layer, 20 Å thick Fe 001 cap layer, 3300 Å thick Cr 001 film, 100 FIG. 6. RHEED and LEED pictures from the surface of a 20 Å Å thick Nb 001 buffer layer on a Al2O3(11¯02) substrate. thick Fe 001 layer on Cr 001 . The top panels show RHEED pic- tures in the a 100 and b 110 azimuth. The lower panels show peaks describe the split peaks having a full width half maxi- the corresponding LEED pictures of the Fe 001 surface. mum of (2 ) 0.062°. This width translates into a struc- tural coherence length of 1600 Å or about 50% of the total C. X-ray characterization film thickness. The two peaks are superimposed on a broader We have characterized the structure of the Fe/Cr samples weak peak with a width (2 ) 0.33°. The broader peak with our laboratory x-ray sources. Small-angle reflectivity most likely reflects some disorder at the Cr/Nb interface, measurements were used to determine the thicknesses of the where most of the structural relaxation takes place during individual layers. Figure 8 shows a typical example from a growth. The scattering from the 20 Å thick Fe cap layer is sample with a layer sequence starting from the top: 20 Å Cr/ completely submerged in this broader component. In Fig. 9 b is shown a transverse scan through the Cr 002 reflec- 20 Å Fe/ 3300 Å Cr 001 / 500 Å Nb/Al2O3(11¯02). The tion at the position of the K 1 peak. The solid line shows a short period oscillations, which are enlarged in the inset, are fit to the data points with just one Gaussian peak with a due to the Cr layer thickness. The longer period oscillations width of 0.23°. The anisotropy in the in- and out-of- originate from the Nb buffer layer. Superimposed on these plane coherence lengths will play an important role in ex- two oscillations is an even longer period oscillation with a plaining the origin of C-SDW's in the system. broad maximum at 0.195 Å Ref. 1 due to the 20 Å thick Fe We have also studied the in-plane structure and epitaxial cap layer and the 20 Å thick Cr of Cr-oxide protective layer. relation of the Cr 001 using surface x-ray scattering meth- Next we study the structural coherence length and the ods under glancing incident and exit angles to the surface. mosaicity of the Cr layers. In Fig. 9 a a radial scan through Since we have reported earlier the epitaxial relation between the 002 Bragg peak of the same sample is shown as dis- Cr 001 and the Nb 001 buffer layer,40 only the structural cussed before. The scan was performed using a Cu rotating parameters will be discussed here. The in-plane structural anode source with a graphite monochromator in the incident coherence length for all samples reported in this paper lies beam. Due to the high structural coherence, the 002 peak is between 250 and 350 Å , and the in-plane mosaicity is on the split in the two components originating from Cu K 1 and order of 0.3­0.4°. These values are slightly worse compared Cu K 2 radiation. The solid line represents a fit to the data to the out-of-plane parameters for which we obtain coher- points using three Gaussian peaks. Two of the Gaussian ence lengths of 50­80 % of the total film thickness and out- of-plane mosaicities of 0.2­0.3°. FIG. 9. a : Radial x-ray scan through the Cr 002 reflection of a 3300 Å thick Cr film. The double peak is due to the indicent Cu radiation containing Cu-K 1 and Cu-K 2 spectral lines. The solid line is a fit to the data points with three Gaussian line shapes. b : Transverse x-ray scan through the out-of-plane Cr 002 peak, mea- FIG. 7. Auger spectrum of the surface of the 20 Å thick Fe layer suring the mosaic distribution in the film. The solid line is a fit to on Cr 001 . Only Fe Auger lines are visible, but no Cr lines, indi- the data points with one Gaussian line shape with a width of 0.23 cating that the Fe layer completely covers the Cr surface. degrees. 9414 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 grees. We used a He-Ne laser beam with a wavelength 632.8 nm and a power of 5 mW. We have chosen the plane of polarization to be perpendicular to the plane of in- cidence (s state . We have investigated the longitudinal and polar Kerr effect over a temperature range from 4­340 K. In Fig. 10 longitudinal MOKE measurements from a 20 Å thick Fe 001 layer on a 2100 Å thick Cr film are reproduced for different temperatures. For the whole temperature range the easy axis remains in the plane. We do not observe a reorien- tation of the easy axis or a reduction of the order parameter over the temperature range investigated here. Therefore, we can safely assume that our 20 Å thick cap layers are in a ferromagnetic state with in-plane magnetization. This is also true for the Co and Ni layers. The shape of the hystereses curves in Fig. 10 changes with temperature. In particular the coercivity field increases with decreasing temperature which is due to the development of magnetic order in the Cr layers when going through the Ne´el temperature. This behavior is in basic agreement with the observations reported earlier by FIG. 10. Magnetic hysteresis curves of the 20 Å thick Fe cap Berger and Hopster.44 layer on a 2100 Å thick Cr 001 film for different temperatures, measured with a high-resolution magneto-optical Kerr setup. IV. SDW IN CR FILMS CAPPED WITH FE LAYERS D. MOKE characterization A. Thick Cr films We have studied the magnetic properties of the overlayers via the magneto-optical Kerr effect MOKE using a setup 1. Synchrotron radiation experiments described in more detail in Ref. 43. With a Faraday modula- In Fig. 11 we reproduce scans with synchrotron radiation tor and applying lock-in techniques we achieve an angular at 30 K for a 2100 Å thick Cr 001 film covered with a 20 Å resolution of our Kerr magnetometer of better than 10 4 de- Fe 001 layer. In order to determine the propagation direc- FIG. 11. Synchrotron measurement of the strain waves in a 2100 Å thick Cr 001 film capped with a 20 Å thick Fe layer. The scans were taken at 30 K. With three scans along the H direction a , the K direction b , and the L direction c the propagation direction of the strain wave can be uniquely determined. In this case the strain wave propagates entirely in the plane along the 100 and 010 directions, while the out-of-plane propagation is completely suppressed. PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9415 FIG. 12. Synchrotron data of the strain waves in 2100 Å thick Cr 001 film capped with a 20 Å thick Fe layer. Scans are recorded along the K direction across the 011 peak for different temperatures. tions of the SDW, at least three scans have to be performed: Scans at the 011 peak along the K direction are shown in two scans at the 011 reflection in the K and H direction to Fig. 12 for different temperatures between 30 and 310 K. determine possible in-plane propagations, and one scan With increasing temperature the satellite intensity decreases along the L direction at the 002 peak position to determine continuously and the peak positions move smoothly towards out-of-plane components. As can be seen by the scans pre- the 011 commensurate position. From the peak position we sented in Fig. 11, CDW/SW satellite peaks exists only in the can calculate the period of the CDW, which is plotted as a vicinity of the 011 peak position along the H and K direc- function of temperature in Fig. 13. Also shown is the tem- tions. No satellite peaks are found at the 002 peak along the perature dependence for another thicker Cr film and for the L direction. This implies that the SDW or CDW in this bulk as reported by Werner et al.29 The period of the CDW sample propagates only in the plane. Since the H and K is enhanced in the thin films as compared to the bulk and satellites exhibit the same intensity, both propagation direc- scales inversely with the film thickness. An increased period tions, along H and K, appear to be equally populated. There for the CDW has already been noticed for plain Cr films and are no perpendicular components. From the width of the sat- can be explained by residual epitaxial strains.13 ellite peaks we determine a coherence length for the CDW/SW of about 300 Å . This is on the same order of The temperature dependence of the satellite peak intensity magnitude as the in-plane structural coherence length of the is shown in Fig. 14 for the two Cr films mentioned above, Cr film, indicating that structural domains limit the coher- and these results are also compared with the intensities for ence of the CDW/SW, not magnetic domains. Before we will bulk Cr measured with synchrotron radiation.32 The dashed determine the Cr spin orientation in relation to the propaga- line denotes the peak intensity calculated in analogy to the tion via neutron scattering, we first study the temperature BCS theory of superconductivity45 yielding dependence of the satellite peak intensity and of the peak position. FIG. 14. Temperature dependence of the intensity of the strain FIG. 13. Temperature dependence of the period of the strain wave satellite reflections as determined for the 2100 and 3300 Å waves in 2100 and 3300 Å thick Cr 001 films covered with a 20 Å thick Cr 001 films. The open squares show the corresponding mea- thick Fe layer. The open squares indicate the temperature depen- surements for bulk Cr from Hill et al. Ref. 32 . The dashed line dence of the period of the spin-density wave in bulk Cr, as deter- is a calculation of the intensity according to Eq. 3 with a Ne´el mined by neutron scattering from Werner et al. Ref. 29 . temperature TN of 311 K. The intensity is normalized to 1 at 100 K. 9416 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 15. Neutron scattering on a 3000 Å thick Cr 001 film covered with 20 Å thick Fe 001 layer to explore the the propagation directions and polarizations of the spin-density waves for different temperatures from 30 to 450 K. Scans are shown in different directions in the reciprocal space as sketched close to the respective panels, where the filled circles represent existing peaks while open circles indicate satellite positions scanned but no intensity detected at 50 K. For more details see text. I T 4 1/2 temperature of 389 36 K for a 3000 Å film.13 This value I 1 T , 3 0 T appears to be somewhat above the experimental result. N We have also varied the thickness of the Fe cap layers using the bulk Ne´el temperature TN 311 K. For most of from 8 to 100 Å , keeping the Cr thickness nearly constant at the temperature range the satellite intensities from the epi- a value of 2000 Å . In all cases the SDW propagates in the taxial films match those of the bulk. Only close to the Ne´el plane and the period of the CDW is again enhanced by the temperature may some deviation to higher values be present. same amount. This shows that the Cr properties observed are However, since the peak intensities close to TN are very low, due to the Fe/Cr interface and do not scale with the thickness it is difficult to judge whether or not the Ne´el temperature in of the ferromagnetic cap layer. Therefore, in the following the thin films deviates from the bulk. Using the relation be- experiments the thickness of the ferromagnetic cap layers tween external pressure and Ne´el temperature TN was kept constant at about 20 to 30 Å . This thickness as- 6.0 kbar 1 p 311 K,46 and the pressure p 13.5 sures that the layers are homogeneously magnetized and do 6 kbar induced by the epitaxy, we would expect a Ne´el not break up into small domains. The Curie temperature of PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9417 the Fe, Co, and Ni layers is also sufficiently high such that they do not interfere with the Ne´el state of the Cr layer. The MOKE measurements discussed in Sec. III D confirm the ferromagnetic state of these cap layers. 2. Neutron scattering In Fig. 15 we show the neutron results for a similar, 3000 Å thick Cr 001 film covered with 20 Å thick Fe layer, as used previously for the synchrotron experiments. The reason for using a slightly different sample is the larger surface area required for performing neutron-scattering experiments as compared to x-ray scattering. Figure 15 shows all four scan FIG. 16. Qualitative phase diagram for the spin-density waves directions described before for different temperatures. The in 3000 Å thick Cr 001 covered with a 20 Å thick Fe film, accord- scans are offset by constant amounts for clarity. Above or ing to the results of the neutron-scattering experiments shown in below each set of scans the scan directions are shown. Open Fig. 15. The arrows indicate the orientation of the magnetic mo- circles refer to satellite reflections which are allowed by the ments in the respective phases, where the vertical direction refers to selection rules but not detected in the scans at 100 K, while the 001 direction. LSDW and TSDW refers to the longitudinal closed circles refer to allowed and detected satellite reflec- and transverse incommensurate spin-density waves, respectively, tions. AF indicates a commensurate phase and P the paramagnetic phase. From 50 K up to about 311 K, satellite reflections due to The small labels ``in-plane'' and ``out-of-plane'' refer to the propa- incommensurate SDW's occur only in the K direction in the gation direction of the I-SDW's. vicinity of the 010 position, i.e., at (0,1 ,0). This con- firms the synchrotron results that the incommensurate SDW perature dependence of the order parameters for the com- propagates parallel to the film plane. This result, combined mensurate and incommensurate phases, it should not be con- with the absence of satellites in the scan along K through cluded that the paramagnetic phase coexists with the 001 determines the spin orientation to be perpendicular to incommensurate spin-density wave phase below the Ne´el the film plane. On the other hand, at 30 K we observe large temperature. As in all ferro- or antiferromagnetic systems the intensities for (0, ,1) satellites, while there are only weak long-range order or order parameter becomes reduced with satellite intensites at the (0,1 ,0) positions. Again apply- increasing temperature due to spin-wave excitations. Never- ing the selection rules described in Sec. II, this indicates a theless, this does not imply a coexistence between paramag- spin-flip transition between 30 and 50 K from a longitudinal netic and spin density wave phases below TN . The paramag- to a transverse SDW, both propagating in the plane along K netic phase with short range order exists only for T TN . but with spins rotating from in-plane below 40 10 K) to However, above the Ne´el temperature of the incommensurate perpendicular to the growth plane above 40 10 K). In the phase, commensurate and paramagnetic phases may indeed bulk, the spin-flip transition occurs at 123 K, whereas in the coexist. present thin film the transition is reduced to 40 10 K. This The most remarkable result of these measurements is the spin-flip transition could not be detected with synchrotron fact that above the spin-flip transition and contrary to our scattering and is only seen by neutron scattering. expectations, the SDW's propagate in the film plane having In addition to the incommensurate state, a commensurate their magnetic moments oriented perpendicular to the sur- antiferromagnetic spin strucure coexists starting from the face, i.e., at right angles to the Fe magnetization. This rather lowest temperature to temperatures of at least 425 K, well unexpected result signifies some roughness at the Fe/Cr in- above the Ne´el temperature for the incommensurate phase. terface causing frustration in the inter- and intralayer inter- At 30 K, the commmensurate 010 and 001 peaks indicate action. This will be discussed in more detail in Sec. VI. a C-SDW with spins oriented in-plane. Above the spin-flip transition at 40 10 K, only the 010 peak remains, consis- tent with a C-SDW with spins out-of-plane. Thus, we ob- B. 3000 Å thick Cr films sandwiched between Fe layers serve a reorientation of the C-SDW at the spin-flip tempera- Next we present results on the SDW's in a sandwich ture of the coexisting I-SDW. Again, with synchroton structure of 20 Å Fe/ 3000 Å Cr/20 Å Fe, i.e., without a scattering the commensurate phase could not be revealed. Cr/Nb interface as in the sample discussed in the previous The origin of the C-SDW will be discussed below in Sec. VI. paragraph. This experiment allows us to study the signifi- A qualitative phase diagram for the 3000 Å thick Cr 001 cance of the Cr/Nb interface for the magnetic phase diagram. film capped with a 20 Å Fe layer as derived from the First we should note that the growth of Cr on Fe does not neutron-scattering experiments is shown in Fig. 16. The rela- have the same high structural quality as the growth of Fe on tive volume fraction of the different phases was estimated Cr. This may lead to a broadening of the Bragg peaks. Sec- from the intensity of the incommensurate satellite or com- ond, two Fe/Cr interfaces on either side of a 3000 Å film mensurate Bragg reflections. At 30 K the sum of all intensi- may be viewed as equivalent to a 1500 Å thick Cr layer with ties was set to 100%. Since the in-plane SDW can propagate just one Fe/Cr interface. along the 100 and 010 directions, their weight is counted In Fig. 17 the neutron results from this sandwich structure twice. are reproduced. Only scans along the (0, ,1) and (0,1 While the phase diagram expresses relative intensities of ,0) positions are shown, the scans along L exhibit no the different coexisting phases and therefore shows the tem- structure at all and are therefore omitted. Starting from the 9418 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 17. Neutron-scattering experiments to explore the spin-density waves in a 3000 Å thick Cr 001 film sandwiched between 20 Å thick Fe layers on both sides as function of temperature. The scans show that the incommensurate spin-density wave propagates in the film plane and that the spins are oriented out-of-plane. A commensurate phase coexists from the lowest temperature of 11 K up temperatures far above the Ne´el temperature for the incommensurate phase. lowest temperature of 11 K, there is a very pronounced ing the volume fractions of the different phases as a function I-SDW, propagating in the plane with spins out-of-plane, of temperature is reproduced in Fig. 18. similar to the situation which we have seen before. This in- commensurate phase is present from the lowest temperature C. 500 Å thick Cr layers measured up to the I-SDW Ne´el temperature. At the same time a commensurate phase coexists with the incommensu- We will now reduce the Cr thickness further and study the rate phase exhibiting the same spin orientation. There is no phase diagram of the SDW's in 500 Å thick epitaxial spin flip transition observable above 11 K. The commensu- Cr 001 films. The neutron data are collected from a super- rate phase persists again to temperatures at least as high as lattice comprising five double layers of 20 Å Fe/500 Å Cr . 475 K. Interestingly, there is a second commensurate phase As mentioned previously this was done to provide enough Cr which occurs at about 200 to 250 K with spins oriented in the experiment. The neutron results are shown in Fig. 19. in-plane. As we will see below, it is important to note that The remarkable feature of these scattering data is the fact this additional C-SDW occurs in the same temperature range that now satellite reflections from the incommensurate phase in which the I-SDW vanishes. The phase diagram summariz- occur in the K scans as well as in the L scans. While the scans shown in the lower right corner reflect the same be- havior as before, a transverse I-SDW propagating out of the plane and with spins in the plane is clearly visible via the (0,0,1 ) and (0,1, ) satellite peaks. Therefore, in this thickness range we have a mixture of in- and out-of-plane propagating I-SDW's. The commensurate phase coexists throughout the temperature range studied. At low tempera- tures the spins of the C-SDW lie in planes perpendicular to the growth direction. At 200­250 K again a second com- mensurate phase occurs with spins in-plane and parallel to the surface, reminiscent of the C-SDW observed before in the 3000 Å thick Cr film sandwiched between Fe. Again, there is no spin-flip transition above 15 K. All I-SDW's have FIG. 18. Qualitative phase diagram for the commensurate and a transverse nature. We should also note that the peaks in incommensurate spin-density waves in a 3000 Å thick Cr 001 both commensurate and incommensurate phases are consid- sandwiched between 20 Å thick Fe layers, as derived from the erably broader than measured before, indicating shorter co- neutron scans shown in Fig. 17. herence lengths and more disorder in the spin lattice. This is PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9419 FIG. 19. Neutron scans similar to those shown in Fig. 15, now for a 500 Å thick Cr 001 film sandwiched between 20 Å thick Fe layers. In these scans a mixture of in- and out-of-plane transverse spin-density waves can be recognized. probably the result of the poly-Q domain state with rather D. 250 Å thick Cr film small domains for each individual Q state. We will now discuss the SDW's in a sample consisting of Unfortunately, for this sample no data for temperatures 10 double layers of 20 Å Fe/250 Å Cr . The neutron scat- above 310 K are available. However, we assume that also tering results are compiled in Fig. 21. For this sample we here the volume fraction of the AF0 phase has a maximum at observe only a transverse SDW T-SDW propagating out of about 350 K. the plane with spins in the plane. There are only (0,0,1 The phase diagram for the present sample is shown in Fig. ) and (0,1, ) satellite reflections visible, all other sat- 20. The most remarkable feature of this phase diagram is the ellite reflections have vanished. Therefore, the partial reori- fact that two instead of one transverse SDW with about equal entation, which was already noticeable in the last sample, is volume fractions coexist. This indicates a reorientation of the completed here. It is also interesting to remark that the in- SDW from propagating out-of-plane to in-plane, a reorienta- tensity of the (0,0,1 ) satellites is due to T-SDW's do- tion, which will continued as we decrease the thickness of mains with spins oriented along either the H or K direction. the Cr films. On the other hand, the (0,1, ) peaks are sensitive to the 9420 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 or paramagnetic films would also be of high interest, how- ever, much less is known on this subject at the present time. For example, reports on SDW's in Cr in proximity with Sn Ref. 47 and Ag Ref. 48 have been published recently. Nevertheless, none of these considered SDW's in thick Cr films. Here, we present the effect of thin ferromagnetic Co and Ni layers, as well as of paramagnetic Pd and Cu layers on the spin-density waves in thick Cr films. We discuss syn- chrotron and neutron-scattering results for roughly constant Cr layer thickness of about 2000 Å covered with the differ- ent ferromagnetic and paramagnetic layers. FIG. 20. Qualitative phase diagram for the commensurate and incommensurate spin-density waves in a 500 Å thick Cr 001 sand- A. Co cover wiched between 20 Å thick Fe layers, as derived from the neutron scans shown in Fig. 19. The arrows indicate the orientation of the The Co/Cr 001 interface has attracted much less atten- Cr spins in the different phases, where the vertical direction corre- tion in the past than the Fe/Cr interface. It is, nevertheless, of sponds to the 001 direction. considerable interest to compare these two interfaces as con- cerns their interlayer-exchange coupling and proximity ef- same T-SDW but with spins oriented only along the H di- fects on the SDW's in Cr. The somewhat lower interest in rection. These two sets of satellite peaks exhibit a 2:1 inten- Co/Cr is, in part, due to the mismatched crystal structures sity ratio, indicating that indeed the propagation of the and to the complex epitaxial relation between Co and Cr. T-SDW is purely out-of-plane, and that each domain with While both Fe and Cr have a bcc structure with a lattice spins oriented along the H and K direction occupies about mismatch of less than 0.4%, the equilibrium crystal structure the same volume fraction. The Ne´el temperature for the in- of Co is hcp. The first few monolayers of Co grow with a commensurate phase is again close to 310 K, as seen previ- pseudomorphic bcc structure on Cr 001 , where the original ously. hcp c axis lies in the film plane and is rotated by a constant In contrast to the samples studied before, there exists no angle of 45° with respect to the Cr 100 in-plane axis. With commensurate phase at low temperatures. The C-SDW only increasing Co thickness the structure continuously relaxes becomes visible at higher temperatures when the I-SDW back into the intrinsic hcp structure, while keeping the hex- vanishes. In the commensurate phase the spins are also ori- agonal c axis in the plane.49­51 This lattice relaxation ented parallel to the film plane. The phase transition for the strongly affects the magnetic anisotropy properties at the commensurate phase is presumably again between 400 and Co/Cr interface.52,43 Co on Cr exhibits a reorientational per- 450 K, i.e., much higher than the Ne´el temperature of the pendicular anisotropy.43 At a Co thickness of about 10 Å the incommensurate phase. easy axis rotates out of the plane but relaxes back into the The phase diagram for this sample is shown in Fig. 22. It plane with decreasing Co thickness. This reorientation is due is much simpler than the phase diagrams for the thicker to the concomitant structural phase transition of Co from hcp samples. Only one T-SDW propagating in the out-of-plane to pseudo-bcc. Here we work with Co thicknesses of 20 Å direction is seen which is the expected propagation and ori- and more. Thus the Co film is almost completely relaxed to entation of the SDW for a well-ordered Fe/Cr system. This the hcp structure and displays an in-plane easy axis. situation is shown schematically in Fig. 23. In Fig. 24 we show synchrotron results from a sample As we decrease further the thickness of the Cr layer, prop- consisting of 2300 Å Cr 001 covered with a 20 Å Co layer. erties connected with the exchange coupling between the Fe In the lower panel we reproduce K scans across the Cr 011 layers become important. Our results have been discussed reflection for different temperatures, in the upper panel an L previously in detail by Schreyer et al.24,27 and will not be scan at 15 K across the Cr 002 reflection. L scans at other dealt with here. Related work by Fullerton et al.25,26 should temperatures are omitted, since they are identical. Similar to also be noted. One important property of thinner Cr films not the Fe/Cr case of comparable Cr thickness compare Fig. further investigated here is the thickness-dependent reduc- 12 , we find in-plane propagation of the CDW/SW for all tion of the Ne´el temperature for the incommensurate temperatures. Compared to the Fe/Cr case, the satellite re- phase.26,27 Finally, at a thickness of less than 45 Å an incom- flections appear broader, reflecting a shorter coherence mensurate spin-density wave cannot be established anymore length for the CDW/SW in Co/Cr and more disorder in the at any temperature and TN becomes zero. In this thickness Cr spin lattice. range the Cr spin structure is completely commensurate an- In Fig. 25 the equivalent neutron results are shown. For tiferromagnetic and becomes strongly affected by lateral these measurements a different and larger sample was nec- thickness fluctuations inducing a spiral Cr spin structure and essary, such that the thicknesses are not identical. This strong noncollinear coupling between the Fe layers.27 should, however, not affect the main conclusions. The I-SDW's and C-SDW's are almost completely identical to V. CR 001... FILMS COVERED WITH CO, NI, CU, AND PD the case which we have discussed before for a 3000 Å Cr 001 film covered with Fe compare Fig. 15 . In particu- The foregoing experiments have demonstrated that a 20 Å lar, a spin-flip transition occurs close to 50 K. There is only thick Fe layer has a dramatic effect on the SDW state of Cr. one slight difference, as can be seen in the lower left panel of The proximity of Cr with other ferromagnetic, ferrimagnetic, Fig. 25. Above the spin flip transition there exists a small PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9421 FIG. 21. Neutron scans similar to those shown in Fig. 15, now for 250 Å thick Cr 001 films sandwiched between 20 Å thick Fe layers. In these scans we can clearly recognize that the incommensurate spin-density waves propagates solely out-of-plane. No commensurate antiferromagnetic structure exists at low temperatue, only above the Ne´el temperature for the incommensurate phase. fraction of a L-SDW propagating in the out-of-plane direc- The scans again show a similar behavior for the SDW as tion, which coexists with the much more dominant T-SDW, seen before for Fe and Co cap layers. Note, however, that for propagating in the film plane. this magnetic film the spin-flip transition is quenched at least Combining the x-ray and neutron results, the phase dia- to temperatures below 30 K. Therefore, the phase diagram is gram for this sample is shown in Fig. 26. Because of tech- simpler, consisting only of a T-SDW with in-plane propaga- nical reasons, data above 300 K are not available. However, tion and a commensurate SDW with spins out-of-plane. we assume from the experience with similar systems that the commensurate phase again persists up to about 400­500 K. C. Cu cover Compared to the previous discussions, the effect of a 20 B. Ni cover Å thick Cu layer on the phase diagram of 2000 Å Cr 001 is Similar synchrotron and neutron data for Cr 001 films completely different. In Fig. 29 characteristic neutron scans covered with a 20 Å Ni layer are shown in Figs. 27 and 28. from this sample are shown. The lower left panel confirms a 9422 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 22. Qualitative phase diagram for the commensurate and incommensurate spin-density waves in 250 Å thick Cr 001 films sandwiched between 20 Å thick Fe layers, as derived from the neutron scans shown in Fig. 21. The arrows indicate the orientation FIG. 23. Schematic representation of the magnetic structure de- of the Cr spins in the different phases. As compared to the phase picted for the situation present in 250 Å thick films in proximity diagrams shown previously, this one is much simpler consisting with Fe layers. The incommensurate spin-density wave propagates only of one dominating transverse spin-density wave at low tem- in the out-of-plane direction and the Cr spins are oriented in the peratures, with spins in the plane and propagation out-of-plane. plane, allowing for an antiferromagnetic exchange interaction at the Fe/Cr interface. L-SDW propagating out-of-plane for all temperatures start- ing at 15 K up to the Ne´el temperature. Therefore, there is no D. Pd cover spin-flip transition in this system. Second, there is no com- Finally we discuss the case of Pd on Cr 001 . Pd is a mensurate phase at low temperatures coexisting with the in- highly polarizable metal with a Stoner enhancement factor of commensurate SDW's as seen for the ferromagnetic cap lay- 9.3.53 Therefore, we expect a considerable interaction be- ers. The commensurate phase occurs first close to the Ne´el tween Pd and the top Cr layer. In fact, for monolayers of Cr temperature. A small amount of a T-SDW propagating in the on Pd 001 , a strong enhancement of the Cr magnetic mo- out-of-plane direction starts at about 100 K, but remains a ment has been predicted.54 Here we are not concerned with small fraction of the total volume. The phase diagram for this the magnetic moments at the Cr/Pd interface, however the sample is shown in Fig. 30. mutual influence is appreciable, as revealed by our experi- ments. FIG. 24. Synchrotron measurements of the strain waves in a 2300 Å thick Cr 001 film covered with a 20 Å thick Co layer. Similar to the Fe covered thick Cr films, the strain wave propagates in the film plane. PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9423 FIG. 25. Neutron-scattering experiments to explore the spin density waves in a 4000 Å thick Cr 001 film covered with a 40 Å thick Co layer for temperatures between 12 K and 300 K. Similar to the Fe covered thick Cr films, the incommensurate spin-density wave propagates in the film plane with spins oriented out-of-plane. Again a commensurate phase coexists from the lowest temperature of 12 K all the way up to 300 K. In Figs. 31 and 32 are shown the x-ray and neutron- between Fe and Cu. In Fe/Cr the incommensurate SDW is scattering results for a 2000 Å thick Cr film capped with a 30 only in-plane transverse, whereas in Cu/Cr it is only out-of- Å thick Pd film. At low temperatures, three phases coexist, plane longitudinal. In Pd/Cr we see a mixture of both. The an in-plane T-SDW, an out-of-plane L-SDW and a minor high magnetic polarizability of Pd appears to be able to ro- fraction of a C-SDW. The minority commensurate phase be- tate, at least partially, the SDW from out-of-plane to in- comes more dominant at higher temperatures with a maxi- plane. Note that the fraction of commensurate phase at low mum at about 300 K, and finally disappears above 400 K. In temperatures is connected with the fraction of the in-plane all three phases the Cr spins point out-of-plane parallel to the propagating T-SDW. film normal. According to the intensities we estimate that the There is another remarkable effect of the Pd cover on the L-SDW phase occupies about 40% of the sample volume and Cr SDW's. With a Pd cap layer the line shape of the x-ray is, therefore, the majority phase at low temperatures. satellite peaks along the K direction see bottom panel of Fig. Comparing the Pd/Cr data with the previous examples it 31 is smoother and more Gaussian like than for any other appears that the Pd effect on the SDW in Cr lies somewhere ferromagnetic cap layer, in particular for Fe Fig. 12 and Co 9424 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 plane is present at low temperatures and an enhanced spin- flip transition from longitudinal to transverse is observed in the thinner of the two samples investigated.13 Possible expla- nations for the out-of-plane propagation of the I-SDW and the out-of-plane orientation of the Cr spins include surface pinning effects, hybridization with the buffer Nb layer, and interaction with the native Cr-oxide layer at the surface. Deposition of a thin Cu layer on the Cr 001 surface does not change this situation very much. The spin-density wave is longitudinal and propagates out-of-plane. However, no spin flip to transverse occurs. We suspect that any other paramag- netic layer aside from Pd will not change these results. FIG. 26. Qualitative phase diagram for the commensurate and As we cover the Cr 001 film with a thin Fe layer, we incommensurate spin-density waves in a 4000 Å thick Cr 001 film expect that the in-plane magnetization of the Fe layer covered with a 40 Å thick Co layer, consistent with the neutron- matches the Cr spin structure, such that at the interface the scattering results shown in Fig. 25. Fe and Cr spins lie antiparallel, as schematically depicted in Fig. 24 . Therefore, in the Pd/Cr system less disorder ap- Fig. 34 a . This requires a reorientation of the spin-density pears to be present and the coherence length for the SDW's wave from a longitudinal out-of-plane propagation to a trans- is larger than in other systems. verse out-of-plane propagation with spins in the plane. The synchrotron and neutron-scattering experiments dis- cussed above contradict this expectation. The overriding ob- VI. DISCUSSION servation for all thick Cr 001 films covered with a ferro- magnetic layer Fe,Co,Ni is an incommensurate transverse A. Influence of overlayers spin-density wave, which, contrary to expectation, propa- The synchrotron and neutron-scattering experiments de- gates parallel to the film plane and with spins pointing out- scribed above provide a very clear and systematic picture of of-plane, perpendicular to the in-plane magnetization of the the proximity effects between the spin density waves in ep- ferromagnetic films. From this observation we can immedi- itaxial Cr 001 films and magnetic or nonmagnetic cover lay- ately conclude that the specific exchange interaction between ers. In order to work out the essential factors, we will discuss Cr and the ferromagnetic layer, which is antiferromagnetic only the dominating phases observed. Let us start with an for Fe/Cr and ferromagnetic for Co/Cr, cannot be responsible uncovered, thick Cr 001 film. In these films a single domain for the unexpected propagation direction of the SDW. There with a longitudinal spin-density wave propagating out-of- must be another reason. FIG. 27. Measurements with synchrotron radiation of the strain waves in a 2200 Å thick Cr 001 film covered with a 20 Å thick Ni layer. Similar to the Fe covered thick Cr films, the strain waves propagate in the film plane. PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9425 FIG. 28. Neutron-scattering experiments revealing the spin-density waves in a 2000 Å thick Cr 001 film covered with a 40 Å thick Ni layer for temperatures between 30 and 450 K. Similar to the Fe covered thick Cr films, the incommensurate spin-density wave propagates in the film plane with spins oriented out-of-plane. In addition, a commensurate phase coexists from the lowest temperature to at least 400 K. The following discussion of Fe/Cr interface may easily be could form either in the Fe or the Cr layer Figs. 34 c or generalized to the other ferromagnetic/Cr interfaces studied. 34 d . For an intermediate JFe-Cr the system can react by Surface roughness introduces steps of varying heights. Any forming a domain wall along the Fe/Cr interface by reorient- step height with an odd number of atomic layers introduces ing the Cr perpendicular to the Fe Fig. 34 e . Reorientation frustration to the interlayer exchange coupling at the Fe/Cr of the Cr moments requires less energy than reorientation of interface due to the antiferromagnetic order of the Cr see the Fe moments. In the latter case work has to be done Figs. 34 b ­34 e . How the system overcomes this frustra- against the shape anisotropy energy, which is not required tion depends on the relative magnitude of the intralayer ex- for the antiferromagnetic Cr film. Recent computer simula- change energies JCr-Cr and JFe-Fe and the interlayer exchange tions using a classical Heisenberg Hamiltonian for describing energy JFe-Cr . In case of a very small JFe-Cr the frustration at the spin structure and exchange coupling for the system stud- the interface can be overcome by breaking the antiferromag- ied here, confirm that in the presence of steps, the Cr mag- netic coupling at the Fe/Cr interface Fig. 34 b , thus avoid- netic moments reorient in the direction perpendicular to the ing the formation of domain walls in the Fe or Cr. On the Fe moments21 Fig. 34 e consistent with our experimental other hand, in the case of a very large JFe-Cr a domain wall observation. Even some interdiffusion at the interface may 9426 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 29. Neutron-scattering experiments revealing the spin-density waves in a 2000 Å thick Cr 001 film covered with a 20 Å thick Cu layer for temperatures from 15 to 450 K. Here the incommensurate spin-density wave propagates in the out-of-plane direction and has dominantly longitudinal polarization. be allowed without changing this conclusion. The simulation Figure 33 summarizes the spin-density waves observed in also indicates that the reorientation causes some spin disor- thick Cr films at about 100 K and covered with different der in the Cr spin structure close to the interface. With graz- ferromagnetic and paramagnetic layers. The origin of the ing incidence surface scattering methods, where the penetra- commensurate phase is considered in the following. tion depth of the beam can be controlled by the glancing angle of the beam to the surface, we have in fact verified this disorder.55 The similarity of the results for all ferromagnetic B. Origin of the commensurate spin-density waves in Cr films overlayers implies that the above discussion is valid for Co There is another dominating feature of the Cr spin struc- and Ni overlayers as well. ture in thick films to be discussed. As soon as the transverse As mentioned before, due to the high polarizability of Pd, spin-density wave propagates in the plane, there occurs si- the effect of a Pd cover on the the SDW in thick Cr 001 film multaneously a commensurate antiferromagnetic spin struc- is somewhere between the ferromagnetic and the uncovered ture coexisting with the incommensurate spin-density wave. case. The reorientation is only partial, such that longitudinal This observation can be explained as follows. A spin density and transverse SDW's coexist. wave, in order to develop, requires a structural coherence PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9427 I-SDW. Recent surface neutron-scattering experiments prob- ing the spin-density waves as a function of depth are consis- tent with this layering of the incommensurate and commen- surate phases.55 It should be noted that this model also holds for those samples which have a Cr/Fe/Nb growth sequence instead of Cr/Nb. Since the Fe layers are always only 20 Å thick, the Fe cannot completely relieve the strain imposed by the misfit with the Nb. Instead, the poor crystal quality will extend into the subsequent Cr layer, causing a small , and thus a C-SDW close the Nb interface. Vice versa, in uncovered thick Cr films the longitudinal spin-density wave propagating normal to the film plane FIG. 30. Qualtitative phase diagram for the commensurate and probes the perpendicular structural coherence length . incommensurate spin-density waves in a 2000 Å thick Cr 001 film Since is always much larger than , an I-SDW can covered with a 20 Å thick Cu layer, according to the the neutron- develop in these latter films. The same is also true for the scattering results shown in Fig. 29. Cr 001 film capped with a Cu layer. Reviewing the phase diagrams presented above, addi- length , which is larger than roughly one period of the spin tional C-SDW's also occur close to T density wave, i.e. N of the I-SDW. In SDW . Neutron-scattering experiments nearly all cases, either a new C-SDW phase occurs near TN by Fullerton et al.26 and Schreyer et al.27 have shown that for of the I-SDW or the intensity fraction of the existing C-SDW any film thickness much smaller than SDW , the Cr SDW is enhanced considerably. Keeping in mind that SDW in- becomes commensurate. This applies also to our case. The creases strongly upon approaching TN , it is plausible to as- transverse SDW in thick epitaxial Cr films, forced by the sume that a C-SDW forms whenever SDW is on the order of ferromagnetic cap layer combined with interfacial roughness a limiting length scale. to propagate in the plane, probes the in-plane structural co- Three different cases can be distinguished. herence length . As outlined in Sec. III A, close to the 1 The limiting length scale can be the film thickness tCr Cr/Nb interface where the misfit is large and the structural for out-of plane propagation and tCr), as shown experi- relaxation rapid, the structural coherence of the Cr film is mentally by Schreyer et al.27 and theoretically by Shi and poor. In this part of the film only a commensurate antiferro- Fishman.56 magnetic Cr spin structure can develop. Further away from 2 For very thick films and out-of-plane propagation the the Cr/Nb interface the film quality improves significantly, limiting length scale would be instead, since then i.e., increases, allowing a formation of an in-plane tCr . FIG. 31. Synchrotron measurements of the strain waves in a 2200 Å thick Cr 001 film capped with a 20 Å thick Pd layer. The top panel shows a scan taken at 15 K along the L direction across the 002 peak, the bottom panel shows scans taken at different temperatures along the K direction across the 110 reflection 9428 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 32. Neutron-scattering experiments revealing the spin-density waves in a 2000 Å thick Cr 001 film covered with a 30 Å thick Pd layer for temperatures between 15 and 450 K. A mixture of spin-density waves can be recognized, partly with longitudinal polarization and propagating in the out-of-plane direction and partly with transverse polarization propagating in the film plane. 3 Finally, for in-plane propagation, the limiting length ring at high temperatures in our samples may be due to scale is . strain, induced by the large lattice misfit between the Nb This picture implies that in case 2 SDW would have to buffer and the rest of the sample. increase up to values on the order of 2000 Å which are the On the other hand, strain is less likely to explain the oc- largest coherence lengths measured for our thickest Cr curence of the coexisting C-SDW for in-plane propagation of films. Such a large SDW may be consistent with our data, the I-SDW at low temperatures. Contrary to the expectation since close to TN a strongly diverging SDW would lead to of Poisson-like elastic behavior, x-ray measurements of the satellites merging into the commensurate peak position while in- and out-of-plane strain in Cr 001 /Nb films as function of their intensity drops dramatically. Cr thickness show a surprising similarity in magnitude and However, an alternative explanation must be considered. sign. Thus, we do not observe a drastic anisotropy between It should be noted that strain is well known to cause in- and out-of plane strain, whereas we do observe a drastic C-SDW's in Cr.9 Specifically, it has been found that in anisotropy in the in- and out-of-plane coherence lengths. strained Cr powders the samples change from incommensu- Therefore, we attribute the occurrence of the C-SDW for rate into C-SDW at elevated temperatures before they be- in-plane I-SDW propagation to the anisotropy in the in- and come paramagnetic.57 Therefore, the C-SDW phase occur- out-of-plane coherence lengths as the dominating factor. Al- PRB 59 SPIN-DENSITY WAVES AND REORIENTATION . . . 9429 though we cannot exclude the significance of strain effects it should be noted that in any case the large lattice misfit at the Cr/Nb interface is the underlying cause of these C-SDW's. Finally, for small Cr thicknesses the strong tCr dependence of the phenomena indicates, that the limiting length scale tCr , not strain at the Cr/Nb interface, is the important parameter determining the existence of a C-SDW in our samples. In conclusion, the presence of C-SDW's in our samples can be explained by strain as well as finite-size effects in- duced by the limiting length scales tCr , , or , depending on the propagation direction of the I-SDW. FIG. 33. Phase diagram for spin-density waves in about 3000 Å thick Cr 001 films covered with different ferromagnetic and para- magnetic thin layers. The phase diagram reflects the situation ob- C. Film thickness dependence served at about 100 K. The arrows indicate the orientation of the Cr magnetic moments, where the vertical orientation refers to the out- Next we discuss the dependence of the spin-density waves of-plane direction. on the Cr film thickness. Systematic studies are only avail- able for Cr 001 films covered with Fe layers. However, we pletely. As outlined in the previous section, this behavior is expect similar behavior for any ferromagnetic/Cr interface. the result of a strong anisotropy in the crystalline in-plane As the Cr film thickness is reduced, we observe a reori- and out-of-plane coherence lengths. entation of the I-SDW from propagating parallel to the film plane to normal to the film plane. This reorientation starts at a Cr film thickness of about 1000 Å , and is finished at 250 VII. SUMMARY Å . Between 250 and about 45 Å there is only a single In summary, we have presented extensive synchrotron transverse I-SDW propagating normal to the film plane and x-ray and neutron-scattering results probing the spin-density with spins in the plane. This is the situation which we ex- waves in epitaxial Cr 001 films. In particular, we have stud- pected in the beginning and which is schematically depicted ied the effect of ferromagnetic and paramagnetic thin cap in Fig. 23. layers on the spin-density-wave state in the Cr. With a 20-Å The reorientation of the spin-density wave indicates that -thick ferromagnetic Fe cap layer and varying Cr film thick- with decreasing thickness more energy is gained by forming ness, the scenario for the proximity effect between the ferro- domain walls in the Cr Fig. 34 d than by forming a 90° magnetic and spin-density-wave state can be described as wall along the Fe/Cr interface Fig. 34 e . The case of do- follows. For large Cr film thicknesses and a perfect Fe/Cr main walls in the Fe Fig. 34 c , which would lead to a interface without roughness a single incommensurate trans- vanishing magnetization of the Fe layers, is not observed verse SDW with propagation out-of-the plane and spins in experimentally. Since the energy gained by domain-wall for- the plane is expected. Instead, we observe an incommensu- mation in the Cr film scales with the Cr film thickness tCr , rate transverse SDW propagating in the film plane with spins while the energy gained by reorienting the Cr moments per- pointing out-of-plane at a right angle to the in-plane magne- pendicular to the Fe/Cr interface scales with the separation L tization of the cap ferromagnetic layer. The incommensurate of the steps and kinks at the interface, we expect that the SDW coexists with a commensurate SDW starting already at crossover from out-of-plane to in-plane spin orientation takes the lowest temperatures investigated. In the commensurate place roughly when the condition JCr-Cr tCr JFe-Cr L is phase the spins have the same out-of-plane spin orientation fullfilled, where JCr-Cr and JFe-Cr are the Cr-Cr and Fe-Cr as in the incommensurate phase. The incommensurate phase exchange energies, respectively. Computer simulations of exhibits a Ne´el temperature essentially identical with the the Cr spin structure with a rough Fe/Cr interface confirm bulk Ne´el temperature, whereas the transition from the com- this estimate.21,58 Since the JCr-Cr and JFe-Cr exchange ener- mensurate antiferromagnetic structure to the paramagnetic gies are roughly on the same order of magnitude, we expect state occurs at much higher temperatures of about 450 K. a reorientation at a film thickness of tCr L. X-ray-scattering The Cr spin structure in relation to the ferromagnetic cap experiments on the interfacial roughness of similarly pre- layer can be understood in terms of interfacial roughnesses, pared Fe/Cr interfaces confirm this estimate.24 If the Cr film causing frustrations of the exchange coupling at the inter- thickness is reduced well below the period SDW of the face, which in turn causes a reorientation of the Cr moments. SDW, the SDW state collapses due to finite-size effects and As the Cr film thickness is decreased, energy gain from Cr becomes commensurate antiferromagnetic, accomodating forming domain walls in the Cr begins to dominate the re- the frustration due to the interface structure by spirals of orientation effect and the Cr spins start to align parallel to the opposing sense of rotation.27 In Fig. 35 the spin-density- ferromagnetic layer. When this procedure is finished at a Cr wave states in epitaxial Cr 001 films covered with a ferro- thickness of about 250 Å , the incommensurate SDW propa- magnetic Fe layer are qualitatively summarized as a function gates perpendicular to the film plane with spins oriented par- of the Cr film thickness, reproducing the situation present at allel to the film plane. During this rotation of the I-SDW the a temperature of about 100 K. The data for the thinnest C-SDW phase vanishes. Finally, when the Cr film thickness samples from Ref. 27 have been added for completeness. becomes much smaller than the period of the incommensu- A striking feature of the phase diagram is that upon reori- rate SDW, the SDW collapses and the Cr film becomes com- entation of the transverse I-SDW from in-plane to out-of- mensurate antiferromagnetic with a Ne´el temperature of 500 plane propagation the concomitant C-SDW vanishes com- K, i.e., somewhat higher than in the commensurate state dis- 9430 P. BO¨DEKER, A. SCHREYER, AND H. ZABEL PRB 59 FIG. 35. Qualitative phase diagram of the spin-density waves in epitaxial Cr 001 films covered with thin a Fe layer as a function of the Cr film thickness. The phase diagram represents the situation at about 100 K. The arrows indicate the orientation of the Cr magnetic moment, where the vertical direction corresponds to spins oriented perpendicular to the film plane. density wave propagating normal to the film is present in FIG. 34. Schematic and simplified representation of the inter- epitaxial Cr 001 films of 500­2000 Å thickness, capped ei- face between a thin ferromagnetic Fe layer and a thicker antiferro- ther with a native oxide layer or with a paramagnetic layer of magnetic Cr film. The white arrows indicate the orientation of the low polarizability. A transverse I-SDW propagating in the magnetic moments in the Fe film, the black arrows the Cr magnetic film plane can be generated in Cr 001 films of about 3000 Å moments. a represents an ideal and flat interface with antiferro- thickness when covered with a ferromagnetic layer. Finally, magnetic coupling between the Fe and Cr moments. b ­ e show a transverse I-SDW propagating in the out-of-plane direction interfaces with monoatomic high steps causing frustration of the is present in thin Cr 001 films of less than 250 Å covered interface exchange coupling. The frustration can be overcome be again with a ferromagnetic layer. Commensurate SDW's can formation of a domain in the Fe layer c , in the Cr film d , or by be obtained by limiting the Cr thickness or crystalline coher- a reorientation of the spin-density wave e . The latter case is ob- ence lengths to values well below SDW , or by increasing served experimentally in thick Cr films. the temperatures to values above TN of the I-SDW. cussed before.59 Fe, Co, and Ni cap layers have the same All the foregoing results lead us to the final and important effect on the propagation of the SDW in Cr, although the conclusion that the spin-density waves in epitaxial Cr 001 interface exchange coupling may be opposite, i.e., antiferro- films can easily be manipulated in a systematic and predict- magnetic in the case of Fe/Cr and ferromagnetic in the case able fashion by the choice of the magnetic cover, the inter- of Co/Cr. A cap layer of Cu on Cr has essentially the same facial roughness, and the chromium film thickness. effect on the SDW's as a Cr/vacuum or a Cr/Cr2O3 interface. In either case we observe a dominant longitudinal SDW ACKNOWLEDGMENTS propagating normal to the film plane. The effect of a Pd cap layer on Cr is different from other paramagnetic cap layers. We would like to acknowledge the fruitful contributions Due to the high polarizability, Pd behaves as a weak ferro- of P. Sonntag and the collaborations with our co-workers at magnet causing a a partial rotation of the SDW. Thus in the different neutron and synchrotron facilities where we Pd-capped Cr films, longitudinal out-of-plane and transverse have collected our data, in particular J. Borchers and C.F. in-plane SDW's coexist. Majkrzak at NIST, K. Hamacher and H. Kaiser at MURR, D. The occurrence of the commensurate phase can be attrib- Gibbs, B. Ocko, and T. Thurston, at NSLS, and F. Gu¨thoff uted to strain and finite-size effects. 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