PHYSICAL REVIEW B VOLUME 59, NUMBER 2 1 JANUARY 1999-II Giant magnetoresistance dependence on the lateral correlation length of the interface roughness in magnetic superlattices R. Schad* Research Institute for Materials, KU Nijmegen, NL-6525 ED Nijmegen, The Netherlands P. Belie¨n, G. Verbanck, V. V. Moshchalkov, and Y. Bruynseraede Laboratorium voor Vaste-Stoffysika en Magnetisme, KU Leuven, B-3001 Leuven, Belgium H. E. Fischer Institute Laue Langevin, 38042 Grenoble Cedex 9, France S. Lefebvre and M. Bessiere LURE, Universite´ de Paris-Sud, 91405 Orsay Cedex, France Received 2 March 1998; revised manuscript received 6 August 1998 The giant magnetoresistance GMR observed in magnetic multilayers, is due to spin-dependent electron transport. In order to study the influence of the interface roughness on the spin-dependent scattering we produced epitaxial Fe/Cr 001 superlattices with negligible bulk scattering. The interface roughness was varied by carefully annealing the samples. The vertical and lateral interface roughness components were quantita- tively determined by specular and diffuse synchrotron x-ray diffraction using anomalous scattering. We find that the magnitude of the GMR effect increases with decreasing lateral correlation length x and increasing vertical roughness amplitude . S0163-1829 99 06001-4 INTRODUCTION interface quality via the exchange coupling. Magnetic pin holes which are also a kind of structural defect will cause The discovery of giant magnetoresistance GMR Refs. ferromagnetic alignment of parts of the sample which conse- 1­3 in Fe/Cr superlattices opened a new field of possible quently do not contribute to the GMR effect, thus diminish- applications for artificially tailored materials. The effect is ing its amplitude. Not only pin holes but also precursors of explained by spin-dependent electron transport4­7 which re- these in the form of larger spacer layer thickness fluctuations sults in different resistivities for the parallel and antiparallel might lead to partially ferromagnetic alignment because of configurations of the magnetization in adjacent magnetic lay- local changes of the exchange coupling. In spite of their ers. The antiparallel configuration is found in the absence of structural origin these magnetic contributions are distinct an applied magnetic field, provided that the Cr layer thick- from the pure electronic contributions and have to be sepa- ness is chosen to produce an antiferromagnetic AF ex- rated experimentally by magnetization measurements. These change coupling. Application of an external field produces a give directly the fraction of the sample which is antiferro- ferromagnetic alignment leading to the resistance change. magnetically ordered AFF and does contribute to the GMR The dependence of the GMR amplitude on the structural effect. properties of the superlattice is quite involved. Here several The other two contributions to the GMR effect, the spin- contributions have to be distinguished: i the magnetic dependent electronic band structure and spin-dependent elec- structure, ii the spin-dependent electronic band structure, tron scattering, are the origin of the spin-dependent transport and ii spin-dependent electron scattering. and form therefore the interesting part. They are, however, The magnetic structure is of importance because the full quite entangled. The electronic band structure on its own can magnitude of the GMR effect is observed only when the generate a GMR effect without any spin-dependent scatter- magnetic configuration changes from fully antiparallel to ing, for example in the limit of diluted scatterers7 or in parallel alignment. The latter will be easily achieved when defect-free point contacts with ballistic transport.12 This band the external magnetic field is strong enough to saturate the structure contribution stems mostly from the asymmetry of magnetization. The antiferromagnetic alignment at zero field, the Fermi velocities for the two spin channels. Adding now however, depends in the case of an exchange coupled su- spin-dependent scattering, the GMR effect can either be am- perlattice on the nature of the exchange coupling and on plified or diminished depending on whether the scattering superlattice imperfections in the form of pin holes. Instead of enhances or counteracts the band structure contribution. This a simple antiferromagnetic alignment, the magnetization di- spin asymmetry of the electron scattering is determined by, rections can form 90° angles between adjacent magnetic first, the density of states DOS available at the Fermi level layers.8 This will reduce the observed GMR by a factor of 2.9 and second, the spin asymmetry of the scattering potential. The strength of the 90° coupling is mediated by the interface The DOS contribution, for instance, causes a spin asymmetry roughness10 or loose spins inside the spacer layers.11 Thus, in for any kind of electron scattering, even for phonon both cases the magnitude of the GMR effect is linked to the scattering.13 In this way, the spin-dependent scattering also 0163-1829/99/59 2 /1242 7 /$15.00 PRB 59 1242 ©1999 The American Physical Society PRB 59 GIANT MAGNETORESISTANCE DEPENDENCE ON THE . . . 1243 includes band structure effects. For Cr impurities in Fe the atomic steps measured ex situ by atomic force microscopy scattering not only enhances but actually dominates the pure AFM . After rinsing in isopropyl alcohol and drying in a dry band structure contribution,7 even in the dilute limit. In prac- N2 flow, the substrates were annealed at 600 °C in UHV for tice, due to the typically high defect densities in magnetic 15 min. The superlattices were prepared in a Riber MBE superlattices, the spin-dependent scattering contribution will deposition system (2 10 11 mbar base pressure equipped likely dominate over the pure electronic band structure ef- with electron beam evaporators, which were rate stabilized to fects. within 1% by a home-made feedback control system27 using It is this spin-dependent scattering to which most publica- Balzers quadrupole mass spectrometers QMS . Addition- tions, experimental and theoretical, are devoted. Here two ally, integration of the QMS signal was used to control the contributions have to be considered separately, the spin- dependent scattering at impurities inside the magnetic layers shutters of the individual evaporation sources. Fe and Cr bulk scattering and the scattering at the interfaces. Of layers starting material of 99.996% purity were evaporated course, both contributions can cause a GMR effect.4-7 How- in a pressure of 4 10 10 mbar at a rate of 1 Å/sec on the ever, if both bulk and interface scattering are present at the MgO 001 substrates. The substrate temperature during the same time, their spin asymmetry could be opposite. In that growth was 50 °C. The superlattices were deposited in a case the total spin asymmetry and hence the amplitude of the single deposition run on all substrates with the substrate GMR effect would be reduced.6 Polycrystalline samples holder rotated at 60 rpm. In this way, six identical samples naturally have a high degree of bulk defects with unknown were produced. Each superlattice consisted of 10 bilayers spin asymmetry of the scattering potential. Since interface with 28 Å Fe and 11 Å Cr starting with a Fe layer. The scattering is also important, this results in a rather involved whole stack was covered with an additional 20 Å Cr layer to system. Changing the structural quality of such samples will protect the multilayer from oxidation.28 All layers grew epi- affect both bulk and interface properties causing unpredict- taxially with 001 orientation.29 Afterwards the samples able changes in the GMR. This effect may account for the were annealed for 1 h in a vacuum of 10 8 mbar at various contradictory experimental observations reported for poly- annealing temperatures (Ta) up to 460 °C: the temperature crystalline samples.14­19 In order to study the influence of the where pin-hole formation starts to destroy the AF coupling. interface scattering alone on the GMR amplitude it is neces- Structural information about the superlattices was ob- sary to produce samples with negligible bulk scattering. This tained from SA XRD measurements performed at the LURE can be achieved by epitaxial growth of ultraclean materials synchrotron light source beamline D23 with wavelength on suitable substrates.20,21 The interface quality can be al- 2.0753 Å 15 eV below the Cr absorption edge . The XRD tered by several methods of which annealing has certain ad- spectra were measured in regular -2 geometry and by vantages over others. For instance, ion bombardment neces- rocks rocking curves . Slight asymmetries in the rocks sarily introduces lots of bulk defects. Annealing experiments were removed by averaging left and right wing of the spec- have been done before.22­25 Usually it is observed that the tra. Quantitative values of the interfaces roughness were de- GMR amplitude first slightly increases upon moderate an- termined by simulating the spectra using the interface corre- nealing and then drops drastically towards zero. The de- lation function:30­33 crease is caused by a loss of the AF order in the samples due to pin-hole formation which is easily understood yet not re- C lated to the spin-dependent transport. Thus far, the increase jk x z j x zk x j ke x/ x 2he z/ z 2 was only studied on samples with undefined bulk properties with z and therefore could not be related to changes of the interface j(x) z j(x) z j , the lateral and vertical correlation lengths structure. It is worth mentioning that a complete description x and z , and the average distance between the interfaces z. This function was successfully applied to ex- of the interface structure must include both the vertical and perimental data before34 and is closely related to models de- lateral roughness components. Any structure analysis based veloped by other authors.35­40 The vertical and lateral rough- on only one of these parameters is incomplete and cannot be ness parameters were obtained from, respectively, /2 scans expected to explain the behavior of the GMR effect. and rocks. These include the roughness amplitude , the In this paper we discuss the transport properties of epitax- lateral correlation length ial Fe/Cr 001 superlattices with exclusively interface elec- x the characteristic lateral dis- tance between ``bumps'' on a given interface , the vertical tron scattering. Identical samples were prepared in a single correlation length deposition run to avoid any irreproducibility of the growth z the distance between interfaces over which they lose their similarity , and the Hurst parameter h process. The interface quality was varied by annealing the representing the jaggedness of the interface for a given samples at different moderate temperatures leading to an x , as 3-h is the Hausdorf fractal dimension of the interface. increase of the GMR amplitude. Quantitative analysis of the The electrical measurements were performed in an Ox- vertical and lateral interface structure is based on respec- ford cryostat 1.5 up to 300 K equipped with a 15 T magnet. tively specular and diffuse small angle SA x-ray diffraction Resistivities were determined using a standard four probe XRD using a synchrotron source. The x-ray scattering con- Van der Pauw method with the current and magnetic field in trast between Fe and Cr was enhanced through anomalous the plane of the film CIP . The absolute and relative mag- scattering, achieved by choosing the x-ray wavelength close netoresistance are defined as to the absorption edge of Cr. 0 s and / s , re- spectively, where 0 is the resistivity in zero field and s the EXPERIMENTAL saturation resistivity. All quoted resistivity values were mea- sured at 4.2 K. The single-crystalline MgO 001 substrates26 (5 Magnetization measurements were performed in a SQUID 15 mm2) showed micron-size flat terraces separated by magnetometer at 4.2 K. The antiferromagnetic fraction 1244 R. SCHAD et al. PRB 59 FIG. 1. Absolute and relative magnetoresistance ( , / s) and the antiferromagnetic fraction AFF as a function of the an- nealing temperature. Note the break in the x axis. The lines are guides to the eye. FIG. 2. Specular SA XRD intensity as a function of the vertical AFF , defined as AFF 1 (Mr /Ms) with Mr and Ms be- scattering vector qz for all Fe 28 Å /Cr 11 Å 10 superlattices an- ing, respectively, the remnant and the saturation magnetiza- nealed to the temperatures indicated. Shown are the measured data tion, was used to quantify the degree of pin-hole formation points and the simulations lines . The data show no plateau for introduced by the annealing. the total external reflection at small angles because no footprint correction was applied to the data but instead taken into account in the simulations. All curves are vertically offset for clarity. RESULTS AND DISCUSSION Figure 1 shows the dependence of the magnetoresistance Fig. 2 show a rich structure including the pronounced su- and / s and the AFF as a function of the annealing perlattice Bragg peaks and the higher frequency Kiessig temperature Ta . Careful preliminary tests had shown that for fringes due to the total film thickness. Already, inspection by Ta 250 °C no significant changes in the transport properties eye reveals little variation in the quality of the spectra except occur. At higher temperatures up to Ta 400 °C and for Ta 460 °C where the superlattice Bragg peaks are more / s increase. At even higher temperatures the AFF strongly damped. The simulation of such spectra includes sharply drops indicating the onset of disintegration of the various parameters describing the different interfaces layered structure. remains constant whereas / s de- substrate-film, Fe/Cr, film-oxide, oxide-air and their sepa- creases because of the increased contribution of the back- ration, i.e., the layer thicknesses. In order to restrict the num- ground resistivity to s . This behavior is in accordance with ber of free simulation parameters we used certain input pa- studies of the high temperature annealing regime (Ta rameters such as the layer thicknesses of Fe and Cr known 450 °C) of similar samples showing the suppression of the from the sample preparation and the upper oxide layer's GMR effect due to the loss of the AF coupling.24 The low- composition, typical thickness and roughness known from temperature regime (Ta 460 °C) discussed here is the most independent experiments on single Fe and Cr films28 . Fur- interesting part since here the changes in the GMR amplitude thermore, we kept the substrate roughness the same for all must be related to changes in the spin-dependent electron simulations. The optical material parameters were taken scattering. Moreover, the reason for these changes in the from Ref. 41. In this way the simulations of the specular SA spin-dependent scattering must be found in changes of the XRD scans contained the Fe/Cr interface roughness as the interface structure since the interfaces are the exclusive only free parameter. Indeed, the simulations show little source for electron scattering in the absence of bulk scatter- variation of being constant at (2.95 0.05) Å for 20 °C ing . As mentioned earlier, the interface structure was char- Ta 410 °C and 4.7 Å for Ta 460 °C. This increased acterized by specular and diffuse SA XRD using anomalous value of is in agreement with the observed start of the scattering to enhance the otherwise low contrast in electron disintegration of the superlattice structure at higher Ta caus- density between Fe and Cr. Simulations of the specular and ing also the reduction of the AFF Fig. 1 . Therefore, the diffuse data reveal, respectively, the vertical component vertical component of the interface roughness is obviously roughness amplitude and the lateral components lateral not the key for understanding the initial increase of the GMR correlation length x and Hurst parameter h of the fractal amplitude Fig. 1 . Thus we have to examine the lateral in- dimension 3-h of the interface roughness. The specular data terface roughness components obtained through analyzing PRB 59 GIANT MAGNETORESISTANCE DEPENDENCE ON THE . . . 1245 FIG. 3. Diffuse SA XRD intensity as a function of the rocking FIG. 4. Diffuse SA XRD intensity as a function of the lateral angle for the unannealed Fe 28 Å /Cr 11 Å 10 superlattice. The scattering vector qx for the not annealed Fe 28 Å /Cr 11 Å 10 su- spectra were measured with a x-ray wavelength of 2.0753 Å 15 eV perlattice. The spectrum was measured with a x-ray wavelength of below the Cr absorption edge with qz at the position of the first 2.0753 Å 15 eV below the Cr absorption edge with qz at the (N 1) and second (N 2) order superlattice Bragg peaks. Shown position of the second order superlattice Bragg peak. Shown are the are the measured data points , the simulations of the diffuse inten- measured data points and the simulations of the diffuse intensity sities dashed lines , the Lorentzian fits to the specular intensities for various values of x 70, 90, 110, 130, and 150 Å . The best fit dotted lines , and the sums of simulated diffuse intensities and with x 110 Å is shown by a full line. fitted specular peaks full lines . The curves are vertically offset for clarity. small value of x of about 100 Å and second, the lateral roughness component of the substrate surface responsible the rocks. A qualitative analysis of such spectra can be for the central small peak in the diffuse intensity, i.e., having misleading since the shape of these curves is determined by a large value of x of about 1 m . The remaining difference several parameters in a rather involved and sometimes coun- between measured intensity and simulated diffuse intensity terintuitive way.33 For the same reasons the quantitative should then be the specular peak which is clearly not sharp analysis of the spectra has also to be performed with utmost around qx 0 Fig. 3 . We can simulate this specular inten- care since a single spectrum can be simulated with different sity by a Lorentzian intensity distribution dotted lines in parameter sets. Therefore we will describe in detail the Fig. 3 which reflects imperfections of the polishing proce- analysis procedure we followed. Reliable data can only be dure of the commercial substrates.26 This interpretation of obtained when additional structural information obtained the central portion of the rock as being the specular inten- from independent measurements is used. The first crucial sity is supported by the fact that rocks taken at different point is to separate the specular peak from the diffuse inten- order superlattice Bragg peaks, are described by Lorentzians sity contributions. Ideally, the specular intensity should be with identical width in as shown in Fig. 3 for 2 at the sharply peaked around qz 0 specular condition but can first and second order Bragg peak the diffuse intensity was also be broadened due to some macroscopic substrate surface also simulated with identical parameters . Similar widths of curvature. The additional aside from specular structure pa- the Lorentzians could be used for all samples. Other combi- rameters determining the diffuse intensity are the lateral cor- nations of parameters result in values of the roughness pa- relation length of the substrate-film interface x(S), the lat- rameters which contradict the AFM and STM studies. For eral correlation length of the interfaces inside the superlattice the analysis of all rocks we kept x(S) constant at 1 m x , the Hurst parameter h and the vertical correlation length even bigger values would not change the analysis since the z . From AFM measurements we know that the typical size central part of the rocks is dominated by the specular in- of the atomically flat substrate terraces is about 1 m which tensity . The Hurst parameter was found to be around h should yield x(S) values 1 m. Additionally, scanning 0.5, however, this value is not defined more precisely by tunneling microscopy STM and AFM studies of single Fe the simulations than within 0.2. In order to limit the num- or Cr films20,42,43 suggest x values of the order of 100 Å and ber of free parameters we kept this parameter constant at h h values around 0.6. The other parameter z does not have 0.5 for all rocks. The vertical correlation length z such a pronounced influence on the qx dependence of the mostly influences the simulations by rounding the intensity diffuse intensity. The resulting simulation of the diffuse in- drop off at high qx values. We found a value of z 200 Å tensity dashed lines in Fig. 3 is defined by first, the lateral which we also used for all simulations. Therefore, the only roughness components of the superlattice interfaces mostly free parameter for the simulation of all rocks is the lateral contributing to the intensity at larger angles, i.e., having a correlation length x . Through careful studies of the influ- 1246 R. SCHAD et al. PRB 59 FIG. 5. Diffuse SA XRD intensity as a function of the lateral scattering vector qx for all Fe 28 Å /Cr 11 Å 10 superlattices an- nealed to the temperatures as indicated. The spectra were measured FIG. 7. The transport properties a with a x-ray wavelength of 2.0753 Å 15 eV below the Cr absorp- s , b , and c / of the Fe 28 Å /Cr 11 Å tion edge with q 10 superlattices as a function of / x which z at the position of the second order superlattice is a structure parameter combining the vertical and lateral interface Bragg peak. Shown are the measured data points and the simula- roughness components. Variations in the AF coupling are taken into tions for the diffuse intensities lines . All curves are vertically account by dividing the magnetoresistance by the AFF. The trian- offset for clarity. gular data points correspond to the samples with constant and only x varying. The lines are guides to the eye. ence of x on the quality of the simulations Fig. 4 the error of its value can be estimated. Figure 5 shows the rocking curves taken at the position of the second order superlattice Bragg peak and the simulations describing the diffuse back- ground. It is worth noting also that the spectra's structure around qx 0.008 Å 1 which is caused by dynamical scattering is nicely reproduced. The simulations reveal a continuous decrease of x from 110 to 80 Å with increa- sing Ta . Obviously the lateral component of the interface structure must dominate the changes in the transport pro- perties. Next we will link structural information and transport properties of these samples. Theoretical models emphasize the influence of vertical and lateral interface roughness pa- rameters. The GMR should increase with both an increasing roughness amplitude or a shrinking lateral correlation length.6 In our case, we find for moderate annealing tempera- ture up to 400 °C a variation of only the lateral correlation length and an almost constant value of . The transport data as a function of x for this annealing temperature regime are shown in Fig. 6. The resistivity s remains unchanged, how- ever, both absolute and relative ( / s) magnetoresis- tance values decrease with increasing x . In order to present all data in a single graph, including the ones of the sample with increased FIG. 6. The transport properties a , we combine the vertical and lateral rough- s , b , and c / of the Fe 28 Å /Cr 11 Å ness parameters in a single interface roughness parameter 10 superlattices as a function of the lateral correlation length / x . Variations in the AF coupling are taken into x . The saturation resistivity s Fig. 7 a is constant for account by dividing the magnetoresistance by the AFF. The lines small values of / x constant , triangular data points and are guides to the eye. increases for the sample with the increased pin-hole forma- PRB 59 GIANT MAGNETORESISTANCE DEPENDENCE ON THE . . . 1247 tion indicating an increase of disorder. At saturation parallel scattering could not be separated from the interface contri- alignment of the magnetization directions the charge trans- bution. This led to two evenly possible, but opposing, inter- port is dominated by the minority electrons. Obviously, these pretations: one using only the interface contribution and the are weakly scattered at the increasing interface step density, other being based on a compensation of bulk and interface as indicated by the decreasing x . The increase of s for the contributions. Since the results reported here are obtained highest annealing temperature is more likely caused by the under elimination of bulk contributions it must be concluded increasing disorder in the form of pin holes. The absolute that the transport properties of the polycrystalline samples magnetoresistance /AFF Fig. 7 b increases linearly with are dominated by bulk scattering. Consequently, no informa- increasing / x whereas the relative magnetoresistance tion over the interplay between interface structure and GMR / s /AFF Fig. 7 c after an initial steep increase varia- amplitude can be deduced from the properties of such tions of x only grows slower because of the higher value of samples.44 s . Clearly, the increasing interface roughness effectively These structural changes found here for epitaxial Fe/ reduces the mobility of the majority electrons leading to the Cr 001 superlattices upon annealing will not necessarily oc- increase of 0 and hence . Since s is constant, this kind cur in samples of other orientation. First, polycrystalline of interface roughness results in a highly spin-selective scat- samples would provide more efficient diffusion channels tering potential. along grain boundaries facilitating intermixing or pin-hole formation. Furthermore, the thermodynamically stable inter- CONCLUSIONS face structure will depend on the crystallographic orienta- tion. For instance, 110 oriented Fe/Cr superlattices prefer a We varied the interface quality of a series of epitaxial zig-zag facetting of the interfaces caused by the formation of Fe/Cr 001 superlattices through annealing at different tem- presumably more stable 100 planes.45 Accordingly, an- peratures. The transport properties of these samples are char- nealing of 110 textured polycrystalline samples23,25 might acterized by negligible bulk scattering thus dominant inter- lead to totally different changes in the interface structure. face scattering. The interface thickness and the lateral The dependence of the GMR amplitude on the interface correlation length x were quantitatively analyzed by specu- structure, in particular its lateral roughness component, will lar and diffuse XRD. For moderate annealing temperatures presumably be the same for all crystallographic orientations. is constant whereas x decreases, indicating a higher step Still, there might be an intrinsic orientation dependence of density at the interfaces. We find an increase of the magne- the size of the GMR effect since different electrons in k toresistance with decreasing x at constant s indicating a space will contribute. However, the experimental verification high spin selectivity of the electron scattering at annealing- will be difficult to achieve because of the difficulty in pro- induced interface defects. This study shows clearly the im- ducing samples with different crystallographic orientation portance of the lateral interface roughness component for the but identical interface structure. understanding of the spin-dependent transport in magnetic multilayers. At higher annealing temperatures starts to in- ACKNOWLEDGMENTS crease causing a further increase of the GMR amplitude. This result is in clear contradiction to recently published This work was financially supported by the Belgian Con- results measured on polycrystalline samples.19 However, as certed Action GOA and Interuniversity Attraction Poles pointed out in Ref. 19, in spite of the very high GMR am- IUAP programs. R.S. and G.V. were supported by the plitudes obtained, the interpretation of the results remained HCM Program of the European Community and the Belgium ambiguous because bulk contributions to the spin-dependent Interuniversity Institute for Nuclear Sciences, respectively. *Author to whom correspondence should be addressed. Present 8 M. Ru¨hrig, R. Scha¨fer, A. Huber, R. Mosler, J. A. Wolf, S. address: University of Alabama, Center for Materials for Informa- Demokritov, and P. Gru¨nberg, Phys. Status Solidi A 125, 635 tion Technology, Box 870209, Tuscaloosa, AL 35487. FAX: 1991 . 1 205 3482346. Electronic address: rschad@bama.49.edu 9 C. D. Potter, R. Schad, P. Belie¨n, G. Verbanck, V. V. 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