PHYSICAL REVIEW B VOLUME 60, NUMBER 6 1 AUGUST 1999-II Correlation of short-period oscillatory exchange coupling to nanometer-scale lateral interface structure in Fe/Cr/Fe 001... C. M. Schmidt, D. E. Bušrgler,* D. M. Schaller, F. Meisinger, and H.-J. Gušntherodt Institut fušr Physik, Universitašt Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland Received 30 March 1999 We investigate Fe/Cr/Fe 001 trilayers grown on Ag 001 /Fe/GaAs 001 substrates at different temperatures. By changing the substrate temperature of the bottom Fe film during deposition, but otherwise keeping the preparation parameters constant, we are able to tailor the roughness of the Fe/Cr interfaces. The interfaces are characterized by means of scanning tunneling microscopy STM . In these differently prepared systems, a clear change of the short-period oscillation amplitude is observed by magneto-optical Kerr effect measurements. A statistical analysis of the STM images allows us to extract the lateral length scale over which the Cr thickness is constant, and it turns out that areas of constant Cr thickness with a diameter larger than 3 ­4 nm are mandatory for the evolution of short-period oscillations. Two mechanisms are discussed which can explain the observed correlation between structure and magnetism, one linked to the propagation of the coupling through the spacer and the other to the response of the ferromagnetic layers to the transmitted exchange field. S0163-1829 99 04430-6 I. INTRODUCTION tures on high-quality substrates. In the whisker system, Pierce et al.6 have demonstrated by Fe/Cr/Fe 001 trilayers and Fe/Cr 001 multilayers were means of scanning tunneling microscopy STM that Cr the first systems to exhibit such exciting properties as mag- grows layer-by-layer at a substrate temperature TS 570 K. netic interlayer exchange coupling,1 giant Fe/Cr/Fe 001 systems prepared accordingly exhibit short- magnetoresistance,2­4 oscillatory exchange coupling,4 and period oscillations between ferromagnetic FM and antifer- short-period oscillatory exchange coupling.5 Although romagnetic AF coupling, i.e., the alignment of the magne- throughout the last decade Fe/Cr/Fe 001 has served as a tizations in the two Fe layers changes from parallel to model system in the field of thin-film magnetism and by now antiparallel and vice versa. In the room-temperature case the belongs to the best studied systems both experimentally and authors explain and nicely model the vanishing of the short- theoretically, many questions are still open. In this paper we period oscillations by weighting a short-period oscillation focus on the short-period oscillatory component of the ex- coupling curve with a Gaussian representing the thickness change coupling and in particular on its dependence on the distribution of several exposed layers of the rough room- structural properties of the interfaces in symmetric Fe/Cr/ temperature Cr growth front. For growth at elevated temperatures on Ag 001 /Fe/ Fe 001 trilayers. GaAs 001 substrates, an exchange coupling contribution fa- It is well known that the structure of the interfaces and voring a perpendicular arrangement of the magnetizations thereby the sample preparation procedure has a crucial influ- (90° coupling is found to dominate. Although several mod- ence on the coupling behavior. Basically, two experimental els relate the 90° coupling to thickness fluctuations of the approaches have been chosen to tailor Fe/Cr/Fe 001 sys- spacer originating from interface roughness,13­15 little is tems: i Fe/Cr 001 bilayers that are grown on Fe 001 known about the quality of the Fe/Cr interfaces and the re- whisker surfaces with terraces of a width of approximately sulting Cr thickness fluctuations. 1 m,6­8 and ii symmetric Fe/Cr/Fe 001 trilayers that are Therefore, the purpose of the present paper is i to evaporated on other substrate surfaces, in particular, on present a detailed real-space study of the relevant surfaces Ag 001 /Fe/GaAs 001 .9,10 As presented in a previous occurring during growth of differently prepared Fe/Cr/ study,11 the surfaces of Fe 001 films on Ag 001 are later- Fe 001 sandwich structures grown on Ag 001 /Fe/ ally structured on the nanometer scale rather than on the GaAs 001 substrates and ii to correlate the specific ex- micrometer level. Additionally one has to be careful with change coupling characteristics to the respective respect to chemical cleanness. Similar structural properties morphological properties. have been reported for Fe 001 films grown on other sub- The paper is organized as follows: in Sec. II information strates, such as MgO 001 .12 about the instrumentation and experimental procedures is Common to all approaches and generally accepted is the given, and the sample structure is introduced. In Sec. III we observation of long-period exchange coupling oscillations of present our results concerning the surface morphologies of about 10 to 12 monolayers ML spacer thickness for growth the bottom Fe 001 layers and the Cr 001 spacer layers to- by sputtering or by molecular-beam epitaxy MBE at room gether with a comparison of the exchange coupling proper- temperature, and the appearance of a superimposed short- ties of different samples. In Sec. IV we discuss the results period oscillatory exchange coupling component of close to with respect to the correlation of the magnetic and the struc- 2 ML spacer thickness for MBE growth at elevated tempera- tural properties. 0163-1829/99/60 6 /4158 12 /$15.00 PRB 60 4158 ©1999 The American Physical Society PRB 60 CORRELATION OF SHORT-PERIOD OSCILLATORY . . . 4159 TABLE I. Notation and substrate temperature TS of the Fe/Cr/ Fe 001 trilayers. Note that both in the MT520 and in the MT570 case all Fe/Cr interfaces are formed at 520 K. Notation Layer TS(K) RT Top Fe 300 Cr 300 Bottom Fe 300 MT520 Top Fe 520 Cr 520 Bottom Fe 100/520 MT570 Top Fe 520 Cr 520 Bottom Fe 100/570 FIG. 1. Layer structure of the Fe/Cr/Fe 001 samples. An Ag 001 buffer layer deposited on Fe-precovered GaAs 001 serves as substrate for the magnetic trilayer. All involved layers are char- and the film thickness is controlled by a quartz microbalance. acterized by AES, XPS, LEED, and STM prior to deposition of the The cleanness of each layer is confirmed by XPS and AES. subsequent layer. Parallel aligned crystallographic axes in the sur- All morphological, chemical, and magnetic characterizations face plane defining the epitaxial relationships are given in the table are performed at room temperature. For the ex situ Kerr mi- together with the layer thicknesses. The Cr interlayer is wedge- shaped with the slope along a magnetic easy croscopy analysis the samples are coated with a 5-nm-thick 100 axis of the Fe 001 layers. Ag protection layer and with a ZnS layer for the enhance- ment of the magneto-optical contrast. MOKE measurements II. EXPERIMENTAL in UHV before and after coating with Ag do not show any Sample preparation and all measurements, with the excep- effect of the cap layer on the width of the plateaus in the tion of Kerr microscopy, are performed in an ultrahigh hysteresis loops. vacuum UHV system with a base pressure of 5 10 11 In order to be able to study the influence of the Fe/Cr mbar that is equipped with a MBE deposition system, STM, interface morphology on the exchange coupling, we prepare low-energy electron diffraction LEED , Auger and x-ray Fe/Cr/Fe 001 sandwich structures by applying three differ- photoemission electron spectroscopy AES, XPS , and a ent recipes. They differ from each other by the substrate magneto-optical Kerr effect MOKE setup which we oper- temperatures during the growth of the Fe and Cr layers. We ate in the usual longitudinal configuration with the external will use the acronyms RT and MTT throughout this paper to magnetic field applied parallel to a 100 magnetic easy axis label the trilayers: RT stands for samples where the whole of the Fe 001 layers. trilayer is deposited at room temperature. MTT refers to Figure 1 depicts a schematic representation of the layer samples prepared according to a two-stage ``mixed- structure of the Fe/Cr/Fe 001 samples, the epitaxial relation- temperature'' preparation sequence: It involves the evapora- ships, and the thicknesses of the different films. A 150-nm- tion of the first 2 nm of the bottom Fe layer at 100 K and the thick Ag 001 buffer layer grown on Fe-precovered final 3 nm at T 570 K and T 520 K, respectively. The Cr GaAs(001) wafers at T interlayer and the top Fe layer are in both cases deposited at S 380 K and postannealed at TA 570 K serves as a substrate system for the magnetic trilay- 520 K. The notation is summarized in Table I. Because of ers. Recently we have presented a detailed investigation of the low-temperature-growth of the very first atomic layers of the morphological properties of the Ag 001 buffer layer:16,17 both the MT520 and the MT570 systems, these trilayers are STM images reveal terraces with a mean width of approxi- free of Ag substrate atoms.11 The degree of interdiffusion at mately 35 nm that are separated by monatomic steps. Most the Fe/Cr interfaces found in Refs. 18 and 19 can be ex- of these steps originate from screw dislocations which are pected to be identical for the MT520 and the MT570 systems found to be the representative kind of defect in this substrate since all interfaces are formed at the same temperature 520 system. Meanwhile, we have been able to extend the average K . Ag terrace width by about a factor of 3 by using GaAs 001 wafers which are passivated by an amorphous As cap instead III. RESULTS of oxidized GaAs 001 substrates. The As layer is removed in situ and a well-defined c(4 4) reconstruction can be pre- A. Morphology of bottom Fe 001... layers pared. A study of the growth of the bottom Fe 001 layer- The wedge-shaped Cr 001 interlayer with a slope of starting with the RT case, proceeding to elevated temperature 0.5 nm/mm and a maximum thickness of 4 nm is grown by growth at TS 570 K, and ending with the optimized two- linearly moving a shutter in front of the sample during depo- stage growth procedure MT570-is described in Ref. 11. Here sition. All STM data of Cr presented in this paper have been we briefly review RT and MT570 Fe films and then extend recorded at an interlayer thickness d 2.5 nm ( 17 ML). the study by presenting MT520 specimens. The spacer is sandwiched by two 5-nm-thick Fe 001 layers. An STM overview image of an RT Fe film is shown in The whole trilayer is grown at a deposition rate of 0.01 nm/s Fig. 2 a . The shape and arrangement of the substrate- 4160 C. M. SCHMIDT et al. PRB 60 FIG. 2. STM overview images image size: 400 400 nm2, a , c , e and detail images image size: 100 50 nm2, b , d , f of 5-nm-thick bottom Fe layers: a RT (z range: 4.0 nm , b RT (z range: 1.0 nm , c MT520 (z range: 1.0 nm , d MT520 (z range: 0.7 nm , e MT570 (z range: 1.5 nm , f MT570 (z range: 1.0 nm . The derivative along the fast scan direction has been added to the plane- subtracted raw data for contrast enhancement. induced steps is very similar to what we observe on the bare 1 Ag 001 surface. However, the terraces between two sub- H r, H r S z z r d2 2 strate induced steps are neither structureless nor flat, they are S rather covered with hillocks as revealed by the detail image in Fig. 2 b . We statistically quantify the vertical roughness is the two-dimensional height-height correlation function de- of detail images by the rms value z2 and the lateral rived from the surface profiles z(r ) of STM detail images. roughness by calculating the lateral correlation length R. The Thus, R corresponds to the mean separation between typical latter quantity is determined by the position of the first maxi- features, e.g., the hillocks in Fig. 2 b . The integration is mum in the pair-correlation function performed over the whole image area S. The offset of z(r ) is such that z 0. Therefore, with the normalization chosen 1 2 in Eqs. 1 and 2 PCF(0) 2 holds. In Fig. 3 PCF(r) PCF r calculated from all Fe and Cr STM detail images in Figs. 2 2 H r, d , 1 0 and 4 are displayed. The resulting morphological quantities and R are summarized in Table II. where Obviously, Fe grows on Ag 001 at room temperature as a FIG. 3. Pair-correlation functions PCF(r) calculated from the Fe and Cr detail images of Figs. 2 and 4. For clarity the curves are displayed with an offset: the left-hand right-hand vertical axis accounts for Cr Fe . The position of the labels marks the respective lateral correlation lengths R: a RT, b MT520 , c MT570 . PRB 60 CORRELATION OF SHORT-PERIOD OSCILLATORY . . . 4161 FIG. 4. STM overview images image size: 400 400 nm2, a , c , e and detail images image size: 100 50 nm2, b , d , f of the Cr spacer layers recorded at a thickness d 2.5 nm: a RT (z range: 1.0 nm , b RT (z range: 1.0 nm , c MT520 (z range: 0.7 nm , d MT520 (z range: 0.7 nm , e MT570 (z range: 1.5 nm , f MT570 (z range: 1.5 nm . The derivative along the fast scan direction has been added to the plane-subtracted raw data for contrast enhancement. continuous film with a rough surface (RRT faces. We argue that the regular morphology with predomi- Fe 6.1 nm and RT nantly square-shaped table mountains with single atomic Fe 0.21 nm). We find that the surface morphology is im- proved by either growing or postannealing the films at el- steps running along bcc-Fe 001 100 axes Figs. 2 e and evated temperatures. However, during deposition at or above 2 f represents the intrinsic surface structure of 5-nm-thick room temperature, an atomic exchange process is activated Fe films on Ag 001 . Driven by the small lattice mismatch that results in a thin Ag film ``floating'' on top of the grow- between Ag 001 and Fe 001 , m 0.8%, it develops even at ing Fe film (0.2 ML at room temperature and up to 1 ML at 570 K, where Fe homoepitaxy proceeds in a near perfect elevated temperatures .11 The exchange is driven by the sig- layer-by-layer growth mode.20 The interface strain can be nificantly smaller surface free energy of Ag 001 as com- relieved by the formation of a regular network of ditches pared to Fe 001 . Since the mechanism is frozen at 100 K, with a separation aFe /m 38 12 nm, which imposes an the MT upper limit on the lateral correlation length. Note that 570 growth procedure yields clean and Ag-free sur- whereas RMT570 Fe 19.7 nm has increased by about a factor of TABLE II. Different preparation procedures and the corre- 3 compared to the RT case, MT570 Fe 0.19 nm has not sponding morphological parameters derived from the STM detail changed significantly. images in Figs. 2 and 4. R measures the lateral correlation length Having found an optimized preparation procedure with Eqs. 1 and 2 and is the rms roughness. D denotes the aver- respect to chemical cleanness and lateral structure size, we age terrace diameter obtained from Eqs. 8 ­ 10 . calculated now introduce the MT520 bottom Fe layer, that additionally according to Eq. 3 stands for the rms fluctuations of the Cr spacer offers a possibility to tune the morphological properties thickness (x,y). The entries in this table are used in the text with without changing the chemical quality. The STM overview subscripts Fe, Cr, and indicating the bottom Fe layer surface, the image of the MT520 bottom Fe layer Fig. 2 c again shows Cr spacer layer surface, and the Cr spacer layer thickness, respec- a fairly regular arrangement of table mountains which tively, and superscripts RT, MT520 , and MT570 referring to the strongly resembles the surface characteristics of the opti- preparation method. mized MT MT520 570 films. The morphological parameters RFe Notation Layer R(nm) (nm) D(nm) (nm) 10.1 nm and MT520 Fe 0.13 nm of the detail image Fig. 2 d are reduced by about one half and one third, respec- RT Cr 6.8 0.18 0.28 tively, in comparison to their MT Bottom Fe 6.1 0.21 570 counterparts. The MT520 Fe surfaces are also free of Ag. MT520 Cr 15.4 0.16 1.6 0.21 Bottom Fe 10.1 0.13 1.4 B. Morphology of Cr 001... interlayers MT570 Cr 22.4 0.19 1.9 0.27 Qualitatively, the differences of the morphology of the Bottom Fe 19.7 0.19 1.7 bottom Fe films also show up for the surfaces of the Cr spacer layers, i.e., a rough irregular structure for the RT 4162 C. M. SCHMIDT et al. PRB 60 preparation Figs. 4 a and 4 b and a fairly regular arrange- ment of table mountains for the MTT preparation methods Figs. 4 c ­4 f . Concerning the RT system, it is impossible from the ap- pearance of the STM images to distinguish between Fe and Cr surfaces: the steps that separate Ag buffer layer terraces are still visible through the Cr/Fe bilayer and cause the large- scale image contrast in Figs. 2 a and 4 a , whereas locally, the two morphologies are dominated by growth hillocks. RRT Cr is slightly larger than RRT Fe Fig. 3 a . Figure 4 e shows an STM overview image of Cr grown on the MT570 Fe surface displayed in Fig. 2 e . The two images strongly resemble each other, and identical rms roughnesses MT570 MT570 Fe Cr 0.19 nm can be deduced. However, in comparison with the Fe equivalent, the average area covered by a single Cr table mountain appears percep- tibly enlarged and the slopes between two table mountains show up steeper Fig. 4 f . The quantitative morphological analysis by means of pair-correlation functions verifies this FIG. 5. Kerr microscopy data recorded from the MT570 sample observation: RMT570 in a demagnetized state at d 2.5 nm, indicating that the MT Cr 22.4 nm is significantly larger than the T sys- corresponding value of the Fe substrate, RMT tems are dominated by 90° coupling image size: 43 43 m2). 570 Fe 19.7 nm Arrows refer to the net magnetization resulting from the superposi- Fig. 3 c . tion of the individual magnetizations of the bottom and the top Fe The MT520 Cr layer Figs. 4 c and 4 d has smaller and layers no arrows shown which are crossed and aligned along less regular structures than the MT570 Cr film Figs. 4 e and 100 magnetic easy axes of the Fe 001 layers. Inset: Correspond- 4 f , reflecting the same trend as observed for Fe Figs. 2 c ing MOKE loop with clearly developed plateaus at M 0.5MS and 4 d in comparison with Figs. 2 e and 2 f . Proceeding indicating a strong biquadratic coupling contribution. in the MT520 case from Fe to Cr, both the rms roughness and in particular the lateral correlation length increase consider- Given the usual phenomenological energy density ably from MT520 MT520 Fe 0.13 nm to Cr 0.16 nm and from ansatz21 with a bilinear coupling term J1(d)cos( ) RMT520 MT520 parametrizing FM and AF coupling, where is the angle Fe 10.1 nm to RCr 15.4 nm Fig. 3 b , respec- tively. between the magnetizations of the two Fe layers, and a bi- Finally, it is worthwhile noting that the increase of the quadratic coupling term J2(d)cos2( ) favoring the 90° lateral correlation lengths, i.e., R arrangement of the magnetizations, one can estimate the Cr RFe , both in the RT and in the MT total exchange coupling strength as J(d) J T systems, has been confirmed by systematic mea- 1(d) J2(d) surements of a large variety of STM images. 0MSdFeHS(d) by measuring the saturation field HS(d), defined as half the field interval between the values C. Exchange coupling of Fe/Cr/Fe 001... trilayers A magnetization curve in units of the saturation magneti- zation MS taken at an interlayer thickness d 2.5 nm is shown in the inset of Fig. 5. The shape of the loop is typical for MTT samples: It reveals the characteristic plateaus at M/MS 0.5 resulting from 90° coupling at small external fields. Corresponding Kerr microscopy images Fig. 5 confirm the presence of magnetic domains with shapes typical for 90°-coupled Fe/Cr/Fe 001 specimens in the demagnetized state.21,22 In particular, the majority of domain walls separat- ing areas with different net magnetizations run along the Fe 100 directions in contrast to characteristic walls occur- ring in FM coupled and AF coupled Fe 001 based systems. Figure 6 shows a three-dimensional 3D rendering of 200 hysteresis curves taken along the Cr wedge of a MT570 sample. The dominance of 90° coupling for Cr thicknesses larger than about 1.2 nm is evidenced by the clearly devel- oped plateaus at M/MS 0.5 and the steep drop of the FIG. 6. 3D representation of 200 MOKE hysteresis loops taken signal between these plateaus. This representation also at different Cr thicknesses along the Cr wedge of a MT570 sample. shows that it is the width of the 90° plateaus that give rise to Each M(H) curve is normalized to its saturation magnetization oscillations as a function of the spacer thickness. MS . PRB 60 CORRELATION OF SHORT-PERIOD OSCILLATORY . . . 4163 FIG. 7. MOKE coupling curves of Fe/Cr-wedge/Fe 001 trilayers. a RT: only long-period oscillatory behavior, b MT520 : tiny short-period oscillations, c MT570 : superimposed large-amplitude 2-ML oscillations. where M(H) M for roughness-occur over a certain lateral length scale given S . M S and dFe denote the bulk saturation magnetization of Fe and the thickness of the Fe layers, re- by the typical distance between variations in layer thickness. spectively. However, this specific contour of hysteresis loops With respect to the 2-ML oscillatory behavior, we are inter- does not allow one to disentangle the bilinear and biquadratic ested in the lateral length scale over which a difference in Cr contributions properly. The MOKE exchange coupling thickness of only one monolayer is to be expected. A deter- curves J(d) taken from the RT Fig. 7 a and the MTT mination requires knowledge not only about the morpholo- Figs. 7 b and 7 c trilayers show a strong dependence on gies of the two Fe/Cr interfaces, but also about the correla- the preparation method. Common to the three systems and in tion between them. Because STM is a surface sensitive accordance with previous measurements9 is the strong technique that yields no straight access to buried interfaces, non-FM background, i.e. J(d) 0 for almost all spacer an investigation of the structure of interfaces is generally not thicknesses. Concerning the MT570 system, the appearance of trivial. However, as will be shown below, the statistical com- the coupling curve is dominated by the superposition of clear parison of STM data taken from the bottom Fe surface and 2-ML oscillations and long-period oscillations of about 12 the Cr surface yields a set of real space information from ML. In the MT520 sample only a tiny amplitude AMT520 of the which the Cr thickness fluctuations may be quantified in 2-ML oscillatory part remains visible in J(d), whereas in the terms of the rms value and the lateral correlation length. RT case only the long-period oscillation component sur- The quantitative morphological analysis derived on the vives. From the insets of Figs. 7 b and 7 c we determine a basis of pair-correlation functions Table II shows that for ratio of the short-period amplitudes AMT570:AMT520 4:1 at each of the three sample types, R the Cr thickness of the morphological characterization i.e., Fe is smaller than and not commensurable to R d 2.5 nm 17 ML), and ART 0. Cr . As described in Ref. 27 for the RT case, the lateral correlation length in Fe/Cr 001 multilayers increases monotonously with the number of Cr/Fe bilayers at IV. DISCUSSION least up to 10 repetitions. Therefore, the roughnesses on both A. Spacer thickness fluctuations sides of the interlayers cannot be correlated and spacer layer thickness fluctuations of 1 ML are to occur on a lateral The decrease of the lateral correlation length of the bot- length scale smaller than RRT . In consistence with this con- tom Fe layer in the MT Fe,Cr 520 case as compared to the MT570 clusion, Schreyer et al.28,29 arrived from x-ray diffraction specimen can be explained by the presence of an Ehrlich- measurements performed on a RT Cr/Fe(001) Schwoebel barrier:23,24 Stroscio et al.25 have shown for Fe 5 sample at a rough estimation of the lateral length scale of constant homoepitaxy on whiskers that a transition from island to near layer thickness of 1 nm. perfect layer-by-layer growth occurs at about 520 K. This The appearances of the MT transition has been modeled by Amar et al.26 taking into 520 and the MT570 Cr mor- phologies differ from each other, indicating that each type of account an Ehrlich-Schwoebel barrier, which causes island Cr surface ``memorizes'' its respective lower lying Fe sub- growth at room temperature, whereas at elevated tempera- strate surface. However, the Cr growth front is expected to tures the effect of the barrier becomes less important, en- evolve in a rather complicated fashion: STM measurements abling layer-by-layer growth. In our case the lattice mis- by Stroscio et al.30 have proven that a few ML of Cr evapo- match between Ag 001 and Fe 001 does not allow pure rated at 573 K on flat high-quality Fe whiskers grow per- layer-by-layer growth even at 570 K; rather it limits RMT570 Fe fectly layer-by-layer. An isolated monatomic Fe substrate to an upper, substrate-induced value, whereas smaller struc- step edge acts as a sink for the diffusing Cr atoms leading to tures may develop at 520 K. a denuded region of an irregular contour a few tens of nm From Sec. III it is obvious that the interface structure of wide. The authors speculate that Cr layer-by-layer growth the samples has a critical influence on the coupling proper- may be inhibited by rough substrates. At the lower substrate ties. We emphasize that thickness fluctuations-as is the case temperature of 488 K the Cr growth front reveals several 4164 C. M. SCHMIDT et al. PRB 60 exposed layers due to the smaller diffusion length. Our properties of the MTT trilayer systems where all interfaces nanometer-scale-structured Fe substrate together with the Cr are formed at the same temperature. Note that in the case of growth temperature of 520 K which is too low to allow true interface alloying the STM images of the bottom Fe layer layer-by-layer growth30 suggests a growth scenario that in- may still be regarded as an approximation of the resulting volves for the initial monolayers a competitive process of i Fe/Cr interface morphology formed upon progressing in the partially filling the Fe step edges and ii Cr island growth trilayer fabrication: we assume the chemically diffuse inter- due to the limited diffusion length. For the subsequent face to be centered around the STM representation of the atomic Cr layers the latter aspect determines the morphology topography of the bottom Fe layer. The STM approximation giving rise to spacer thickness fluctuations. The clearly dif- of the upper Fe/Cr interface is supposed to excel that of the ferent lateral correlation lengths, RMTT MTT Fe RCr which reflect lower one, since for this case a chemically sharp interface the incommensurability of the Cr structures with the corre- has been reported.31 sponding Fe structures establish uncorrelated roughness of the two interfaces on the lateral length scale of the table B. Pillar-and-edge model mountains. Note furthermore, that in both cases the top sides of the Cr table mountains do not only cover larger areas but We introduce the microscopic interlayer exchange field their contours are also smoother as compared to the Fe sub- Hex(x,y). It is defined as the field experienced by an isolated strate structures. spin at the lateral position (x,y) in the top Fe layer exclu- Uncorrelated roughness implies that the rms value of the sively due to the presence of the Cr/Fe bilayer underneath. thickness fluctuations of the Cr spacer layer The intrinsic interlayer exchange coupling, i.e., the coupling may be cal- culated from the rms roughnesses of the interfaces by of an ideal sample with perfect interfaces with a period of two ML, causes a sign change of Hex(x,y) wherever the 2 2 spacer thickness varies by an odd number of monolayers. Fe Cr. 3 sgn Hex(x,y) 1 corresponds to FM interaction, and The results are listed in Table II. RT MT570 sgn H ex(x,y ) 1 refers to AF coupling. By means of im- , whereas MT age processing algorithms applied to STM detail images, we 520 is found to be somewhat smaller. aim to extract sgn H From STM measurements of Fe/Cr/Fe 001 whisker sys- ex(x,y ) for the two MTT systems. The analysis is illustrated in Fig. 8 for the MT tems, Pierce et al.6 extract the rms roughnesses of the Cr 570 sample, but it is equally valid for the MT spacer layers, which coincide with 520 specimen. For the pur- because for whiskers pose of noise reduction we start with the discretization of the Fe 0. In their samples, strongly depends on the growth STM detail images z temperature. The vanishing of the 2-ML oscillations for Cr Fe(x,y ) Fig. 2 f and zCr(x,y ) Fig. 4 f in units of ML. Figures 8 a and 8 b display growth at 320 K is modeled by weighting a coupling curve derived from a 620 K specimen which is shown to grow Int zMT570 x,y /l layer-by-layer, i.e., with a very small Cr Cr nCr , 4 ) with a thickness- dependent Gaussian representing the increasing width of the and Cr growth front at lower temperatures. Comparing the RT and the MT MT570 570 systems, we find almost Int zFe x,y /lFe nFe 5 equal values for RT MT570 and Table II . Therefore, a respectively, where Int( ) denotes the integer part of . l model solely based on the averaging of the coupling Fe and l strengths by thickness fluctuations as considered in Ref. 6 Cr are the monatomic step heights of Fe 001 and Cr 001 , respectively, and the integer constants n would lead to the same attenuation of the 2-ML oscillation Fe and nCr are chosen to adjust the average layer thicknesses close to the for both samples, and could not account for our experimental nominal deposition values of 5 nm 35 ML for Fe and (5 observations. MT520 MT570 is even slightly smaller than , 2.5) nm (35 17) ML for Cr, respectively. which should correspond to an increase of the amplitude Because of the presence of uncorrelated roughness at the AMT520 of the 2-ML oscillation. However, we observe the two interfaces, a statistical representation of the lateral extent opposite: AMT520 is smaller. of constant Cr thickness is provided by the subtraction of the The clearly different lateral correlation lengths are the ob- lower from the upper interface32 and leads to the Cr thick- vious distinctions of the three samples, and it seems natural ness fluctuation image in Fig. 8 c , to relate the different coupling curves to this finding, in par- ticular since the R values of all samples reflect the same x,y Int zCr x,y /lCr Int zFe x,y /lFe nCr nFe . trend as the amplitudes A of the 2-ML oscillation: RRT 6 Fe,Cr RMT520 MT570 Fe,Cr RFe,Cr and ART AMT520 AMT570. However, there Finally, in Fig. 8 d all areas with spacer thicknesses of an is a second difference between the RT and the MTT prepa- even number of ML are gray-colored, whereas the ones with ration procedures: the interfaces are formed at room tempera- an odd number of ML are printed in black. Hence, the color ture in the RT case and at 520 K in the MTT cases. As code equals a statistical representation of sgn Hex(x,y) for interface alloying has been observed for Cr growth on the MT570 sample. Qualitatively, one finds parts in Fig. 8 d Fe 001 ,18,19 we cannot exclude chemically different inter- where sgn(Hex) is a laterally rather rapidly fluctuating func- faces affecting the coupling behavior. For this reason, we tion between other parts where sgn(H) remains constant will not go any further into the comparison of RT samples over larger areas. and samples grown at elevated temperatures. From now on Figure 9 presents a cross section of the MT570 trilayer we will exclusively focus on the structural and magnetic derived from line sections taken along the vertically running PRB 60 CORRELATION OF SHORT-PERIOD OSCILLATORY . . . 4165 FIG. 8. STM image processing, shown for the MT570 system, leading from surface roughnesses to interlayer fluctuations and to pillars with FM- or AF-like character. a Discretization image in units of ML of the STM detail image zMT570 Cr (x,y) shown in Fig. 4 f (z range: 8 ML . b Same for the detail image zMT570 Fe (x,y) of Fig. 2 f (z range: 6 ML . c Statistical representation of the Cr spacer thickness fluctuations (x,y) calculated by subtracting Fig. 8 b from Fig. 8 a (z range: 12 ML . d sgn Hex(x,y) derived from Fig. 8 c indicating spacer thicknesses of even gray and odd black numbers of ML. e Pillars with AF-like character gray , pillars with FM-like character black , and the area of the edges white for a chosen minimum pillar diameter 3.0 nm. f Same for 4.0 nm. Line sections taken along the dashed line (x0 ,y) are displayed in Fig. 9. dashed lines (x0 ,y) of Figs. 8 a ­8 d . The two Fe/Cr inter- thickness fluctuations e.g., (x0 ,y) 19 ML for 17 nm faces middle two traces exhibit fluctuations in units of y 24 nm between sections with frequent fluctuations monolayers around their nominal deposition thicknesses. The e.g., nine steps for 24 nm y 31 nm . Since in practice corresponding curve of Cr spacer thickness fluctuations bot- spacer thickness steps higher than one monolayer are negli- tommost trace is characterized by sections without any gible, this decomposition matches the sign changes in the microscopic interlayer exchange field uppermost trace : Hex(x0 ,y) is characterized by sections with constant sign e.g., sgn Hex(x0 ,y) 1 for 17 nm y 24 nm be- tween sections with frequent sign changes e.g., nine sign changes for 24 nm y 31 nm). The schematic picture of a cross section given in Fig. 10 reproduces our STM data for both the MT570 and the MT520 system in terms of the the lateral decomposition of the Cr spacer layer into parts with no thickness fluctuations which are called pillars in the following hatched areas in Fig. 10 and into other parts with frequent thickness fluctuations, hereafter referred to as edges. In order to make this distinc- tion one has to choose a minimum pillar diameter . Given FIG. 9. Cross section of a MT570 sample derived from cutting line sections along the dashed lines in Fig. 8 in top-to-bottom di- rection. The middle two curves represent the fluctuations of the interface morphologies around their nominally deposited thick- nesses dashed lines . The bottommost curve shows their difference, FIG. 10. The pillar-and-edge structure. Schematic cross section i.e., the fluctuations of the Cr spacer thickness (x0 ,y), whereas of an Fe/Cr/Fe 001 trilayer prepared by the MTT procedures. In the topmost curve, sgn H(x0 ,y) , is obtained from (x0 ,y) by some areas hatched with a diameter larger than or equal to , the assuming a sign change at each monostep. The sign convention is in Cr thickness does not fluctuate. Such areas are called pillars, accordance with the measured curve in Fig. 7 c . Note that the whereas the other parts are denoted as edges. An AF-like or an vertical length scale is magnified by about a factor of 4 compared to FM-like character can be associated with each pillar according to the lateral one. the sign of Hex shown in the lower part of the image. 4166 C. M. SCHMIDT et al. PRB 60 FIG. 11. Fraction f of the spacer area taken by pillars see text for definition as a function of for the MT570 (fMT570, ) and the MT520 (fMT520, ) sample. Inset: Ratio fMT570:fMT520 as a function of . an area with constant Cr thickness, only the set union of the compact parts that are large enough to enclose a circle with FIG. 12. Schematic response of the top Fe layer to the H diameter are considered to contribute to the pillar area. All ex profile shown between the Fe layers under the assumption of a other parts belong to the edges. An AF-like or FM-like char- homogeneously magnetized bottom Fe layer. a For acter can be attributed to each pillar because in practice the 0 of the order of micrometers, FM and AF domains develop at the positions of definitions of a pillar by (x,y) const and by pillars, and 90° domains in between. b For sgn 0 of the order of Hex(x,y) const are equivalent due to a negligible nanometers, the spin orientation of the top Fe layer is locally per- number of biatomic or higher steps. turbed, resulting in positive or negative angular deviations from the The character of each pillar changes from FM-like to AF- overall 90° coupling. All magnetizations are in-plane. like and vice versa when one ML of Cr is added to the spacer layer, leading to an oscillating behavior as a function of the mean spacer thickness with a period of 2 ML. The amplitude of sgn Hex(x,y) on a nanometer length scale have been depends on the fraction f of the total area S taken by all shown by Slonczewski13 to induce an effective 90° coupling pillars. The effect of the pillar height distribution is dis- due to the averaging effect of the intralayer direct exchange cussed below. Here it is sufficient to assume that the contri- interaction in each of the two Fe layers. Let us first assume butions of all pillars do not completely compensate each that 0 is large, e.g., of the order of micrometers. In that case other. f is a function of the chosen and can directly be each pillar would give rise to an AF or FM domain in a sea determined by image processing algorithms from difference of 90° coupling. This situation is sketched in Fig. 12 a . images (x,y) such as the one displayed in Fig. 8 c or Note the micrometer length scale. The arrows indicate the equivalently Fig. 8 d . The resulting functions f MT570( ) and direction of the domain magnetization. f MT520( ) are shown in Fig. 11. They deviate significantly As we reduce 0, the domains cannot become smaller from each other for 1.5 nm 6 nm. The ratio than the width of the domain walls in the system. For our f MT570: f MT520 inset of Fig. 11 increases from 2 at sample geometry superimposed NeŽel walls33 are preferred to 3 nm to 5 at 4 nm, becomes very large for 4 nm uncoupled NeŽel walls, because the two magnetic layers can 6 nm because f MT520 0, and finally equals 1 for efficiently compensate their stray fields in the superimposed 6 nm, where f MT570 0, too. If the pillars are to explain configuration. The width dNeŽel of superimposed walls in FM the different amplitudes AMT570 and AMT520 of the 2-ML os- exchange coupled trilayers has been calculated34,35 as a func- cillations in J(d) Fig. 7 , one has to assume a minimum tion of the intrinsic coupling strength. For Fe/Cr/Fe 001 and pillar diameter 0 in the range of 3 ­4 nm. Figures 8 e the spacer thickness of interest 2.5 nm , dNeŽel is of the order and 8 f show the results of the analysis performed on the of 150 nm. dNeŽel is even larger in the case of AF coupling MT570 specimen for 0 3.0 nm and for 0 4.0 nm, re- because the core of the domain wall with antiparallel align- spectively: with increasing 0 a decreasing number of pillars ment of the film magnetizations is then stabilized by the of FM-like character black or AF-like character gray are interlayer exchange coupling term. surrounded by the growing area contributing to the edges Obviously, the value of 0 found in our experiments is at white . least one order of magnitude smaller than dNeŽel , and we can In agreement with our value of 0, x-ray diffraction ex- no longer talk about domains. Instead, we have to consider periments by Schreyer et al.28,29 revealed a rough order-of- noncollinear spin configurations in each of the two Fe layers magnitude estimation of the lateral length of constant inter- with angular deviations from the perfectly 90°-coupled situ- layer thickness of 10 nm for a Cr/Fe 9 sample grown at ation. They are the answer of the system to all competing 523 K. interactions: intralayer direct exchange, Hex(x,y) due to in- What is the physical meaning of 0? Periodic fluctuations terlayer exchange coupling, anisotropies, and demagnetiza- PRB 60 CORRELATION OF SHORT-PERIOD OSCILLATORY . . . 4167 tion. Figure 12 b sketches this situation. Note the nanometer Throughout Sec. IV B we have assumed that Hex(x,y) is length scale. The arrows now represent the slowly varying local in the sense that it depends only on the spacer thickness direction of individual spins. at the position (x,y). In the framework of RKKY interaction The model sketched in Fig. 12 is confirmed by calcula- Bruno and Chappert38 have shown that the loss of transla- tions by Ribas and Dieny:36 They study numerically tional invariance for distances larger than D leads to a finite 90°-coupling in Fe/Cr/Fe trilayers on samples characterized in-plane coherence length of the electrons of the order of D. by different terrace widths D. The important parameter If the electrons mediating the coupling have a Fermi velocity which determines the behavior or the magnetization direction component parallel to the interface, the coherence length per- on terraces separated by monatomic steps turns out to be the pendicular to the interfaces dmax is also limited ratio between the size of the terraces D and lwall , that char- acterizes the width of the area in which the magnetization is perturbed by the change of sign of the coupling at the border D between two semi-infinite terraces. Dependent on the size of dmax tan , 7 the terraces, these authors find either complete FM and AF alignment of the magnetizations on terraces separated by monatomic steps (D/lwall 1) or only small oscillatory de- where is the angle between the Fermi velocity and the viations of the magnetization direction from an average rela- interface normal. The exchange field is suppressed by de- tive orientation of 90° (D/lwall 1). The amplitude of the structive interference for spacer thicknesses d dmax . As deviations decreases with decreasing terrace width. Neglect- mentioned by these authors, interface roughness breaks the ing anisotropies, the characteristic width of the wall is given translational invariance. The in-plane coherence length D by lwall 12 AexdFe /JCr, where Aex denotes the exchange can roughly be described by the average diameter of the flat stiffness of Fe, dFe is the thickness of the Fe films, and JCr is portions of the interfaces.38 In order to obtain D, we again the interlayer exchange coupling at a certain Cr thickness. consider the function f ( ), which we now determine sepa- From Figs. 7 b and 7 c we estimate JCr 0.15 mJ/m2 at rately for the Fe and Cr surfaces zFe(x,y) and zCr(x,y) of the the spacer thickness of interest 2.5 nm and obtain lwall MTT systems. f( ) can formally be written as 38 nm. Obviously, our samples must be described in a picture with the local spin orientation slightly deviating from 1 the exact 90° alignment as sketched in Fig. 12 b . f N x x 2dx. 8 The total effect of all pillars within a certain area e.g., S 2 within the laser spot in MOKE experiments , finally, is the sum over all their coupling contributions. The contribution of N(x) is the number of flat portions with diameter x within an each pillar is proportional to its height to the power , image with area S and can be derived from Eq. 8 as where is the decay exponent of the intrinsic bilinear ex- change coupling. This sum is nonzero, except for special and 4S d f improbable pillar height distributions. Our reasoning as- N x sumes that for the spacer thicknesses of interest dx x 2. 9 (15­20 ML) the height distribution function does not change significantly upon adding one ML of Cr, except that The average terrace area is the mean pillar height increases by one ML. In a macroscopic experiment such as MOKE the noncol- linear configuration shown in Fig. 12 b is expected to yield an effective 90° coupling in agreement with our MOKE hys- teresis loops and the Kerr microscopy data Fig. 5 . The overall effect of the pillars is a modulation of the biquadratic effective coupling strength as a function of the spacer thick- ness with a period of 2 ML, which shows up as oscillations in Figs. 7 b and 7 c . C. Loss of translational invariance So far, we have made no specific assumptions about the intrinsic spin structure of the Cr interlayer. Now, we explic- itly suppose the presence of paramagnetic Cr. With regard to the ongoing research about the actual intrinsic spin structure of Cr 001 sandwiched by Fe 001 layers, the picture of FIG. 13. Fermi surface cross section of paramagnetic Cr in the paramagnetic Cr and pure Ruderman-Kittel-Kasuya-Yosida 001 plane after Ref. 39. The horizontal arrow represents the nest- RKKY interaction may prove to be oversimplified, and ing vector q(001) that gives rise to the 2-ML period of the interlayer more quantitative analysis will be needed to adapt the quali- coupling. The short arrows indicate the directions of the Fermi ve- tative picture presented below to the true internal Cr spin locities of the states connected by q(001) . is the angle between the structure see, e.g., Ref. 37 . interface normal and the Fermi velocities. 4168 C. M. SCHMIDT et al. PRB 60 V. SUMMARY N x x 2dx 2 S f D 2 Our experimental data shows a clear dependence of the 2 . 10 N x dx N x dx interlayer exchange coupling on the interface morphologies: short-period oscillations turn up if the Cr spacer contains The lower integration boundary is set to 0.5 nm in order to compact regions of constant thickness pillars with diam- exclude terraces with diameters smaller than two nearest- eters larger than 0 3 ­4 nm, and their amplitude increases neighbor separations. The values of D for all four surfaces with increasing lateral extent of these pillars. This observa- are listed in Table II. The average diameters of the two in- tion has been related to two mechanisms which are sensitive terfaces of the MT to the interface morphology on the nanometer scale: i the 570 and MT520 samples are DMT570 (DMT570 MT570 MT520 response of the spin configuration in the magnetic films to Fe DCr )/2 1.8 nm and DMT520 (DFe the exchange field, and ii destructive interference of the DMT520 Cr )/2 1.5 nm, respectively. electrons mediating the short-period coupling due to the bro- Figure 13 shows a Fermi surface 001 cross section of ken translational invariance at the Fe/Cr interfaces. The two paramagnetic Cr. The 2-ML period of the intrinsic exchange mechanisms are expected to occur simultaneously. The first coupling across Cr 001 spacer layers is associated with a nesting vector describes the response of the magnetic layers to H q ex(x,y ) in (001) 0.95 H that connects the electron and hole pockets of the Cr Fermi surface around the points competition with other magnetic interactions, in particular and H of the bcc Brillouin zone.40 The Fermi velocities of intralayer exchange, whereas the second deals with the the states on the edges of the pockets connected by q propagation of Hex(x,y) in the spacer layer. (001) have an orientation with 45°, giving rise to a coherence length dmax D. Therefore, the contribution of these states to H ACKNOWLEDGMENTS ex decays for d larger than D. Hence, this scenario also provides a mechanism to explain the dependence of the am- plitude of the short-period oscillation on subtle morphologi- cal changes on the nanometer scale. We thank J. McCord for the Kerr microscopy data and B. For our samples DMT520 DMT570 d 2.5 nm, and we O. 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