PHYSICAL REVIEW B, VOLUME 63, 024413 Interdiffusion and exchange coupling in Cr overlayers on a Fe 001... substrate I. Turek,1,2 M. Freyss,3,4 P. Weinberger,2 D. Stoeffler,4 and H. Dreysse´4 1Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Z iz kova 22, CZ-61662 Brno, Czech Republic 2Center for Computational Materials Science, Technical University of Vienna, Getreidemarkt 9/158, A-1060 Vienna, Austria 3Institut fu¨r Festko¨rperforschung, Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany 4Institut de Physique et de Chimie des Mate´riaux de Strasbourg, 23, rue du Loess, F-67037 Strasbourg Cedex, France Received 26 June 2000; published 18 December 2000 The influence of interfacial interdiffusion on the magnetic order in ultrathin epitaxial Cr films on a Fe 001 substrate was studied by means of electronic structure calculations. The total coverage of the films was assumed to be one, two, and six monolayers of Cr while the interdiffusion was simulated by two-dimensional Cr-Fe alloys in the two atomic layers forming the Cr/Fe interface. Two limiting cases were considered: i perfectly ordered alloys, described in terms of a semiempirical tight-binding method using the recursion technique, and ii substitutionally disordered alloys, whose electronic structure was determined ab initio using the tight-binding linear muffin-tin orbital method and the coherent-potential approximation. In both cases, the magnetic coupling of the Cr overlayer to the ferromagnetic Fe substrate exhibits similar transitions ( phase shifts due to varying compositions at the interface. The calculated results provide additional support for recent interpretations of experiments on Fe/Cr/Fe 001 trilayers. DOI: 10.1103/PhysRevB.63.024413 PACS number s : 75.70.Ak, 75.70.Cn I. INTRODUCTION and magnetic structure within the local spin-density approxi- mation LSDA and the coherent-potential approximation The discovery of the oscillatory interlayer coupling in Fe/ CPA . For the sake of completeness, we present the previ- Cr 001 multilayers a decade ago1,2 initiated extensive re- ous SE-TB results7 together with the new LSDA-CPA ones. search of this layered system. At present, a general agree- Finally, we compare both sets of obtained data and relate ment exists regarding the two types of oscillations of them to other theoretical and experimental findings. exchange coupling in Fe/Cr/Fe 001 trilayers: the short pe- riod of about two monolayers ML is related directly to the II. MODELS antiferromagnetic ground state of bulk bcc Cr, whereas the longer period 12 ML can be explained by the Cr Fermi We considered epitaxial Cr overlayers on a Fe 001 sub- surface.3 However, the experimentally observed phase of the strate with all atoms occupying the positions of an ideal bcc short period4,5 is opposite to that predicted theoretically.3,6 A lattice parent lattice with the experimental lattice constant similar situation was reported for epitaxial Cr thin films on a of pure iron. The interdiffusion at the Cr/Fe interface was Fe 001 substrate:4 in contrast to theoretical expectations, the simulated by the following composition in the atomic layers: measured magnetization of the top surface Cr layer is anti- vac/Cr parallel parallel to the Fe magnetization for an even odd n /Cr1 xFex /CrxFe1 x /Fe 001 , 1 number of Cr layers. where x is a concentration variable (0 x 1) and n denotes A possible explanation of this discrepancy was suggested the number of pure Cr layers. This model refers to a chro- on the basis of electronic structure calculations7 and has been mium film of a total coverage (n 1) ML Cr with interdif- verified by recent experiments on Fe-whisker/Cr/Fe 001 fusion confined to a two-monolayer region, which approxi- systems:5 the reversal of exchange coupling is due to inter- mates quite well the chemical profiles in experimental diffusion at the Cr/Fe interface, which is often found in this samples.5 The limit of x 0 corresponds to the case without system under the usual preparation conditions.5,8­10 How- interdiffusion, while the opposite limit of x 1 describes a ever, the validity of the conclusions in Ref. 7 should be complete exchange of one monolayer of Fe and Cr at the accepted with caution for two reasons: i the interdiffusion interface. We performed the study for n 0, 1, and 5, which was simulated using two-dimensional-ordered Cr-Fe alloys is equivalent to 1, 2, and 6 ML Cr/Fe 001 , respectively. We formed in one or two monolayers at the interface, and ii the considered ordered 2D alloys as well as substitutionally dis- electronic structure of the model systems was calculated us- ordered random 2D alloys. In the case of the ordered alloys ing a semiempirical tight-binding SE-TB d-band Hamil- studied here and in Ref. 7, the 2D unit cells employed are tonian. shown in Fig. 1; they correspond to the following discrete set Similarly, recent first-principles calculations of spin struc- of the concentration variable x: tures in Fe/Cr superlattices with intermixing considered only ordered alloys at the interface.11,12 The main purpose of the x 0.11, 0.25, 0.33, 0.5, 0.67, 0.75, 0.89, 2 present work is to perform a study complementary to Refs. while, in the case of the random alloys, the concentration 7,11 and 12, namely, to simulate the interdiffusion in terms range was sampled by of random substitutionally disordered two-dimensional 2D alloys and to determine the corresponding electronic x 0, 0.1, 0.3, 0.5, 0.7, 0.9, 1, 3 0163-1829/2000/63 2 /024413 9 /$15.00 63 024413-1 ©2000 The American Physical Society I. TUREK et al. PHYSICAL REVIEW B 63 024413 tonian 4 up to the Fermi energy. The densities of states are calculated by means of the real-space recursion method13 with eight levels of the continuous fraction and the Beer- Pettifor terminator.14 The parameters tim i m and Ii in Eq. 4 were set identical to Ref. 7: this choice reproduces the mag- netic properties of bulk Fe and Cr metals as well as those of Cr films on Fe 001 obtained with an ab initio full-potential augmented-plane-wave method. The magnetic moments are calculated self-consistently for all inequivalent atoms in the Cr overlayer, in the two mixed layers, and in ten iron layers below the interface. The mag- netic moments of the rest substrate atoms are kept frozen to the Fe bulk value. In order to find the magnetic ground state FIG. 1. Unit cells of the ordered alloys for special values of for a given atomic configuration, total energies of the differ- concentration x. In here, Cr atoms are shown as empty circles and ent self-consistent magnetic structures are evaluated and ana- Fe atoms as full circles. The unit cells for the complementary con- lyzed. The present scheme leads to numerical accuracy of the centration (x 1 x) are obtained by an exchange of the atomic total energies better than 0.1 mRy per interface atom. species. B. TB-LMTO-CPA method where the limits x 0 and x 1 describe perfect layers, in which single impurities can be considered. The all-electron TB-LMTO-CPA method for substitution- ally disordered layered systems15­17 is based on the atomic- III. COMPUTATIONAL TECHNIQUES sphere approximation ASA and the exchange-correlation potential given in Ref. 18. The valence states were described The electronic structure and the local magnetic moments using lmax 2 and the scalar-relativistic approximation. In for the systems with ordered interfacial alloys were calcu- order to simplify the treatment of a simultaneous presence of lated by means of the SE-TB method and the recursion tech- chemical and magnetic disorder in the system, we assumed nique. The models with random alloys were treated by an ab only one magnetic state for each atomic species Fe, Cr in a initio approach based on the tight-binding linear muffin-tin given layer. The coupled CPA conditions16,17 were then orbital TB-LMTO method and the CPA. In both cases, only solved, thus taking into account the inhomogeneity of the collinear magnetic structures were assumed. model system, Eq. 1 . As a consequence, all interlayer and intralayer contributions to the LSDA-CPA total energy are A. Semiempirical tight-binding method fully included in the present approach. The spherically sym- metric one-electron potentials within the individual atomic In the SE­TB method, the electronic wave function is spheres were constructed not only from the spherical com- expanded in a fixed basis of atomic orbitals. Here, only the ponent of the electron charge and spin densities, but they atomic d orbitals im are taken into account, where i la- included also the contribution to the Madelung term due to bels the atomic sites, m refers to the type of d orbital, and the dipole moments of the full charge densities.19 Self- is the spin index ( , ). The one-electron Hamiltonian consistency of the one-electron potentials and the calcula- is then given by tions of total energies were restricted to a finite region com- prising 12 atomic layers 3 empty-sphere layers and 9 H im i m im metallic layers on top of an undisturbed semi-infinite ii mm i ti m , ii mm Fe 001 substrate. The integrals over the occupied part of the valence bands were evaluated using 14 points on a semicircle 0 contour in the complex energy plane. The irreducible part of i i 2 IiMi . 4 the two-dimensional Brillouin zone was sampled by 45 spe- cial k The quantity points. The accuracy of the Brillouin zone integra- i in Eq. 4 is the center of the i band, while tions with respect to local magnetic moments and the total- the tim i m are the spin-independent interatomic hopping inte- energy differences was checked for a few selected cases grals, Ii is the effective exchange integral, and Mi is the local employing a greater number 120 of special k points. The magnetic moment on site i. The self-consistent spin- resulting total-energy differences are accurate within an error independent energy levels 0 bar of 0.1 m Ry per interface atom. i are obtained iteratively to- gether with the self-consistent local magnetic moments Mi . The latter are defined in terms of the local occupations N i as IV. RESULTS AND DISCUSSION M 0 i Ni Ni , while the values of i are chosen in order to A. 1-ML CrÕFe 001... - nÄ0 satisfy a condition of local neutrality of all sites, i.e., the sum N 1. Ordered alloys i Ni must equal the value for the corresponding bulk metal. The local occupations N i are obtained by integration For the 1-ML Cr overlayer with ordered interface alloys of the spin-polarized local densities of states of the Hamil- several different magnetic structures were found. An ex- 024413-2 INTERDIFFUSION AND EXCHANGE COUPLING IN Cr . . . PHYSICAL REVIEW B 63 024413 FIG. 2. The magnetic structure of the ground state left and the metastable state right found for n 0 and x 0.5 referring to an ordered alloy at the Cr/Fe interface. The empty and full triangles correspond to the Cr and Fe moments, respectively. The size of a triangle scales with the magnitude of the moment, while the triangle orientation defines the sign. The energy differences are given per interface atom. ample of multiple solutions is shown in Fig. 2 for the case of x 0.5 see Fig. 1 for the corresponding unit cell for which two solutions were obtained. In both solutions, the Cr mo- ments within one layer are coupled ferromagnetically, whereas they are coupled antiferromagnetically from layer to FIG. 4. The magnetic structures found for n 0 and x 0.1 layer. The Cr surface moments for the ground state left referring to a random alloy at the Cr/Fe interface. The empty circles panel of Fig. 2 are coupled antiferromagnetically to the Fe and the full squares correspond to the Cr and Fe moments, respec- tively. The energy differences are given per interface atom. The substrate in contrast to the metastable state right panel of layer numbering starts at the top surface layer, denoted by 0. Fig. 2 with ferromagnetic coupling. The Fe moments in all layers and for both solutions are coupled ferromagnetically 2. Random alloys to the bulk substrate. Figure 3 shows the ground-state average magnetic mo- Solving the LSDA-CPA self-consistency problem for ments for both species in the mixed layers: the top surface 1-ML Cr systems with random interface alloys leads also to layer S and the first subsurface layer (S 1). The most a number of different solutions that have to be classified according to the resulting spin structures and total energies. remarkable feature of the plotted dependences is an abrupt Figure 4 presents the magnetic profiles for all solutions change in the surface Cr moment around x 0.6, which is found for x 0.1 together with their total energies relative to accompanied by change of sign of this moment. The subsur- a particular given solution. The six solutions obtained corre- face Cr moment exhibits a similar but less pronounced be- spond to combinations of the surface Cr moment having ei- havior, whereas the Fe moments in the mixed layers depend ther a large positive, a large negative, or a small value, and only weakly on x in the concentration range studied. of the surface Fe moment coupled ferromagnetically or anti- ferromagnetically to the bulk substrate. The values of the surface Fe moments are significantly enhanced as compared to the corresponding bulk value. The ground state Fig. 4 c is featured by a large positive surface Cr moment, a smaller negative subsurface Cr moment, and positive Fe moments in all layers. The lowest metastable state Fig. 4 f differs from the ground state only by a reversal of the surface Fe moment. It should be noted that the calculated magnetic ground state of the perfect 1-ML Cr film on Fe 001 (x 0) agrees with existing results for this system:20­22 a large local Cr moment (3 B) coupled antiferromagnetically to the substrate magne- tization. The concentration dependence of the ground-state local magnetic moments in the mixed layers is shown in Fig. 5. The individual moments exhibit behavior very similar to that in the ordered case cf. Fig. 3 : an abrupt change of both Cr FIG. 3. Average ground-state Cr and Fe magnetic moments in moments around x 0.6 and nearly constant positive Fe mo- the mixed layers as a function of x for n 0 referring to ordered ments. alloys at the Cr/Fe interface. The open symbols correspond to a Figure 6 presents the total energy of all the different so- metastable solution that is nearly degenerate with the ground state. lutions found throughout the whole concentration range. We 024413-3 I. TUREK et al. PHYSICAL REVIEW B 63 024413 FIG. 5. Ground-state local Cr and Fe magnetic moments in the mixed layers as a function of x for n 0 referring to random alloys at the Cr/Fe interface. took the solution in Fig. 4 a which exists from x 0 to x 1) as a reference system for the total energies. The abrupt FIG. 7. Comparison of the magnetic structures for the ground change in Cr moment in Fig. 5 is now easily identified as a states left and the lowest metastable states right obtained for n transition between two qualitatively different ground states 0 and x 0.5 referring to a random alloy top and a c(2 2)-ordered alloy bottom at the Cr/Fe interface. The empty labels a and c in Figs. 4 and 6 . It should be noted that circles and the full squares correspond to the Cr and Fe moments, additional solutions to those in Fig. 4 were found for higher respectively. The layer numbering starts at the top surface layer, concentrations (x 0.5). These solutions contain subsurface denoted by 0. Fe moments coupled antiferromagetically to the Fe substrate. Inspection of their total energies empty symbols in Fig. 6 proves that they represent metastable states lying relatively both approaches describe essentially the same physical far above the ground state. mechanism. As detailed accounts of the various spin solu- tions for our two models were given elsewhere,7,23 let us 3. Comparison and discussion concentrate here on a brief comparison and summary of the results. The results for a 1-ML Cr film on a Fe 001 substrate In Fig. 7 the calculated spin structures of the ground state both with ordered and disordered alloys show surprisingly and of the lowest metastable state are compared for both similar concentration dependences, see Figs. 3 and 5: in both models at x 0.5: it can be seen that the agreement is nearly models the surface Cr moment changes its sign for concen- perfect. The ground state of both models contains a large tration x slightly above x 0.5. This agreement indicates that negative Cr moment in the top surface layer and a nearly negligible subsurface Cr moment. The metastable state con- FIG. 6. Concentration dependence of energy differences per FIG. 8. Average ground-state Cr and Fe magnetic moments in interface atom for various LSDA-CPA solutions for n 0 referring the top surface layer S and the first (S 1) and second (S 2) to random alloys at the Cr/Fe interface. The labels a­f correspond subsurface layers as a function of x for n 1 referring to ordered to those in Fig. 4. The empty symbols connected by dotted lines alloys at the Cr/Fe interface. The open symbols correspond to meta- mark solutions with negative subsurface Fe moments. stable solutions that are nearly degenerate with the ground state. 024413-4 INTERDIFFUSION AND EXCHANGE COUPLING IN Cr . . . PHYSICAL REVIEW B 63 024413 FIG. 9. The ground-state mag- netic structures found for n 1 and three values of x referring to ordered alloys at the Cr/Fe inter- face. The empty and full triangles correspond to the Cr and Fe mo- ments, respectively. tains a large positive Cr surface moment and a smaller but In addition to the averaged moments the individual spin well-developed negative subsurface Cr moment. The only structures are shown in Fig. 9 for three values of x. It can be quantitative difference between the two models refers to the seen that the site- and species-resolved local moments for x magnitude of the Fe moments: the SE-TB approach yields 0.5 do not deviate significantly from the corresponding smaller iron moments at the surface, while LSDA-CPA iron layer averages shown in Fig. 8. For higher concentrations, moments are clearly enhanced as compared to the bulk Fe the top surface Cr moments exhibit large fluctuations around value. This behavior is in full analogy to ab initio results for the average, and the surface layer consists of large moments systems without interdiffusion.16,20,24 of both signs cf. Fig. 9 for x 0.67). As observed in Fig. 8, The basic species-resolved magnetic exchange interac- this kind of in-plane antiferromagnetism then reduces the tions in the Cr/Fe alloy systems can be inferred, e.g., from average surface Cr magnetization for high concentrations. the ground-state spin structure for x 0.1 Fig. 4 c : the nearest-neighbors NN Cr-Cr moments prefer an antiferro- The values of the Fe moments are positive in the whole magnetic coupling, the NN Fe-Fe moments tend to align fer- concentration range studied; the only exceptions are the romagnetically, and the NN Cr-Fe moments are coupled an- nearly vanishing Fe moments in the first subsurface layer at tiferromagnetically. Quite clearly, these tendencies can be x 0.11 and x 0.89. The Fe moments in the second and fully satisfied only for chemically perfect systems (x 0 and next subsurface layers are nearly constant with a value close x 1). The interdiffused systems become inevitably frus- to that of bulk bcc iron. trated, which leads to a number of competing spin structures. The magnetic frustrations are responsible not only for the 2. Random alloys observed reversal of the surface Cr moment at x 0.6 but also for the reduction of the sizes of particular local For 2-ML Cr and a randomly interdiffused Cr/Fe inter- moments,7,23 as illustrated, e.g., by the subsurface Cr mo- face, the number of different LSDA-CPA solutions found for ment in the ground states for x 0.5, see Fig. 7. a given concentration was at least 8 and exceeded 12 for x 0.7). However, the ground-state configurations result from a competition among three qualitatively different spin struc- B. 2-ML CrÕFe 001... - nÄ1 tures listed in Table I. The ground-state structure for small x label a in Table I for x 0.1) is derived from that of a 1. Ordered alloys perfect Cr bilayer on Fe 001 :20 a large surface Cr moment Multiple solutions were found also for the case of a 2-ML coupled ferromagnetically to the Fe substrate and a smaller Cr coverage. The average ground-state local moments are Cr subsurface moment coupled antiferromagnetically. For in- summarized in Fig. 8 as functions of x. The behavior of the termediate and high concentrations of interdiffusion the sign average Cr moment in the top surface layer S is quite un- of the surface Cr moment is changed labels b and c in Table expected. For small values of x, this moment is large and I for x 0.5 and 0.9, respectively . The difference between positive, it changes sign at x 0.2, remains negative up to the ground states at x 0.5 and x 0.9 is due to the first x 0.75, and finally vanishes for yet higher values of x. subsurface Fe moment, being slightly negative for x 0.9. TABLE I. The ground-state local magnetic moments in B) for 2-ML Cr films on a Fe 001 substrate with random alloys at the Cr/Fe interface for three values of x. Only the moments in the top surface layer (S) and in the first three subsurface layers (S 1, S 2, S 3) are given. x Label Cr(S) Cr(S 1) Fe(S 1) Cr(S 2) Fe(S 2) Fe(S 3) 0.1 a 2.65 1.34 1.70 0.27 2.19 2.32 0.5 b 2.81 1.14 1.83 0.99 2.29 2.17 0.9 c 2.92 1.11 0.39 0.85 2.43 2.07 024413-5 I. TUREK et al. PHYSICAL REVIEW B 63 024413 FIG. 10. Ground-state local Cr and Fe magnetic moments in the top surface layer (S) and the first (S 1) and second (S 2) sub- surface layers as a function of x for n 1 referring to random alloys at the Cr/Fe interface. As shown in Fig. 10, the concentration dependence of the FIG. 12. Comparison of the magnetic structures for the ground individual moments is relatively weak: the only abrupt state left and the lowest metastable state right obtained for n changes occur at x 0.3 for all moments and at x 0.8 for 1 and x 0.5 referring to a random alloy top and a the first subsurface Fe moment. The total energies for the c(2 2)-ordered alloy bottom at the Cr/Fe interface. The empty most stable solutions are presented in Fig. 11. It can be seen circles and the full squares correspond to the Cr and Fe moments, that the energy separations for small concentrations (x respectively. The layer numbering starts at the top surface layer, 0.2) are quite pronounced in contrast to higher values of x denoted by 0. where the three competing solutions labeled by a, b, and c become nearly degenerate. moment is observed. This transition occurs for relatively small values of x, namely, at x 0.2 and x 0.3 for the or- 3. Comparison and discussion dered and disordered cases, respectively. Second, another A comparison of concentration dependence of the ground transition in the ground-state configuration is observed for state of 2-ML Cr films with ordered and random Cr/Fe inter- higher values of x, namely, at x 0.7 and x 0.8 for the faces Figs. 8 and 10 reveals good overall agreement be- ordered and disordered cases, respectively. In both cases, this tween both cases. First, a transition from the ground state of transition is accompanied by a sign change and a reduction the perfect Cr bilayer (x 0) with a positive surface Cr mo- in size of the first subsurface Fe moment. ment to a different ground state with a negative surface Cr However, there are also qualitative discrepancies between the two cases. One of them is the value of the first subsurface Fe moment for small concentrations: this moment is negli- gible for ordered alloys at x 0.11 Fig. 8 , whereas it is quite large and positive in the random case for x 0 Fig. 10 . Another difference concerns the average surface Cr mo- ment for higher concentrations (x 0.5): it remains large and negative in the random case, whereas its magnitude de- creases essentially down to zero at x 0.89) in the ordered case. The origin of the last discrepancy can be understood from Fig. 12, which shows the two lowest energy solutions ob- tained for both cases at x 0.5. While a reasonable agree- ment is seen for the ground states, the metastable solutions differ substantially: the pure surface Cr layer exhibits an in- plane antiferromagnetism in the case of ordered alloys, which is qualitatively different from the CPA solution as- suming a fixed sign of the local moment for each species in FIG. 11. Concentration dependence of the energy differences a given layer. The displayed metastable state at x 0.5 in the per interface atom for various LSDA-CPA solutions for n 1 re- ordered case Fig. 12 becomes the ground state for higher ferring to random alloys at the Cr/Fe interface. The labels a, b, and concentrations cf. Fig. 9 for x 0.67) and the in-plane anti- c correspond to Table I. Higher metastable solutions are omitted in ferromagnetism reduces the average surface Cr magnetiza- the plot. tion. 024413-6 INTERDIFFUSION AND EXCHANGE COUPLING IN Cr . . . PHYSICAL REVIEW B 63 024413 FIG. 14. Average ground-state Cr and Fe magnetic moments in the top surface layer (S) and the first five (S 1 to S 5) subsur- face layers as a function of x for n 5 referring to ordered alloys at the Cr/Fe interface. The full symbols refer to the pure Cr layers; the open ones refer to the two mixed Cr-Fe layers. FIG. 13. Comparison of the magnetic structures for the ground state left and the lowest metastable state right obtained for n 5 and x 0.5 referring to a random alloy top and a The number of different LSDA-CPA solutions for the c(2 2)-ordered alloy bottom at the Cr/Fe interface. The empty films with the disordered interface was substantially higher circles and the full squares correspond to the Cr and Fe moments, than 2 for each concentration e.g., 11 for x 0.7). The respectively. The layer numbering starts at the top surface layer, higher lying metastable solutions were characterized either denoted by 0. by a different magnetic order at the interface, or by magnetic defects in the pure Cr film nearly vanishing Cr moments, The transition in the ground-state configuration at small ferromagnetically coupled neighboring Cr layers . However, values of x, found in both cases and accompanied by a as is documented by the behavior of the local moments in change of sign of the top surface Cr moment ( phase shift , Fig. 15, as well as by the concentration dependence of the can explain some of the discrepancies between existing theo- total-energy differences in Fig. 16, the ground-state configu- ries and experiments. Let us emphasize that an occurrence of ration undergoes a very similar transition like that in the the phase shift due to the Cr/Fe interface intermixing can ordered-alloy case cf. Fig. 14 . The phase shift occurs be easily understood and could be anticipated on the basis now at x 0.25, i.e., at a smaller concentration than found of the exchange interactions between the NN pairs in the for the 2-ML Cr film cf. Fig. 10 . Similar to the cases n frustrated Cr-Fe system see Sec. IV A 3 and Ref. 7 . How- 0 and n 1, the origin of the phase shift can be ex- ever, it is the relatively small degree of the intermixing cor- plained as a consequence of magnetic frustrations due to in- responding to x 0.2 or x 0.3 in our models that makes termixing at the Cr/Fe interface. this mechanism highly relevant for currently prepared metal- lic multilayers.5 C. 6-ML CrÕFe 001... - nÄ5 Finally, let us briefly summarize the results obtained for a 6-ML Cr coverage. Throughout the whole concentration in- terval, only two qualitatively different ground-state configu- rations were found, irrespective of the chemical order in the interdiffused layers. These two competing spin structures are shown for x 0.5 in Fig. 13. They correspond to an antifer- romagnetic coupling between the neighboring pure Cr layers with an enhanced moment in the top surface Cr layer. The only qualitative difference between these two spin structures is the different sign of the surface Cr moment. For the system with ordered interface alloys and for all concentrations studied, the above two solutions were the only ones found by the SE-TB scheme. The concentration FIG. 15. Ground-state local Cr and Fe magnetic moments in the dependence of the ground-state average local moments, de- top surface layer (S) and the first five (S 1 to S 5) subsurface picted in Fig. 14, proves that a transition ( phase shift layers as a function of x for n 5 referring to random alloys at the between the two different states takes place at x 0.2 simi- Cr/Fe interface. The full symbols refer to the pure Cr layers; the larly to the case n 1 cf. Fig. 8 . open ones refer to the two mixed Cr-Fe layers. 024413-7 I. TUREK et al. PHYSICAL REVIEW B 63 024413 terface. The interdiffusion was taken into account in terms of two-dimensional ordered and disordered alloys located in the two neighboring layers forming the interface. The electronic structure was calculated by a semiempirical tight-binding scheme for the ordered interfaces and by the first-principle TB-LMTO-CPA method for the random interfaces. The results of both approaches exhibit a reasonable semi- quantitative agreement with each other which, in turn, proves that the basic mechanism driving the exchange coupling of the imperfect Cr overlayers to the iron substrate is not very sensitive to the details of the applied model. The most im- portant fact is undoubtedly the phase shift in the sign of the surface Cr moment that is due to intermixing and mag- netic frustrations. This phase shift was found in both the- oretical models and-for Cr coverages greater than 1 ML-at relatively small degrees of intermixing correspond- ing to an interchange of 20­30 % of atoms in the two neigh- FIG. 16. Concentration dependence of energy differences per boring layers . The same features were observed in recent interface atom for various LSDA-CPA solutions for n 5 referring experiments on Fe/Cr/Fe 001 trilayers and ascribed to inter- to random alloys at the Cr/Fe interface. Higher metastable solutions mixing at one of the interfaces.5 are omitted in the plot. However, there are still points to be clarified in the future. On the theoretical side, some differences were found in the Let us finally make a quantitative comparison of the spin two sets of results, which might be explained either by dif- structures in the two competing states and for the two chemi- ferent calculational procedures the size of Cr moments in- cal orders considered. As can be seen in Fig. 13 for x side thicker Cr films or by different models adopted the 0.5, the magnitudes of the Cr magnetic moments calcu- in-plane antiferromagnetism in pure Cr layers . As concerns lated by the SE-TB method are systematically greater than the relation of theory to experiment, systems with intermix- the LSDA-CPA results, especially for layers well below the ing in a single layer, described by the model surface. This discrepancy can be ascribed to the fact that Crn /CrxFe1 x /Fe(001), remain yet to be understood: too standard LSDA calculations have a tendency to underesti- big a difference was found between the theoretical7 and mate the local moments in bulk bcc chromium,12,25 whereas experimental5 determination of the transition concentration the SE-TB scheme uses the experimental bulk Cr moment as for the phase shift in this case. an input to fix the parameters of the Hamiltonian 4 . How- ever, the LSDA moments at the Cr surface are influenced ACKNOWLEDGMENTS mainly by the surface magnetic enhancement and can be This work was supported by the Grant Agency of the considered reliable. This is probably one of the reasons for a Czech Republic No. 202/97/0598 , the Czech Ministry of very good quantitative agreement between the SE-TB and Education, Youth, and Sports No. OC P3.40 , the Austrian TB-LMTO-CPA values of the Cr moments in the top surface Ministry of Science No. GZ 45.442 , the Project ``Scientific and first subsurface layers Fig. 13 . and Technological Cooperation between Germany and the Czech Republic'' No. TSR-013-98 , the TMR Network V. CONCLUSIONS ``Interface Magnetism'' No. EMRX-CT96-0089 , and the RTN Network ``Computational Magnetoelectronics'' No. We have investigated the electronic structure, magnetic RTN1-1999-00145 . Part of the calculations were performed moments, and exchange coupling in thin Cr films on a on the Origin 2000 ``Seven'' of the University Louis Pasteur Fe 001 substrate in the presence of interdiffusion at the in- of Strasbourg. 1 P. Gru¨nberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sow- 6 D. Stoeffler and F. Gautier, Prog. 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