PHYSICAL REVIEW B, VOLUME 63, 104407 Fe ÕCr interface magnetism: Correlation between hyperfine fields and magnetic moments V. M. Uzdin ICAPE, Saint-Petersburg State University, V.O. 14 Linia 29, 199178, St. Petersburg, Russia W. Keune, H. Schro¨r, and M. Walterfang Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t Duisburg, Lotharstr. 65, D-47048 Duisburg, Germany Received 28 February 2000; revised manuscript received 14 November 2000; published 14 February 2001 The magnetic hyperfine field hff in epitaxial Fe/Cr 001 superlattices on Mg 001 with different thick- nesses of interfacial 57Fe probe layers was measured by Mo¨ssbauer spectroscopy. Self-consistent calculations of the Fe and Cr atomic magnetic moments in the interface region were performed within the periodic Anderson model for the same superlattice structure. Different kinds of interface roughness/interdiffusion were modeled using special algorithms. For every kind of interface roughness the distribution of local magnetic moments among the Fe atoms with a given number of nearest and next-nearest Cr neighbors was calculated. We obtain a strong correlation between the experimental hff and calculated local Fe magnetic moments. Peak positions in the hff distribution and correlated positions of maxima in the distribution function for local magnetic moments are observed to be stable relative to changes in the alloylike interface roughness. We found that the hff of 20 T must correspond to interdiffused Fe atoms inside the Cr spacer layers a few atomic layers away from the ideal interface, contrary to earlier interpretations of Fe atoms at the atomically ``flat'' interface. As a measure of the Fe-Cr interface roughness on an atomic scale our results suggest an enhanced hff in the second Fe layer below the ideal interface in case of atomically smooth interfaces with large flat terraces. DOI: 10.1103/PhysRevB.63.104407 PACS number s : 75.70.Cn, 76.80. y, 73.40.Jn I. INTRODUCTION methods became one of the principal topics for the Fe/Cr systems. Fe/Cr overlayers, sandwiches, and magnetic superlattices Most of the experimental techniques give only indirect are the classical systems where recently a number of new information about chemical and magnetic roughness of the phenomena important both for understanding of the nature of interfaces on an atomic scale. Averaging over the whole in- low-dimensional magnetism and for application in micro- terface region or even on several interfaces in multilayers electronics have been discovered.1 Among these new phe- makes it difficult to reconstruct the microscopic interface nomena are short- and long-range oscillations of exchange structure from the experimental data. Only recently several coupling, giant magnetoresistance GMR , and noncollinear experimental approaches were reported that allow to find the magnetic ordering in the superlattices. It is well established layer-by-layer distribution of Cr and Fe atoms for a Cr over- now that most of the properties of the Fe/Cr systems cru- layer on the Fe surface. Scanning tunneling microscopy cially depend on the interface structure on an atomic scale, STM investigations, in combination with tunneling spec- which is determined by the very delicate conditions of the troscopy, showed the formation of an interfacial Cr-Fe alloy sample preparation: temperature during the epitaxial growth, that is observed as a distribution of single atomic Cr impu- quality of the substrate, etc. Spatial defects steps at the in- rities dispersed in the Fe substrate in the submonolayer- terface, embedded atoms and clusters of Fe in Cr and Cr in coverage regime,5 or Fe50Cr50 surface alloy formation of Fe, pinhole defects , which cannot be avoided during sample submonolayer Fe on Cr 001 after annealing.6 Proton- and preparation, not only modify the magnetic characteristics of electron-induced Auger-electron spectroscopy7 and angular the whole system but often prove to be responsible for the resolved Auger electron studies2,8 also unambiguously con- firmed the presence of interface alloying during growth of Cr new properties, being of large practical importance. Accord- on Fe. However, all of these methods work only for a Cr ing to Ref. 2 the bilinear exchange coupling in Fe/Cr trilay- coverage of less than a few monolayers, and they cannot give ers can be changed by as much as a factor of 5 by varying the information about the magnetic roughness associated with substrate temperature during the growth of the first Cr atomic the chemical roughness of the interface. Quantitative atomi- layer. In situ magnetometry measurements demonstrated a cally resolved information on magnetic moments near the very large decrease of the macroscopic integral moment interface may be derived, in principle, from an analysis of during Cr evaporation on smooth Fe surfaces, whereas for magnetic hyperfine fields hff that are obtained, in particu- rough Fe surfaces no change of the integral moment was lar, by using Mo¨ssbauer spectroscopy.9­16 By introducing a 1 observed at all.3 All the theories of noncollinear magnetic to 2-monolayer ML -thick 57Fe probe layer at the Fe/Cr ordering in Fe/Cr systems4 presuppose the existence of spa- interface, one can obtain local information about the distri- tial defects, which are the real reason for noncollinear struc- bution P(Bhf) of the hff in this region. The existence of 57Fe ture formation. Therefore, investigation of roughness, inter- atoms with various magnetic moments and with different diffusion, their dependence on the growth condition, and the local environments near the Fe/Cr interface leads to the ap- control of the interface structure using different experimental pearance of satellite lines in the Mo¨ssbauer spectra. How- 0163-1829/2001/63 10 /104407 15 /$15.00 63 104407-1 ©2001 The American Physical Society V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 ever, the interpretation of these data for low-dimensional Fe/Cr structures is very complicated and an ambiguous prob- lem. The total hff can be conveniently decomposed into the contribution from the valence (4s) electrons and into the contribution from the core electrons, polarized by the local- ized magnetic moment on a given 57Fe atom. For the bulk materials it is generally accepted that the hff scales approxi- mately with the magnetic moment.17 For surfaces, interfaces, and multilayers such an approach can be applied only for the core contribution, whereas the 4s part has to be investigated separately in every concrete case.17 Surprisingly, for most of the Fe/Cr multilayer structures the spectral positions of satellite Mo¨ssbauer lines do not dif- fer very much,9­16 although all other characteristics like GMR, parameters of exchange coupling, etc., as a rule, are very different. Comparison of hff distributions for Fe-Cr in- terfaces in the multilayers and for the Fe-Cr random alloys has led to the conclusion that as a first approach the interface FIG. 1. Distribution of hff peak positions in Fe/Cr structures upper abscissa . The 57Fe-probe-layer thickness is region can be considered as a bulk alloy with varying con- underlined. Hatched square with cross at 1.5 centration. For the treatment of Mo¨ssbauer spectra most in- B : calculated local Fe moment antiparallel to overall magnetization direction. vestigations follow the empirical procedure, which was sug- 1-W 110 /Cr 110 : 40 ML/Fe 110 :3 ML 2 ML 21 ML 2 ML gested initially for the description of random alloys.18 The 3 ML/Cr 110 Ref. 12 ; 2-W(110)/Cr 110 : hff, Bhf , on the Fe atoms is assumed to decrease linearly in 40 ML/Fe 110 :3 ML 25 ML 3 ML/Cr 110 Ref. 12 ; magnitude with the number of the nearest neighbor (n1) and 3-W(110)/Cr 110 :40 ML/Fe 110 :3 ML 4 ML 3 ML/Cr 110 next-nearest neighbor (n2) Cr atoms: Ref. 12 ; 4-W(110)/Cr 110 :40 ML/Fe 110 :6 ML/Cr 110 , Ref. 12 ; 5-W(110)/Cr 110 :40 ML/Fe 110 :4 ML/Cr 110 , Bhf Bhf bulk n1 B1 n2 B2 , 1 Ref. 12 ; 6-W(110)/Cr 110 :40 ML/Fe 110 :3.3 ML/Cr 110 , Ref. 12 ; 7-W(110)/Cr 110 :40 ML/Fe 110 :2 ML/Cr 110 , where B1 (B2) is the contribution to the hff from one Cr Ref. 12 ; 8-Si/Fe-6 nm Cr-1.1 nm/Fe-3 nm 60/Cr-1.1 nm, atom in the first second shell around the Fe atom under Ref. 15 ; 9-MgO/Fe 001 /Cr 001 , Ref. 14 ; 10- consideration. Improvement of the resolution of the measure- MgO/Cr 50 Å / Fe 100 :3 ML 8 ML 3 ML/Cr 100 ments and development of the epitaxial growth techniques 10, present work sample 1 ; 11-MgO/Cr 50 Å / Fe 100 : offered the opportunity to refine the alloy model. For the 0.7 ML 8 ML/Cr 100 , present work average of samples 2­4 ; description of the set of hff, Klinkhammer et al.10 suggested 12- MgO 100 /40 nm Cr/57Fe 100 2 ML/56Fe:2 nm/Cr:4 nm, the following relation: Ref. 10 ; GaAs 100 /Fe:1 nm/Ag 150 nm/56Fe:4 nm/57Fe 100 : 2 ML/Cr:1 nm/56Fe 4 nm; 13-magnetic moment calculations Bhf Bhf bulk n1 B1 n2 B2 B B i 2 . 2 within PAM present work lower abscissa Besides, of the fitting parameters B1 2.5 T and B2 2.05 T, W(110) substrate.12 Interpretation of CEMS spectra using which give the hff changes per Cr neighbor similar to the the empirical approach Eq. 1 or Eq. 2 leads for the same simple alloy approach of Eq. 1 , this relation contains two set of hff to different conclusions about the local environ- additional parameters: B 1.75 T, which the authors10 ment of 57Fe atoms, their numbers of nearest (n1) and next- connected with the broken spatial symmetry in the transverse nearest (n2)Cr neighbors and, consequently, to the distinct direction; and B(i 2) 1.2 T, when n1 0, n2 1 and spatial structure of the Fe/Cr interface region. The micro- equal to zero otherwise. Note, that n1 0, n2 1 corresponds scopic analysis of Fe/Cr interface magnetism, taking into ac- to an Fe atom in the second atomic Fe layer below the ideal count roughness and interdiffusion, then becomes very im- Fe/Cr interface. Taking into account that Bhf bulk is nega- portant for understanding the real physical information that tive 33.3 T at room temperature , we obtain from Eq. 2 can be extracted from CEMS data. an enhancement of the magnitude of Bhf for these atoms. Most of the calculations of magnetic-moment distribu- Such an enhancement was detected experimentally only for tions in intermixed Fe/Cr layers of multilayer systems were molecular-beam grown epitaxial samples with smooth restricted to the ordered structure of the interface and to the interfaces,10,12 and was never reported for sputtered very thin interface region, which include usually one to two multilayers.11,15,16 monolayers. Coehoorn19 performed the first-principal band- Figure 1 illustrates schematically the distribution of dis- structure calculations for 110 - and 100 -oriented Fe/Cr su- crete hff values that were obtained for Fe/Cr interfaces by perlattices with intermixed monolayers at the interfaces. He different groups using conversion electron Mo¨ssbauer spec- concludes that Fe and Cr moments at the Fe/Cr interface troscopy CEMS . We underline again that the enhanced hff show almost no dependence on the nearest-neighbor environ- in the subsurface Fe layer exists only for smooth interfaces, ment. A change of the Fe concentration in the interface layer and that its intensity is larger for those cases where interdif- mainly affected the Fe moments in the Fe layer one atomic fusion is minimized or suppressed, e.g., like in the case of a layer below the mixed layer. This is not very surprising, 104407-2 Fe/Cr INTERFACE MAGNETISM: CORRELATION . . . PHYSICAL REVIEW B 63 104407 because for a bcc lattice and for 100 interface orientation tion of electron emission from rough surfaces, the calculated atoms do not contain nearest neighbors in the same layer, but magnetic structure of a nonideal Cr/Fe overlayer gave rea- only in the previous and next layers. The moments in the sonable agreement with experimental results by Knabben second and third layers below the mixed interface proved to et al.23 be already quite independent of the concentration in the In the present work we will use the same theoretical mixed layer, although they were found to be slightly above approach for the calculation of magnetic moments in the calculated value for bulk (2.26 Fe/Cr 001 superlattices with different types of interface B). Freyss et al.20 mod- eled an interfacial alloy by either a one- or a two-monolayer- roughness, and we investigate the correlation between the thick ordered compound whose concentration was varied. calculated magnetic structure and experimental hff distribu- They performed self-consistent calculations within a tight- tions. binding model Hamiltonian for a Cr overlayer on an Fe sub- The paper is organized as follows. In Sec. II, the experi- strate, and showed that the more Cr and Fe interdiffused at mental procedure of sample preparation and CEMS measure- the interface inside two mixed layers , the more important is ments are described. In Sec. III we discuss the modeling of the decrease of the sample magnetization due to Cr coverage. the interface roughness and interdiffusion by different ran- All these approaches, which presuppose ordered interface dom algorithms. In Sec. IV the results of self-consistent cal- layers instead of real rough interfaces, can give only a quali- culations for interfaces with different roughness are pre- tative picture of the interference between magnetic and sented. In Sec. V we discuss the approach of Eqs. 1 and 2 chemical structure. The role of interface chemical ordering for hff within the light of our calculations, and we compare as well as of the sensitivity of the calculated magnetic prop- magnetic-moment distributions for different rough interfaces erties on this assumption needs special consideration. with experimentally observed hff. Finally the paper is con- The magnetic structure of disordered rough Fe/Cr inter- cluded in Sec. VI. faces was investigated on an atomic scale within the periodic II. EXPERIMENTAL PROCEDURE AND RESULTS Anderson model PAM in Ref. 21. Self-consistent calcula- tions of magnetic moments were fulfilled for the set of rough Fe/Cr 001 superlattices were epitaxially grown by ultra- interfaces modeled in the ballistic approach using the special high-vacuum deposition of the metals on epipolished algorithm ``epitaxy.'' This algorithm allows one to simulate MgO 001 substrates. The substrate surface was cleaned us- random Fe/Cr multilayer structures with different, but con- ing isopropanol and after insertion into the ultrahigh- trolled, alloying at the interface region. Magnetic character- vacuum system heating at 900 K for 1 h to remove surface istics of the Fe sample covered by thin Cr films, which were contaminants and to anneal the surface. At a substrate tem- measured by different experimental methods, then can be perature of 900 K a 50-Å-thick Cr buffer layer was grown modeled using an appropriate averaging procedure. In such a on MgO first. Preparing the buffer layer at this temperature way the roughness-induced transition from the oscillation be- gave the best results for epitaxial growth of Fe on Cr. Sub- havior to the exponential decrease of the total magnetic mo- sequently the Fe/Cr 001 superlattice was grown at 433 K at ment of the Fe sample with Cr coverage was described theo- a pressure 5 10 9 mbar. This growth temperature pro- retically in Ref. 21. This transition takes place with vides good epitaxy and is below the growth temperature of increasing interface alloying, governed by the parameters of 500 K, where severe long-range Fe-Cr interdiffusion the epitaxy algorithm. An exponential decrease of the total occurs.9 High-purity materials natural Fe: 99.9985 at. %, Cr: moment was detected experimentally by Turtur and 99.999 at. %; 57Fe: 95.5% and 56Fe: 99.5% isotopically en- Bayreuther3 using magnetometer measurements. In Ref. 22 a riched were evaporated from resistively heated Knudsen similar approach was used for the description of magnetic cells with deposition rates of 0.2­0.3 Å s 1, as measured by dichroism and spin-resolved photoemission data from rough calibrated quartz-crystal oscillators. We have investigated interfaces. Together with the simplified theory for descrip- four types of samples of different composition: MgO/Cr 50 Å / 57Fe 3 ML /natFe 8 ML /57Fe 3 ML /Cr 8 ML 10 sample 1 MgO/Cr 50 Å / 57Fe 0.7 ML /natFe 8 ML /Cr 8 ML 40 sample 2 MgO/Cr 50 Å 57Fe 0.7 ML /natFe 8 ML /Cr 8 ML 200 sample 3 MgO/Cr 50 Å / 57Fe 0.7 ML /56Fe 8 ML /Cr 8 ML 200 sample 4 . In sample 1, 3-ML-thick 57Fe probe layers were artifi- 0.7-ML 1 Å -thick 57Fe probe layers were deposited at one cially placed at both types of interfaces Fe deposited on type of interface only ``dusting'' of the Fe/Cr interfaces . Cr Fe/Cr, ``lower'' interface... and Cr deposited on Fe The probe-layer method24,25 provides an 57Fe nuclear reso- Cr/Fe, ``upper'' interface . In samples 2­4, ultrathin nance Mo¨ssbauer signal predominantly from 57Fe atoms in 104407-3 V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 FIG. 2. Low-angle XRD intensity measured on a sample 1, b sample 3. The order of the Bragg diffraction peaks is marked by numbers. Note that the second-order peak is forbidden for sample 3 Cu K radiation . FIG. 3. High-angle XRD intensity measured on a sample 1, b sample 3. The arrows in b mark the first-order satellite peaks the interface region in samples 1­3, and exclusively in the observed around the 200 Bragg peak of Fe. Note that the second- interface region in sample 4. order satellite peaks are forbidden for sample 3 . The strong peaks The multilayer structure of our samples was qualitatively near 43° and 93° belong to the 200 and 400 reflections, respec- characterized by conventional ­2 low-angle and high- tively, of the Mg 001 substrate Cu K radiation . angle diffraction XRD . Representative XRD results are shown in Fig. 2 low angle and Fig. 3 high angle for Mo¨ssbauer CEMS spectra were measured at room tem- sample 1 and sample 3. The samples with a low number of perature RT using a He/CH4-filled proportional counter and stacked Fe/Cr bilayers e.g., like sample 1 generally exhibit a 57Co-in-Rh source. The incident radiation was perpen- first- and second-order low-angle superstructure Bragg peaks dicular to the sample surface. Typical CEM spectra of and intensity oscillations from total thickness interference samples 1­4 are shown in Fig. 4 a ­4 d , respectively. As Fig. 1 a . Due to the large total thickness these oscillations compared to the simple Zeeman sextet of ferromagnetic bulk disappear in samples with a high number of bilayers like bcc Fe, the spectra in Fig. 4 exhibit distinct shoulders and sample 3 ; but a strong first-order and weaker third-order extra peaks as a result of changes of the 57Fe hff that are low-angle superstructure peak is observed Fig. 1 b . Note induced by neighboring Cr atoms in the interfacial that the second-order superstructure peak is forbidden for 57Fe-probe layers region. sample 3, because the individual Fe and Cr thicknesses are The CEM spectra were least-squares fitted with two hff about equal. These observations demonstrate that our distributions ranging from 0 to 18 T low-field region and samples have flat surfaces and good multilayer quality, from 18 to 35 T high-field region for sample 1, and from 0 which is preserved even up to a thickness of 200 bilayers to 15 T low-field region and from 15 to 35 T high-field e.g., like sample 3 . In high-angle XRD Fig. 3 , the 200 region for samples 2­4. For the fitting, the NORMOS com- and no other Bragg reflection of bcc Fe was detected. The puter program by Brand26 was used, which is based on the typical full width at half maximum FWHM of the rocking histogram method by Hesse and Ru¨bartsch.27 In order to curve not shown of this peak was found to be about 2° for achieve satisfying fitting, a linear correlation between hff and all samples. These results demonstrate the single-crystalline isomer shift had to be assumed, and, further, the line- epitaxial nature of our samples. Typically two first-order intensity ratios of the basic sextets in the hff distributions satellite peaks arrows in Fig. 3 b around the fundamental were supposed to be 3:4:1, implying Fe-spin orientation in 200 reflection of bcc Fe were observed in samples with a the film plane. large number of bilayers e.g., like sample 3 . Again, the The hff distributions, P(Bhf), are shown in Fig. 5. The second-order satellite peaks are forbidden for sample 3 . high-field distributions of all samples exhibit six pronounced These observations provide a proof of the high superlattice maxima, located at Bhf 33.1, 30.6, 28.0, 25.2, 22.7, and quality of our samples up to 200 bilayers. However, for 19.6 T, respectively, for sample 1, and at Bhf 33.2, 30.3, samples with a low number of bilayers e.g., like sample 1 27.9, 25.0, 22.6, and 19.7 T for samples 2­4 averaged . An satellite peaks around 200 are difficult to detect, as ex- additional peak at 16.9 T is observable in Fig. 5 for samples pected Fig. 3 a . According to magnetization hysteresis 2­4 only, which have a smaller average probe-layer thick- loops not shown , the samples exhibit zero remanence, i.e., ness 0.7-ML 57Fe than sample 1 3-ML 57Fe . The ob- strong antiferromagnetic AFM interlayer coupling,13 as ex- served hff value of 33.2 T is equal to the bcc-Fe bulk value, pected for 8-ML Cr layers. Bhf bulk , at 300 K, and evidently is associated with 57Fe 104407-4 Fe/Cr INTERFACE MAGNETISM: CORRELATION . . . PHYSICAL REVIEW B 63 104407 FIG. 5. Hyperfine-field distribution, P(Bhf), obtained from Fig. 4: a sample 1, b sample 2, c sample 3, and d sample 4. FIG. 4. CEM spectra of Fe/Cr 001 superlattices, measured by Landes et al.,9 the experimental hff of 20.9 T which is at 300 K: a sample 1: 57Fe 3 ML /natFe 8 ML /57Fe 3 ML / close to our 19.7-T value was attributed to the ideal flat Cr 8 ML 10; b sample 2: 57Fe 0.7 ML /natFe 8 ML / interface site, while Schad et al.14 assigned a value of 19 T Cr 8 ML 40; c sample 3: 57Fe 0.7 ML /natFe 8 ML / Cr 8 ML for this site. In a refined analysis Klinkhammer et al.10 re- 200; d sample 4: 57Fe 0.7 ML /56Fe 8 ML / Cr 8 ML 200. Full-drawn curves: result of least-squares fit with ported a value of 23.0 T for the ideal flat interface site distribution of hyperfine fields, P(B n hf). 1 4, n2 1 or 4/1 site.... It is remarkable in Fig. 5 that the low-field P(Bhf) distri- atoms in a ``bulklike'' environment without nearest (n1 butions contribute only very little about 3% or less to the 0) or next-nearest (n2 0)Cr neighbors. Note in Fig. 5 total area of the hff distribution or to the total area of the that the relative intensity relative area of this bulk peak is Mo¨ssbauer spectra . In particular, there is a neglible contri- remarkably higher for sample 1 40% than for samples 2, 3, bution near Bhf 0 T of a paramagnetic subspectrum for our and 4 19, 19.5, and 15.9%, respectively , as is expected samples, such as it arises for paramagnetic isolated Fe atoms regarding the larger probe-layer thickness 3-ML 57Fe of in a bulk Cr matrix. sample 1, and assuming the same degree of slight and un- In Fig. 1 we compare the hff values at the observed avoidable intermixing of 56Fe and 57Fe on an atomic scale of maxima in P(Bhf) of our samples with corresponding results 1 to 2 ML9,10 in all types of samples. The weakest 33-T peak reported in the literature top abscissa in Fig. 1 . Obviously, relative area 15.9% is observed in the distribution of there is reasonable agreement regarding certain hff values in sample 4 Fig. 5 a , because 57Fe does not exist in the cen- our samples, in molecular beam epitaxy MBE -grown9,10,14 tral part of the 56Fe films. Conversely, one should notice in and sputtered samples,15 and even in MBE-grown samples Fig. 5 the strikingly higher relative intensity of the hff dis- with 110 orientation.12 Not included in Fig. 1 are hff dis- tribution peak at 19.7 T for samples 2­4, as compared to tribution peaks of sputtered Fe/Cr superlattices on MgO 001 sample 1. Since only the relative intensity of the individual that were observed16 at Bhf 33.3, 30.7, 26, 22, 20, and 10 T hff distribution peaks or of the individual subspectra is and are negligible near zero-hff paramagnetic contributions modified by changing the 57Fe-probe-layer thickness, and not at Bhf 1.0 T , similar to our case. We like to emphasize their individual positions, each P(Bhf) peak originates from again that the enhanced larger than bulk Bhf value, which a certain characteristic 57Fe environment site within the appears to be characteristic of the second Fe layer below the Fe-Cr interfacial region. For instance, according to the model ideally flat Fe/Cr interface, has been convincingly detected 104407-5 V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 only in molecular-beam grown epitaxial Fe/Cr systems with relatively smooth interfaces.9,10,12 The enhanced hff was observed neither in our UHV-deposited superlattices, nor in sputtered Fe/Cr systems,11,15,16 very likely due to a larger interface roughness as compared to MBE-grown structures. III. MODELING OF THE ROUGH INTERFACES The evolution of a growing interface is a very compli- cated phenomenon that depends on the internal interactions between atoms as well as on the number of external factors.28 For the Fe/Cr systems, where both elements have almost the same lattice constant, alloying processes cannot be completely avoided. Epitaxial growth leads to an interface structure that, as a first approach, can be considered as a superposition of steps and an alloy with varying concentra- tion. It is also important that the process of alloying may be substantially nonsymmetric: this is essential, when the sub- strate material has a lower melting temperature than the ada- tom material.2,8 This will be the case for evaporating Cr on Fe, but for Fe on Cr alloying should be suppressed. How- ever, for the rough Cr surface alloying after Fe deposition also can occur. The scenario of alloying as well as the result of this process at different interfaces in Fe/Cr multilayers can be essentially different. For the investigation of the magnetic-moment distribution near the rough Fe/Cr interface, and for further comparison of FIG. 6. Modeling of stepped interface. it with the distribution of hff obtained from the CEM spectra, we developed several random algorithms that allow one to 64 1 cell with periodic boundary conditions. The total create the superlattices with different types of interface length of the cell 64 sites was divided into an even number roughness. The period of all superlattices was taken equal to of equal intervals L0 Fig. 6 a , where L0 is the parameter of 22 monolayers: 8-ML Cr and 14-ML Fe, in order to obtain the algorithm. Then, for every pair of neighboring intervals a the structures, similar to the ones studied in the experiment random number l L0 was chosen, and l successive interface Sec. II . We also used different kinds of Fe atoms sites for Fe atoms from the first interval have been exchanged with l comparison with Mo¨ssbauer results, when only hff at the successive interface Cr atoms from the second interval Fig. 57Fe nuclei are measured. Taking into account that in our 6 b . The position of l atoms inside the interval L0 was experiments we used about 1- and 3-ML-thick 57Fe-probe taken as random. As a result we obtained the stepped inter- layers in the interface region, for the modeling of such a face where one-ML high upsteps alternate with one-ML high system we create superlattices with period Fe1 1 ML /Fe2 2 downsteps, and the lateral size of every step does not exceed ML /Fe3 8 ML /Fe2 2 ML /Fe4 1 ML /Cr 8 ML . Here, L0 Fig. 6 c . Obviously only atoms Fe1 and Fe4 can be in through the label Fe1, Fe2, etc., we denote the different the mixed Fe/Cr layers. Decreasing the parameter L0 leads to kinds of Fe atoms within an individual Fe layer of the Fe/Cr the formation of interfaces with larger density of steps per multilayer. All of these Fe atoms are fully identical and have unit of length. In the direction perpendicular to the plane the same set of parameters in the model Hamiltonian, but the direction the system stays spatially homogenous. Modeling distribution of magnetic moments can be obtained not only of every superlattice was repeated 20 times to obtain the on all the Fe and the Cr atoms, but also separately on the Fe distributions that do not depend on concrete realization. atoms of a given type. For example, for comparison of the Alloying and interdiffusion have been simulated in the hff distribution measured for the superlattice with 3-ML 57Fe ballistic regime using the algorithm epitaxy.21,22 This algo- at every ``Fe/Cr'' and ``Cr/Fe'' interface with the calculated rithm fills the prism with cross section 8 8 atomic sites by distribution of the magnetic moments, we have to find the Fe and Cr atoms. Outside the prism the structure was re- magnetic moments localized on Fe1, Fe2, and Fe4 sites, peated periodically. The height of the prism was taken as 30 whereas for a superlattice with only 1-ML 57Fe at the Cr/Fe layers, but only 22 layers were cut for self-consistent calcu- interface we need the magnetic moments of Fe4 atoms. lations of magnetic moments to reproduce the superlattice Interface roughness was introduced into the model by two structure with period 22 ML. Initially, the bottom layer of kinds of random procedures: the first one produces atomic the prism was filled by Fe3 atoms, and all the other sites steps at the interface, whereas the second one models inter- inside the prism were empty. Then new atoms are thrown on face alloying and interdiffusion. For modeling of the stepped the top level of the prism with a random procedure, and the interfaces we started from the ideal superlattice, where all the epitaxy routine provided their descending through empty layers contain only Cr or Fe atoms. In the plane we used a sites in the bcc lattice until the sliding is blocked. Transfer of 104407-6 Fe/Cr INTERFACE MAGNETISM: CORRELATION . . . PHYSICAL REVIEW B 63 104407 and Fe atoms using two different procedures: i on an empty place we put Fe, if most of the nearest-neighbor sites are filled by Fe, and in the opposite case this place was filled by Cr; ii all the empty sites were filled by Fe atoms. For pro- cedure i additional Fe atoms cannot appear inside the Cr spacer. The concentration of Fe in Cr and Cr in Fe decreases toward zero away from the interface. Due to the relatively thick interface region we will call such an interface as ``rough.'' Procedure ii gives the structure with a constant, although relatively small, Fe concentration far enough from the interface. In the following such a structure will be de- noted as ``rough alloy.'' Note that our epitaxy algorithm corresponds to the ``bal- listic deposition'' in the theory of epitaxial growth.29 Vari- ants A and B of the algorithm move or stop atoms depending FIG. 7. Modeling of alloying using the epitaxy algorithm. on the number of bonds with its nearest neighbors that the deposited atom has. This can be considered as a simplified atoms from one layer to the next layer occurs with equal ``bond counting'' approach. probability to any of the nearest-neighbor sites. If we put on The distribution of Fe atoms, which have given numbers the top of the prism 64 NFe atoms of Fe and after that of Cr nearest (n1) and next-nearest (n2) neighbors, is pre- 64 NCr atoms of Cr we will obtain the structure sented in Table I for different kinds of rough interfaces. The Cr(NCr)/Fe(NFe) with a rough interface. Taking into account left column in the table specifies the local environment of Fe that the surface layer is not fully filled by the atoms, we atoms, n1 /n2 . For every structure we depicted the numbers throw away a few top and bottom layers and put periodic for the whole Fe atoms I , for the Fe atoms from the 3-ML- boundary conditions for the remaining layers in the prism. In thick interfacial layers at every Fe/Cr and Cr/Fe interface: such a way we obtain a Fe/Cr superlattice with rough Fe/Cr Fe 1 Fe 2 Fe 4 II , and for 1 ML at the Fe/Cr interface: and Cr/Fe interfaces. Every such modeling was repeated 20 Fe 4 III . Note that for the structure ``rough alloy'' addi- times, like in the case of the stepped interface. tional Fe atoms, which appear inside the Cr spacer, instead Figure 7 shows the random walk of the atom in the bcc of empty places were taken as Fe 4 , and inside Fe layers as lattice. Empty circles depict sites that are not filled by atoms. Fe 3 . The atom stops its movement, if all four possible next posi- Simple analysis of the data in Table I shows that the frac- tions are blocked. If only part of these four position is tion of Fe atoms with a given local environment is strongly blocked, the atom may either continue its descent with prob- connected with the type of interface roughness. Stepped in- abilities pi through each empty site or it may stop at a par- terfaces contain only Fe atoms in 0/0, 0/1, 2/1, 2/2, 4/1, 4/2, ticular site with the probability 1 ipi . The quantities pi and 4/3 configurations, and all Fe atoms that have Cr neigh- have been taken to depend on the amount of blocked path. bors lie in the 3-ML-thick interface layers. Among atoms The set of pi values is the input parameter of the epitaxy from first interface layers there are no bulklike atoms 0/0 . It algorithm. Different pi values lead to distinct surface and means that for such stepped structures with 1-ML 57Fe at the interface structures. In our modeling we used two sets of pi : interface the bulk contribution to the hff has to be almost A pi 1/n, where n is the number of empty nearest- fully suppressed. Comparison of the distributions for 1- and neighbor sites in the next layer. In this case the atom is 3-ML-thick interface layers demonstrates that, depending on forced to move, if at least one of the nearest sites in the next the size of the steps, different configurations become more or layer is empty. Surfaces and interfaces generated by the al- less probable. In particular, for L0 16 one can find Fe atoms gorithm epitaxy turn out to be relatively smooth. The width in the 4/1 state much more often than in the 4/2 state. For of the interface region, where there are both Fe and Cr at- L0 4, the corresponding ratio among these Fe sites from the oms, does not exceed 3 to 4 ML, and the sample does not 3-ML-thick interface is not far from unity, and it becomes contain any empty sites in inner layers. We will identify such less then unity for the atoms in the 1-ML-thick interface. an interface as ``smooth.'' The structure with interface alloying is characterized by a B pi 1/4 for n 1 and for n 2; pi 1/3 for n 3. wider atomic distribution between states with different local Here, the atom can stop its descent, if there are only one or environments. This distribution expands with increasing two available sites in the next layer. The interface structure roughness due to Fe atoms that penetrate deeper into the Cr proves to be more irregular with some hollow sites and in- spacer and fill the states with a large number of Cr neigh- terface mixing of Fe and Cr atoms in a 7- to 10-ML-thick bors. Whereas for the ``smooth'' interface only Fe atoms region. with n1 4 are present, for the rougher structures there are To simulate interface intermixing of Fe and Cr atoms we states with all possible numbers of Cr nearest neighbors up used the B variant for Fe-on-Fe and Cr-on-Cr growth and the to eight. The number of nearest neighbor Cr atoms n1 and A variant for growth Fe on Cr and Cr on Fe. However, even next-nearest neighbors n2 is also correlated for the rough so, some empty sites remained in the inner layers. To remove structure under investigation. For every n1 there is n2* , these pores inside the sample we filled empty places by Cr which corresponds to the most probable configuration with a 104407-7 V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 TABLE I. Simulated distribution of Fe atoms that have given number of nearest (n1) and next-nearest (n2) Cr neighbors for different kinds of rough interfaces. Left column: local environment of Fe atoms, labeled n1 /n2 . For every structure stepped, smooth, rough, or rough alloy interface the numbers for all of the Fe atoms I , for Fe atoms from 3-ML-thick layers at every Fe/Cr and Cr/Fe interface Fe 1 Fe 4 II , and for 1 ML at the Cr/Fe interface Fe 4 III are depicted. Stepped L0 16 Stepped L0 4 Smooth Rough Rough alloy Config. I II III I II III I II III I II III I II III 0/0 1919 3835 0 1922 3864 0 19 200 3915 17 13 908 4064 90 1403 4139 97 5 4 5 0/1 3600 3600 489 2911 2911 386 2197 2123 95 1569 1078 95 1625 1108 109 0/2 0 0 0 0 0 0 0 0 0 75 56 0 144 102 1 1/0 0 0 0 0 0 0 0 0 0 986 599 72 1226 771 99 1/1 0 0 0 0 0 0 1169 1168 145 1461 1128 188 1415 1075 198 1/2 0 0 0 0 0 0 0 0 0 364 283 44 423 304 58 1/3 0 0 0 0 0 0 0 0 0 48 37 4 87 58 7 2/0 0 0 0 0 0 0 0 0 0 145 103 21 267 207 56 2/1 431 431 91 1427 1427 239 863 863 196 835 658 220 847 679 239 2/2 49 49 29 431 431 241 74 74 20 615 480 145 616 466 159 2/3 0 0 0 0 0 0 0 0 0 203 152 36 249 158 46 2/4 0 0 0 0 0 0 0 0 0 24 17 5 64 42 16 3/0 0 0 0 0 0 0 0 0 0 3 1 1 64 50 12 3/1 0 0 0 0 0 0 824 824 295 400 317 108 437 355 129 3/2 0 0 0 0 0 0 317 317 119 601 462 159 541 434 174 3/3 0 0 0 0 0 0 50 50 24 397 300 93 421 325 137 3/4 0 0 0 0 0 0 0 0 0 108 76 24 200 128 57 3/5 0 0 0 0 0 0 0 0 0 8 7 3 46 23 16 4/1 3177 3177 1098 1592 1592 462 662 662 295 71 56 16 103 93 27 4/2 415 415 207 1211 1211 607 658 658 295 276 223 75 293 259 133 4/3 8 8 2 108 108 47 400 400 194 407 336 113 415 362 220 4/4 0 0 0 0 0 0 303 303 147 283 225 74 323 280 197 4/5 0 0 0 0 0 0 163 163 78 69 55 21 166 146 126 4/6 0 0 0 0 0 0 0 0 0 0 0 0 22 18 18 5/1 0 0 0 0 0 0 0 0 0 4 4 0 24 24 11 5/2 0 0 0 0 0 0 0 0 0 37 36 11 90 89 56 5/3 0 0 0 0 0 0 0 0 0 154 136 50 266 265 197 5/4 0 0 0 0 0 0 0 0 0 220 197 82 333 333 288 5/5 0 0 0 0 0 0 0 0 0 106 88 40 285 285 267 5/6 0 0 0 0 0 0 0 0 0 7 6 1 82 80 80 6/3 0 0 0 0 0 0 0 0 0 14 13 4 92 92 79 6/4 0 0 0 0 0 0 0 0 0 67 65 25 262 262 246 6/5 0 0 0 0 0 0 0 0 0 82 80 40 340 340 333 6/6 0 0 0 0 0 0 0 0 0 11 11 5 196 196 195 7/3 0 0 0 0 0 0 0 0 0 0 0 0 26 26 25 7/4 0 0 0 0 0 0 0 0 0 7 7 5 124 124 123 7/5 0 0 0 0 0 0 0 0 0 22 22 19 250 250 250 7/6 0 0 0 0 0 0 0 0 0 14 12 10 208 207 204 8/4 0 0 0 0 0 0 0 0 0 1 1 1 28 28 28 8/5 0 0 0 0 0 0 0 0 0 6 6 4 79 79 79 8/6 0 0 0 0 0 0 0 0 0 24 22 16 99 99 99 given n1 . With increasing n1 the value n IV. DISTRIBUTION OF MAGNETIC MOMENTS 2* also monoto- nously increases. Among the atoms within 1 ML at the in- FOR INTERFACES WITH DIFFERENT ROUGHNESS terface the state without neighboring Cr atoms 0/0 for the Calculations of the magnetic moment distribution were alloyed interfaces is also suppressed, but not fully like in the performed within the PAM in Hartree-Fock approximation case of stepped structures. by the real-space recursion method.21,30 For numerical calcu- 104407-8 Fe/Cr INTERFACE MAGNETISM: CORRELATION . . . PHYSICAL REVIEW B 63 104407 next-nearest neighbor Cr atoms we plotted the distribution of magnetic moments among the atoms that have a given num- ber of Cr neighbors. Analysis of these dependencies for the stepped interface shows that enhancement of the magnetic moments takes place mainly for Fe atoms in the 0/1 state. Note that similar enhancement of magnetic moments for the Fe atoms inside clusters and pinhole defects embedded into the Cr matrix was observed in Refs. 30, 33, and 34. This moment enhancement is correlated with hff data,9,10,12 where for the second Fe layer below the ideal interface an enlarged hff was assumed see Eq. 2 . There is, however, also a very small amount of Fe atoms in the same 0/1 state, which has a small moment of about 1.5­ 1.6 B . A clearer separation in low- and high-spin states can be seen, for example, for the Fe atoms with two Cr nearest and one next-nearest neighbors Fig. 9 a and 9 b . The low-spin state has the moment 1.70­ 1.78 B for 2/1 configuration and 1.65­ 1.75 B for 2/2 configuration, not shown . Correspondingly, high-spin FIG. 8. Calculated distribution of magnetic moments in B in moments lie in the regions 1.95­ 2.10 B Fig. 9 a and 9 b the 3-ML-thick interface layers for the stepped interface with L0 and 1.98­ 2.05 4. The inset shows the distribution of moments for the Fe atoms B not shown . Among the Fe atoms at the interface that have four nearest-neighbor Cr atoms we found with opposite direction of magnetization antiparallel to the overall magnetization direction . a noticeable part that changes the direction of their moments opposite to the direction of the average magnetization. lations we used the modification of the ``zero and poles'' In general, there is the tendency for a decrease of the method, which allows to determine very effectively the poles moments by increasing the number of Cr neighbors. How- of the mass operator and the Green function, and to avoid ever, the existence of two different magnetic states with es- time-consuming numerical integration of density of sentially different moments for the same number of Cr d-electron states in the process of self-consistency.31,32 The neighbors does not allow to conclude on an additive influ- self-consistency procedure starts from the state where all ence of the Cr neighbors. Similar results concerning nonad- magnitudes of the magnetic moments on Fe and Cr sites ditive perturbation of Fe magnetic moments were obtained in were equal to the corresponding bulk values and the direc- Ref. 35 for the dilute FeCr alloy, and were explained by the tion of the moments on Fe sites were taken to coincide, sensitivity of Cr magnetic moments to the local environment. whereas on Cr sites both spin polarizations were available The Cr moments for the stepped interface have a very wide with equal probability. Calculations of magnetic moments distribution with moments ranging from 0 to 1.2 B Fig. were performed to obtain self-consistency both on every site 10 a . Such a behavior is caused by frustration effects that and between magnetic moments localized on different sites. appear due to Fe-Cr and Cr-Cr antiferromagnetic AF cou- One more procedure fitted the Fermi energy, which fixes the pling. The ground state in the superlattices with stepped in- total number of d electrons during self-consistency. terfaces corresponds to the noncollinear ordering.36 For both stepped interfaces with L0 4 and L0 16 we Alloying and interdiffusion at the interface lead to a dis- obtain very similar distributions of magnetic moments, tribution of the magnetic moments that contains a larger where deviation from the bulk value takes place only inside number of maxima, although some of them confluence with 3-ML-thick interface layers. In Fig. 8 such a distribution is increasing roughness. Figures 11 a and 11 b show such dis- shown for L0 4. The distribution function contains few tributions corresponding to 3-ML-thick layers at both inter- sharp maxima, one of which corresponds to the bulk mo- faces and to 1-ML-thick layers at the Fe/Cr interfaces, both ment, and others to the enhanced moment up to 2.40 B . for the case of a ``smooth'' structure. The distribution func- There are two extended maxima with less amplitude in the tions contain well-separated maxima, which give the most region 1.5­ 1.8 B and 1.95­ 2.05 B . The shape of the dis- probable values of the Fe moments. The largest maximum tribution function is essentially asymmetrical near these 1690 atoms in the 3-ML-thick interface with a moment of maxima. In the neighborhood of the first maximum it slowly 2.20­ 2.21 B corresponds to the bulk Fe moments. For the increases from 1.5 to 1.75 B , and then drops to zero very 1-ML-thick layer at the Fe/Cr interface this peak becomes fast. Around the second maximum it has a longer tail from much lower, which reflects the reduction of the number of Fe the side of larger moments. There are also some Fe atoms atoms in the 0/0 state for 1 ML at the interface see Table I . that change the direction of magnetization under the action In both figures, 11 a and 11 b , there is a peak for the en- of Cr neighbors. Their moment distribution is shown in the hanced magnetic moment of order 2.35 B . For 1 ML at the inset of the Fig. 8. Fe atoms from the 1-ML-thick interface interface this peak is well separated from the bulk peak by a layer show really full suppression of the bulk moment in gap Fig. 11 b , but for 3-ML-thick interface layers the gap accordance with data in Table I. disappears Fig. 11 a . Other maxima correspond to lower- As a check of the assumption about the additivity of the than-bulk moments: around 2.0 B , 1.85 B , and in the re- Fe-magnetic moment perturbation by nearest neighbor and gion 1.6­ 1.7 B . These intervals, where the distribution 104407-9 V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 FIG. 9. Calculated distribution of magnetic moments in B of 2/1 Fe atoms with two Cr near- est neighbors and one Cr second- nearest neighbor: a and b for the stepped interface with L0 16 and L0 4, respectively. c ­ e for the interfaces with interdiffu- sion: c smooth d rough, e rough alloy. function has its maxima, are shown also in Fig. 1 for com- 1.93­ 2.08 B ; 1.70­ 1.90 B , and 1.3­ 1.7 B , respectively. parison with hyperfine fields measured by CEMS. One can Such a separation of the possible values of magnetic mo- see a strong correlation between distribution peaks of hff and ments for every local environment does not mean additive magnetic moments. However, calculated peaks for magnetic perturbation of the Fe moments by Cr atoms. For rougher moments lower than 1.5 B cannot be reproduced for the interfaces the peak positions of the distribution function do smooth interface. The moment distribution for Fe atoms with not change essentially. Figure 12 shows the moment distri- a given number of nearest-neighbor and next-nearest neigh- bution for a 3-ML-thick interface in the case of the rough bor Cr atoms shows a relatively complex fine structure. For Fig. 12 a and the rough alloy Fig. 12 b structure. Now the Fe atoms in the 2/1 state Fig. 9 c there is no separation the state with the enhanced moment cannot be separated of low- and high-spin states with a large difference in the from the main peak corresponding to the bulk moments. moments, but the magnetic moments lie in the interval Taking into account the large amplitude of the bulk peak and 1.95­ 2.08 B without deep well-pronounced minima inside its close position to the nearest peak from the left side about this interval . States with a larger number of neighboring Cr 2.15 B , one can conclude that only an increase of the half- atoms typically have a distribution function with several width of the bulk maximum, but not its fine structure, will be maxima 2/2, 3/2, 3/3, 4/3, 4/4, 4/5 states , but the distance possible to observe experimentally. The next maxima at between these maxima does not exceed 0.2 B . At the same 2 B , 1.85 B , and near 1.7 B change their position only time, every configuration is characterized by the interval of slightly with increasing roughness. For rough interfaces with possible values of magnetic moments, and for some configu- alloying, we found some Fe atoms, as a rule, with a large rations these intervals do not overlap. For example, Fe atoms number of Cr neighbors that change their magnetic moment in 0/1 configuration have moments between 2.25 and direction opposite to the overall magnetization direction. The 2.41 B , whereas for atoms in 1/1 configuration the moments distribution of moments for such Fe atoms is shown in the lie in the interval 2.11­ 2.25 B . Fe atoms with two, three, inset of Fig. 12 b . It is a Gaussian-like distribution centered and four nearest Cr neighbors have moments in the intervals at 1.5 B with a half-width of about 0.3 B . Fe atoms re- 104407-10 Fe/Cr INTERFACE MAGNETISM: CORRELATION . . . PHYSICAL REVIEW B 63 104407 FIG. 10. Calculated distribu- tion of magnetic moments in B of Cr atoms for the superlattice with different interface roughness: a stepped interface with L0 4; b ­ d interfaces with interdiffu- sion: b smooth, c rough, and d rough alloy. sponsible for this peak have five and more Cr nearest neigh- spacer and Cr atoms into the Fe layer over a distance of bors. The corresponding hff value was detected in some several ML from the interface give a more regular distribu- CEMS experiments, where the interface was not very tion of the moments with two sharp peaks around 0.55 B . smooth. In Fig. 1 the value of the moment (1.5 B) for such The appearance of additional Fe atoms inside of the Cr Fe atoms is shown by a hatched square. spacer far from the interface leads to additional polarization For the rough interface we obtain also the peak near of Cr moments. The layered AF structure remains un- 1.4 B . However, for other roughnesses it is not seen, be- changed, however, and Fe atoms surrounded mainly by Cr cause small Fe moments strongly depend on the states of the atoms acquire the direction of the moments like Cr in the surrounding atoms and give a very wide distribution without same layer. The presence of the Fe atoms surrounded by distinct peaks. Maybe including some correlations in the al- relatively large Cr magnetic moments induces an increase of gorithm of growth will lead to preferred configurations and the average Cr moments from 0.55 to 0.8 B Fig. 10 d . An to the formation of peaks, as compared to an almost constant additional peak in the distribution function for Cr moments distribution of moments. at large negative moments near 1.1 B appears due to Cr The intervals of possible values of the magnetic moments atoms at the interface with a large number of Fe neighbors. for Fe atoms with given numbers of nearest and next-nearest This peak is stronger for the stepped interface and decreases Cr neighbors almost do not change with increasing rough- with increasing intermixing of Fe and Cr atoms. ness, as is seen in Figs. 9 c ­ e , although the fine structure of the distribution function is gradually washed out. In ran- V. DISCUSSION dom alloys there is a correspondence between the perturba- tion of Fe magnetic moments and the numbers of nearest and The calculated distributions of magnetic moments for next-nearest Cr neighbors in the average, but on an atomic Fe/Cr superlattices including interface alloying and interdif- scale such mapping fails. fusion show a strong correlation with distributions of hff Very sensitive to the interface roughness proves to be the measured by CEMS. We found that both the position of sat- distribution of the moments on Cr atoms. At the beginning of ellite peaks in the CEM spectra and the position of maxima the self-consistency procedure the directions of the moments in the distribution function for local magnetic moments are at the Cr sites were chosen ``up'' and ``down'' with equal stable relative to changes in the alloylike interface rough- probability. However, self-consistency leads to the AF struc- ness. The observed correlation allows to say that in Fe/Cr ture, when Cr moments change their direction from layer to layered structures the localized magnetic-moment scales layer. For the smooth interface, significant intermixing of the with the hff on 57Fe nuclei in a similar way as for bulk Fe and Cr atoms takes place only in two interface layers. materials.17,37 This is at variance with calculations according Frustration, which is determined by the tendency of Cr to AF to the embedded cluster model for bulk Fe/Cr alloys,38 where coupling with Fe as well as with Cr neighbors, leads to the the proportionality between hff and local magnetic moments strong suppression of the moment, as is seen in Fig. 10 b . was not found. However, our findings for the moments are in Increasing roughness and penetration of Fe atoms into the Cr good agreement with results of ab initio calculations19 and of 104407-11 V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 FIG. 11. Calculated distribution of magnetic moments in B of Fe atoms for a smooth interface: a 3-ML-thick layers for both FIG. 12. Calculated distribution of magnetic moments in interfaces; b 1-ML-thick layer for the Cr/Fe interface Cr on Fe B of Fe atoms from 3 ML at the interface with interdiffusion: a interface . rough, b rough alloy. The inset shows the distribution of mo- computations based on the Hubbard-like tight-binding ments of Fe atoms opposite to the overall magnetization direction. model20 for the special cases of ordered structures, which were considered there. In our calculations we do not repro- never observed in CEMS spectra. The calculated value of the duce peaks in the distribution of magnetic moments corre- Fe moment at the flat interface about 1.7 B proves to be sponding to small hff magnitudes less then 20 T. Note that essentially higher than the moment M* the satellite with hff Bhf* 19 to 20 T was associated in pre- Bhf*/Bhf bulk Mbulk of about 1.3 B , which corresponds vious studies9,11 and 13­15 with Fe atoms in the ``flat'' inter- to the hff Bhf* . If we accept the proportionality of magnetic face Bhf* 23 T in Ref. 10 . Correspondingly, the increase of moment and hff Ref. 39 , which is suggested by Fig. 1, the its amplitude in the Mo¨ssbauer spectra, which takes place in field Bhf* is associated with Fe atoms that have a larger num- particular by raising the substrate temperature during the ber of Cr neighbors than those in ``flat'' interfaces and, con- sample preparation or by annealing, was interpreted as sequently, must lie inside of Cr spacer layers a few mono- smoothing of the interface.15 The number of 57Fe atoms with layers away from the ideal interface. Then, a large amplitude this hff can be larger then the number of 57Fe atoms with of the satellite with Bhf* cannot be a signature of the atomi- other field values, especially in the case of one monolayer of cally smooth ``flat'' interface, but, to the contrary, indicates 57Fe at the interface. Note, however, that in the case of one- alloying and interdiffusion near the interface. The absence of monolayer high-stepped interfaces with average step width maxima in the moment distribution around M* in our calcu- Nst the number of Fe atoms in ``flat interface'' positions lations can be explained by the following reason: we consid- should be Nsf 1 times larger than the number of step edge ered only structures where Fe atoms cannot penetrate too far or kink positions. Even for relatively narrow steps (Nst from the interface. Only the rough alloy structure contained 20) such a relation between the amplitude at Bhf* and that Fe atoms inside the Cr spacer, in particular, in the state 8/6. of other lines with higher fields in the hff distribution was However, in this case Fe atoms effectively interact through 104407-12 Fe/Cr INTERFACE MAGNETISM: CORRELATION . . . PHYSICAL REVIEW B 63 104407 the Cr atoms, because, as is seen from Fig. 10, they strongly There are, however, some experimental indications that polarize Cr moments. It is worth mentioning that we perform alloying cannot be avoided even for Fe growth on Cr, al- our calculations for zero temperature, whereas most Mo¨ss- though the specific scenarios of intermixing on Fe/Cr and bauer CEMS measurements were made at room tempera- Cr/Fe interfaces can be different. As was noted by Heinrich ture. Fe atoms with their local moments being reduced by the et al.,2,40 scanning electron microscopy with polarization Cr surrounding at a first glance seem to be much more sen- analysis SEMPA and Brillouin light scattering BLS show sitive to the influence of temperature than bulk Fe moments, that the phase of the short-wavelength oscillations in the in- especially taking into account that room temperature is not terlayer coupling for Fe whisker/Cr/Fe 001 structures is ex- very far from the Neel temperature of bulk Cr. However, actly opposite to that expected from AF coupling for Fe-Cr we have also performed CEMS at 80 K, and these results did and Cr-Cr layers. This was explained by interdiffusion at the not show a significant difference in the hff distributions mea- Fe/Cr interface, and recent calculations of Freyss, Stoeffler, sured at 300 or 80 K. In particular, Bhf* values at 300 K 19.7 and Dreysse20 confirmed the possibility of changing the ex- T and at 80 K 20.9 T were observed to be nearly the same. change coupling phase for the ordered interface structure Therefore, these ``loose spins,'' 4 associated with field Bhf* , with two intermixed layers CrxFe1 x /Cr1 xFex for x 0.2. even if they have configuration 8/6, lie very close to the For one mixed layer the calculations gave a phase change interface and essentially differ from the paramagnetic Fe im- only for a higher degree of intermixing: a mixed layer with purities in the bulk Cr. iron concentration less than 50 at. % behaves like a pure Cr The conclusion that the hff Bhf* is associated with Fe atomic layer. This last conclusion, however, was not in atoms inside the Cr spacer a few ML away from the ideal agreement with experiments,40 where it was shown that in- interface leads to some important consequences related to troduction of one mixed Cr85%-Fe15% layer instead of one the mechanisms of epitaxial growth of Fe on Cr Fe/Cr Fe layer does not change the phase of the interlayer coupling. and Cr on Fe Cr/Fe , which are in contradiction with the This contradiction between theory and experiment can be traditional model. Mo¨ssbauer studies24 show that for probe explained, if we accept interdiffusion at the Fe/Cr interface. 57Fe layers at the Fe/Cr interface ``lower'' the amplitude of In this case the interface Cr layer contained Fe atoms already the B without artificial alloying, and additional 15 at. % in concen- hf * satellite is enhanced in comparison with that of the Cr/Fe interface ``upper'' . In the spirit of the traditional tration change can be crucial for the sign of interlayer ex- model9,11 and 13­15 this was interpreted as evidence for sup- change coupling. Note also that losing some Fe atoms pressed intermixing during Fe growth on a Cr substrate.24 through the interface to the Cr spacer can change the effec- However, according to our present result the interpretation tive thickness of Fe and Cr layers, and also may cause the must be reverse. Such an asymmetry of two interfaces can be phase change observed in SEMPA and BLS experiments. understood from simple thermodynamic considerations.40 In- Note also that a direct proof by STM of the surface alloy terface alloying may be governed by the binding energy be- formation of Fe on Cr was reported recently by Choi et al.6 tween the substrate and ad-atom material, which are propor- For the interdiffusion process the temperature of the epi- tional to the melting points of the solids. The melting point taxial growth is very important. SEMPA studies46 demon- of Cr 2130 K is higher than for Fe 1808 K and, therefore, strate that with increase of the substrate temperature a tran- interface mixing for the Fe/Cr interface ``lower'' might be sition from a three-dimensional to a layer-by-layer growth suppressed. For certain interfaces these simple consider- mode takes place. At the same time the temperature rise ations were checked experimentally.41,42 However, in some leads to more intense diffusion at the interface. In Ref. 47, by cases they are not valid. For example, in Ref. 43 surface using high-resolution low-energy electron diffraction and alloying of Au on Ni was reported, when the melting point of Auger electron spectroscopy, it was found that interdiffusion the substrate 1728 K for Ni essentially exceeds the melting is responsible for the interface roughness, when the growth point of the ad atom 1337 K for Au and, moreover, Au and temperature exceeds 400 K. A recent study of the growth of Ni are immiscible metals. For a theoretical analysis of the a thin Fe layer on Cr by means of reflection high-energy intermixing process on the microscopic level proper allow- electron diffraction RHEED shows that the largest number ance must be made for changes of magnetic properties and of RHEED intensity oscillations was observed at the lowest the related energy due to exchange of the atoms at the inter- growth temperature.48 For an explanation of this phenom- face as well as to the effects of interface roughness. enon a special scenario was developed in Ref. 48, which is In Ref. 44 calculations based on the local-density func- based on the special form of interface roughness with steps tional theory and the Korringa-Kohn-Rostoker KKR - higher then one monolayer, although probably alloying at the Green-function method demonstrate a strong tendency for a interface which was excluded from the model plays an im- direct site-exchange mechanism into the first surface layer portant role here. for Cr on the ideal Fe surface Cr/Fe or upper interface . New information about changes of the interface structure There is no similar calculation for Fe on Cr due to the com- can be given by Mo¨ssbauer studies after thermal treatment. plex spin-density-wave structure of bulk Cr and the necessity In Ref. 15 Fe/Cr multilayers were annealed for 1 h at tem- to take into account its modification by the surface and ad- peratures of 200­450 °C. The authors essentially observed a sorbed Fe atoms. In addition, a nonideal Fe/Cr interface weak increase in amplitude of the hff Bhf* 20 T after anneal- forms noncollinear magnetic structures,23,36,44,45 which also ing at 300 °C. Their interpretation is based on the supposition can be important for the calculation of the energy balance for that the field Bhf* corresponds to Fe atoms in the ``flat'' in- the intermixing process. terface. In this case they had to conclude that there is in- 104407-13 V. M. UZDIN, W. KEUNE, H. SCHRO¨R, AND M. WALTERFANG PHYSICAL REVIEW B 63 104407 plane diffusion inside the superlattice during annealing that distribution of local moments among the Fe atoms with a leads to smoothing of the interfaces. This is an unlikely pro- given number of nearest and next-nearest Cr neighbors. cess, however. If, however, Bhf* corresponds to the Fe atoms These dependencies show that the assumption of an additive in the Cr spacer a few atomic layers away from the ideal influence of Cr neighbors on the Fe magnetic moment fails interface, such a behavior can be explained in a much more for multilayers on a microscopic level, but can be valid in the natural way: simply increasing the degree of intermixing at average for a random alloy. the annealing temperature. We found that the hff of Bhf* 20 T corresponds to inter- Note also that our calculation gives a new criterion for diffused Fe atoms inside the Cr spacer layers but not far determining the quality of the interface roughness: it is the away i.e., 2­4 ML from the interface , contrary to the appearance of the enhanced hff near 34 T that evidences the traditional interpretation of Fe atoms at the atomically ``flat'' atomically flat interface via the hff of the 0, 1 subsurface Fe interface. For atomically smooth interfaces with large flat site. However, its observation is a much more complicated terraces an enhanced hff must be observed in the second Fe problem than the field Bhf* and can be done only on particu- layer below the ideal interface, and it can provide a measure larly prepared samples, where the roughness is artificially of the Fe-Cr interface roughness on an atomic scale. For suppressed.10 instance, knowledge of the latter quantity is of fundamental importance for the understanding of the origin of magnetore- VI. CONCLUSIONS sistance bulk or interface scattering14,49­51 in Fe-Cr hetero- structures. We performed measurements of the magnetic hyperfine field hff in Fe/Cr 001 superlattices with different thick- nesses of 57Fe probe layers at the interface, and we made ACKNOWLEDGMENTS self-consistent calculations of the atomic magnetic moment in the interface region for the same multilayer structure. Dif- Valuable technical assistance by U. von Ho¨rsten is highly ferent kinds of interface roughnesses were modeled using appreciated. We are particularly grateful to Dr. Chr. Sauer special algorithms. We obtain a strong correlation between Ju¨lich for enlightening discussions, and to Dr. J. S. Jiang the 57Fe hff measured by CEMS and local Fe magnetic mo- Argonne for some of the XRD measurements. This work ments calculated within PAM. Peak positions of satellites in was supported by INTAS Grant No. 96-0531 , the ``Univer- the CEM spectra and positions of maxima in the distribution sities of Russia'' Grant No. 992780, and Deutsche Fors- function for local magnetic moments prove to be stable rela- chungsgemeinschaft SFB 491 Bochum/Duisburg . V.M.U. tive to changes in the alloylike interface roughness. would like to express his gratitude to the Alexander von For every kind of interface roughness we calculated the Humboldt-Stiftung for financial support. 1 H. Zabel, J. Phys.: Condens. Matter 11, 9303 1999 . Rensing, B. M. Clemens, and D. L. Williamson, J. Appl. Phys. 2 B. Heinrich, J. F. Cochran, D. Venus, K. Totland, D. Atlan, S. 79, 7757 1996 . Govorkov, and K. Myrtle, J. Appl. Phys. 79, 4518 1996 . 12 J. Zukrowski, G. Liu, H. Fritzsche, and U. Gradmann, J. Magn. 3 C. Turtur and G. Bayreuther, Phys. Rev. Lett. 72, 1557 1994 ; S. Magn. Mater. 145, 57 1995 . 13 Miethaner and G. Bayreuther, J. Magn. Magn. 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