PHYSICAL REVIEW B VOLUME 60, NUMBER 5 1 AUGUST 1999-I Magnetic behavior of thin Cr layers sandwiched by Fe A. B. Klautau* and S. B. Legoas Instituto de Fi´sica, Universidade de Sa o Paulo, Caixa Postal 66318, 05315-970 Sa o Paulo, SP, Brazil R. B. Muniz Departamento de Fi´sica, Universidade Federal Fluminense, 24210-340 Niteroi, RJ, Brazil S. Frota-Pesso a Instituto de Fi´sica, Universidade de Sa o Paulo, Caixa Postal 66318, 05315-970 Sa o Paulo, SP, Brazil Received 23 September 1998 The magnetic behavior of thin layers of Cr in Fe/Cr/Fe 001 trilayers and superlattices is studied using the first principles self-consistent RS-LMTO-ASA real space ­ linear muffin-tin orbital ­ atomic sphere approxi- mation method. The effects of lattice compression and interface mixing are investigated, and it is shown that they can cause large reductions of the Cr magnetic moments. S0163-1829 99 12625-0 I. INTRODUCTION retically the incommensurate state of Cr is difficult to treat. Recent LSDF-KKR calculations have shown that for the ex- Magnetic multilayers exhibiting giant magnetoresistance perimental lattice constant a SDW state with a wave vector have stimulated a considerable amount of research on mag- close to the observed one is energetically more favorable netic thin films. The magnetoresistance effect, which is cur- than the antiferromagnetic state, but for the Cr lattice con- rently being used by the information processing industry to stant which minimize the total energy, the calculated ground develop magnetoresistive read/write heads, occurs in a vari- state is nonmagnetic.12 Bulk Cr is in the verge of a transition ety of systems, but it was originally observed in Fe/Cr between magnetic and nonmagnetic states and slight differ- multilayers.1 Adjacent Fe layers in Fe/Cr multilayers couple, ences in lattice parameters or theoretical procedures can mediated by the Cr layer, and the coupling oscillates as a drive the system nonmagnetic. If one neglects incommensu- function of the Cr spacer thickness, between ferromagnetic rability, bulk Cr is an antiferromagnet with each site having and antiferromagnetic. The Fe/Cr interface quality can sig- a magnetic moment of 0.6 B ; the magnetic moments of nificantly affect both the magnetoresistance and the ex- the atoms occupying the body-centered positions align in one change coupling between the Fe layers.2,3 It influences the direction, and opposite to those in the bcc vertices. The com- ``magnetic contrast'' which is related to the spin dependent mensurate antiferromagnetism in bulk Cr can be stabilized transmission and reflection of carriers across the interface. It by the presence of impurities, such as Mn and Fe among is easier from a theoretical point of view to treat systems others.13 In Fe/Cr/Fe systems, the presence of the Fe layers with perfect interfaces having translational symmetry paral- affects the magnetic properties of the Cr layer. Since the Cr lel to the layers and for a long time first-principles calcula- moments couple antiferromagnetically with the Fe moments, tions were restricted to these systems.4­6 However, experi- one would expect in-plane ferromagnetic order in Fe/Cr/ mentally, it is very difficult to completely avoid interface Fe 001 sandwiches. For sufficiently large Cr thicknesses, mixing and the formation of islands in the deposition of Cr the incommensurate SDW may form in the Cr spacer layer.12 on Fe.7,8 Therefore, it is important to consider deviations However, below a critical thickness, the Cr layer is unable to from perfect interfaces and investigate their influence on the sustain a stable incommensurate SDW, even at very low properties of Fe/Cr multilayers. With the advances in the temperatures.14,15 Previous works have shown that the mag- theoretical approaches and better computer facilities, first- netic moments in the Cr layer depend on the relative orien- principles calculation of multilayers in the presence of inter- tation of the magnetizations of the adjacent Fe layers as well face mixing is now possible.9,10 However, values for the lo- as on the growth orientation of the multilayer.16­19 The mag- cal moments of Cr sites in the bcc structure are extremely netic ordering of the Cr layer is also strongly influenced by sensitive to small changes in the lattice parameter11 and, as inhomogeneities at the Fe/Cr interfaces. The presence of we show here, a lot of care must be taken when comparing steps at the interface can lead to noncollinear spin ordering different theoretical results with experiments. in the Cr layers.20­22 It is also recognized that in addition to The magnetic properties of Fe/Cr systems have been ex- steps, mixing in the Fe/Cr interfaces always occurs, even in tensively studied and a considerable amount of information the best grown samples.7,8 The formation of a disordered about this system is currently available. The ground state of Fe/Cr alloy at the interface generates frustrations which may bulk bcc Cr exhibits a spin density wave SDW antiferro- substantially suppress the moment of some Cr neighboring magnetism which is not commensurate with the lattice. The sites.5 Such frustrations may also induce noncollinear ar- wave vector of the SDW lies along one of the 001 cubic rangements of the local magnetic moments which can be directions and its wavelength is 21 lattice spacings. Theo- rather intricate, depending on the degree of interface mixing. 0163-1829/99/60 5 /3421 7 /$15.00 PRB 60 3421 ©1999 The American Physical Society 3422 KLAUTAU, LEGOAS, MUNIZ, AND FROTA-PESSO A PRB 60 A relevant aspect that has not been sufficiently explored is method, the solutions of the Schro¨dinger-like equations related to the fact that the magnetism of Cr is rather sensitive within the WS spheres are obtained by the same procedures to the application of pressure.11,12 The Fe lattice parameter is as those used in the k space-LMTO-ASA method, including 0.6% smaller than that of Cr. Thus, when sandwiched by the approximations which are usually made in treating the Fe, the Cr layer is slightly compressed, and this effect is exchange and correlation terms. more pronounced for very thin Cr spacers. It is noteworthy In the RS-LMTO-ASA scheme we work in the orthogonal that earlier perturbed angular correlation spectroscopy and representation of the LMTO-ASA formalism,29 for which the transport measurements in Fe/Cr 001 multilayers have overlap is approximately given by the unit matrix. Using the found no antiferromagnetic order in the Cr layers with thick- first-order approximation, where only linear terms in (E nesses tCr 42 Å.23,24 Neutron scattering results, however, E ) are retained, the Hamiltonian H takes the usual tight- exhibited magnetic scattering, consistent with a commensu- binding form, and the corresponding eigenvalue problem can rate antiferromagnetic order in Cr on samples with thinner Cr be written as25,26 layers.9,14 It is, therefore, important to determine the elec- tronic structure of Cr layers sandwiched by Fe, taking into H E u 0, account interface mixing and lattice relaxation effects. In this article we have investigated the effect of pressure where and interface mixing on the local magnetic moments of very thin Cr layers sandwiched between Fe slabs in Fe/Cr 001 multilayers. We have performed first-principles calculations H C¯ ¯1/2 S¯ ¯ 1/2. of the electronic structure of Fe/Crn /Fe(001) trilayers and Fe C¯ and ¯ are the potential parameters and S¯ is the structure 3 /Crn(001) superlattices with n 1, 3, 5, and 7 atomic planes for different values of the lattice parameter and de- constant in the tight-binding LMTO-ASA representation. S¯ grees of interface mixing, using a self-consistent and real is entirely determined by the lattice structure, i.e., by the space linear-muffin-tin method within the atomic sphere ap- position of the lattice sites. The potential parameters (C¯ and proximation RS-LMTO-ASA method . The magnetic mo- ¯) are related to the solutions of the Schro¨dinger-like equa- ments of all inequivalent sites are calculated in each case. tion inside the WS spheres around each site, and are deter- The different roles played by interface mixing and lattice mined self-consistently. The corresponding wave functions relaxation in the reduction of the local magnetic moment of are given by sites in the Cr layers are discussed. The plan of the paper is as follows: in the next section, a brief account of the theory employed in our calculations is given. In Sec. III, we discuss E l rR E E l rR YL r R uRL E , our results for Fe/Cr RL n /Fe(001) sandwiches with perfect Fe-Cr interfaces. Calculations for Fem /Crn(001) superlat- tices considering interface mixing are presented and dis- where l (r) and l (r) are the radial part and its first en- cussed in Sec. IV. Finally, in Sec. V, we compare our results ergy derivative at E E ) of the solution of the Schro¨dinger with previous works and draw our main conclusions. equation in the WS sphere at site R. YL(r R) are spherical harmonics with quantum numbers L (l,m), and uRL(E) are the solutions of the eigenvalue problem given above. II. THE RS-LMTO-ASA SCHEME In our calculations for Fe/Cr/Fe 001 trilayers we have In this section we give a brief outline of the RS-LMTO- fixed the Fermi energy EF of the system to be that of bulk ASA method used in our calculations. A detailed description Fe. Charge transfers in each inequivalent site have been de- of this procedure can be found elsewhere.25­27 The RS- termined by integrating the corresponding local density of LMTO-ASA is a first-principles and self-consistent scheme states LDOS up to EF . These charge transfers were then which is based on the LMTO-ASA formalism.28,29 It is simi- used in a two-dimensional Ewald summation34 to obtain the lar to the reciprocal-space-LMTO-ASA method; however, in Madelung potential and the value of the electrostatic poten- contrast, the local density of states is determined in real tial VES at each site. When treating the semi-infinite Fe space, using the recursion method,30 rather than by solving layers, only the Fe sites occupying the first two atomic the eigenvalue problem in k space. The RS-LMTO-ASA is planes close to the Fe-Cr interface have been treated self- an order N method which can be used to treat complex sys- consistently in our calculations. For those further away we tems with large number of inequivalent atoms in the unit have taken the bulk Fe parameters C¯ and ¯. The use of bulk cell. It has been successfully applied to study crystalline parameters does not render the procedure less accurate, pro- systems,25 substitutional and interstitial impurities in metallic vided a sufficiently large number of atomic planes close to hosts,26,31 as well as other local defects in metals,32 and me- the interface is treated self-consistently.26,33 tallic surfaces,27,33 yielding results which agree well with We have performed our RS-LMTO-ASA calculations for those obtained by other first-principles approaches. The RS- superlattices using a supercell approach in which transla- LMTO-ASA is a linear method, and its solutions are more tional symmetry, with the supercell periodicity, is assumed accurate around a given energy E , which is usually chosen in the direction perpendicular to the layers. In this case, the to be the center of gravity of the occupied part of the band. It Fermi level of the system is determined, at each iteration, by also uses the atomic sphere approximation ASA , where the filling the bands with the correct number of electrons, and Wigner Seitz WS cell around each site is substituted by a the electrostatic potential VES is obtained, in the usual way, WS sphere with the same volume. In the RS-LMTO-ASA by Ewald sums. PRB 60 MAGNETIC BEHAVIOR OF THIN Cr LAYERS . . . 3423 III. RESULTS FOR Fe/Cr/Fe 001... SANDWICHES Our aim is to investigate the effect of the Fe layers on the magnetic state of the Cr spacer layer in Fe/Cr/Fe 001 sand- wiches. The natural reference system with which one should compare the Cr layer results is bulk Cr. One may ask, for instance, whether the presence of the Fe layers or the com- pression of the Cr lattice caused by them enhances or di- minishes the magnitude of the Cr local magnetic moments with respect to its bulk value. As mentioned earlier, the ground state of bcc Cr shows an incommensurate SDW an- tiferromagnetism, where the maximum observed local mo- ment is 0.59 B , for an equilibrium WS radius of 2.684 a.u.13,35 However, the commensurate antiferromagnetic state of Cr is close to the ground state, and most theoretical cal- culations of the electronic structure of bulk Cr assume it as an approximation for the ground state of Cr. Nevertheless, even in this case, the theoretical determination of the correct local moment in bulk Cr is rather subtle. The calculated mo- ment of bulk bcc Cr is extremely sensitive to the value of the lattice parameter used, as well as to details of the calculations.11,12,36 It has been reported, in the context of FIG. 1. Magnetic moment distribution for Fe/Crn /Fe(001) LMTO-ASA calculations, that it is necessary to consider a sandwiches with a 2.935 Å n 1 a , n 3 b , n 5 c , and slightly larger lattice parameter than the one experimentally n 7 d . Dashed dotted line shows the bulk Fe Cr moment for observed to obtain a reasonable description of the magnetic the lattice parameter used in the calculations. properties of bulk bcc Cr.11 Moruzzi and Marcus,36 using total-energy band calculations within the local spin density lattice parameter in this range will be used in our investiga- approximation LSDA , have shown that bcc Cr has a first- tions of Fe/Cr systems. order transition from non-magnetic to antiferromagnetic be- Having established the range of lattice parameters which havior at lattice constants expanded by approximately 1.5%. we will consider, we now present our results for Therefore, in studying the changes of the Cr moments due to Fe/Crn /Fe(001) sandwiches. Initially, we take a common the presence of Fe layers in Fe/Cr systems, it is important to lattice constant a 2.935 Å for the whole Fe/Cr system, and calculate the magnetic moment of pure Cr with the same investigate the magnetic moments of the Cr sites for different method, to set our reference state on an equal footing. This is thicknesses of the Cr spacer layer. This is a reasonable necessary in order to be able to infer the correct trends. For choice of a to study the tendencies obeyed by the local mag- example, if an LSD calculation for an Fe/Cr system assumes netic moments in unstrained Cr layers sandwiched by Fe, a lattice constant at which pure bulk Cr is nonmagnetic, any because the calculated magnetic moment of pure Cr, with finite local magnetic moment found in the Cr layer of the this lattice constant, is rather close to the observed value. We Fe/Cr system would represent an enhancement of the Cr mo- have performed calculations for Cr layers with thicknesses ment. On the other hand, the same results for the Fe/Cr sys- n 1, 3, 5, and 7 atomic planes. tems would be interpreted differently if the magnetic mo- Our RS-LMTO-ASA calculations for Fe/Cr/Fe 001 sand- ment found for pure Cr is mCr 0.6 B . Therefore, before wiches require the determination of the Fermi level of the proceeding to investigate Fe/Cr systems, we use the RS- system and the bulk potential parameters associated with the LMTO-ASA scheme to calculate the electronic structure and Fe sites far from the Fe/Cr interface. In order to obtain these the magnetic moment of pure bulk bcc Cr. quantities we have performed a calculation for bulk Fe with In all our calculations we have used the LSDA with the the chosen lattice constant a 2.935 Å. For this value of a exchange and correlation potential of von Barth and Hedin.37 we found a magnetic moment mFe 2.31 B , which is We have considered a basis set with nine orbitals per site slightly larger than the observed value of 2.21 B obtained representing the valence s, p and d electrons, and have used with the Fe lattice constant aFe 2.861 Å. Having obtained the Beer and Pettifor terminator,38 with a cutoff parameter the parameters for bulk Fe we can now use the procedure LL 20 in the recursion chain. For bcc Cr, we consider two described in Sec. II to calculate the electronic structure and sublattices, allowing the occurrence of antiferromagnetic magnetic moments in the Fe/Cr/Fe 001 sandwiches. alignment. A cluster of 3600 atoms was used in the calcu- In Fig. 1 we show the RS-LMTO-ASA results for the lations. We found that the local moments of the Cr sites are magnetic moment distribution of a /Fe/Cr1 /Fe(001), b extremely sensitive to the lattice parameter. The system does /Fe/Cr3 /Fe(001), c /Fe/Cr5 /Fe(001), and d /Fe/Cr7 / not develop a local magnetic moment if the experimental Fe(001) sandwiches. In all cases we have labeled the central lattice constant of Fe is used. However, it is found to be Cr atomic plane as Cr1, and the Fe plane at the Fe/Cr inter- antiferromagnetic, with mCr 0.54 B , for a Cr lattice pa- face as Fe1. The other Cr planes are numbered in increasing rameter aCr 2.935 Å, which is 1.75% larger than the ex- order from Cr1 to the interface, as shown in the correspond- perimentally observed bulk Cr value. This is in good agree- ing figures. For comparison we also show the local magnetic ment with other LSD calculations,11,36 and variations of the moments of bcc Cr dotted line and Fe dashed line , both 3424 KLAUTAU, LEGOAS, MUNIZ, AND FROTA-PESSO A PRB 60 TABLE I. Magnetic moment profiles in Fe2 /Cr3(001) superlat- TABLE III. Local magnetic moments in B) of the Fe at the tices, calculated with different lattice parameters a1 2.935 Å and interface Fe1 , of the Cr at the interface Cr4 , of the other adjacent a2 2.872 Å arithmetic average of bulk Fe and Cr observed lattice Cr layers Cr2 and Cr3 , and of the Cr in the central layer Cr1 , constants . For comparison, we also show earlier first-principles for the system Fe/Cr7 /Fe(001) sandwiches. LMTO-ASA results. All magnetic moments in units of B . a(Å) Cr1 Cr2 Cr3 Cr4 Fe1 RS-LMTO-ASA LMTO-ASA Ref. 4 2.935 0.81 0.83 0.83 1.10 2.25 a1 a2 a2 2.905 0.54 0.56 0.58 0.84 2.16 Fe1 2.43 2.23 2.1 2.884 0.43 0.44 0.46 0.71 2.10 Cr2 0.96 0.59 0.5 2.872 0.33 0.34 0.36 0.60 2.06 Cr1 0.79 0.43 0.4 2.861 0.25 0.27 0.29 0.53 2.02 calculated with the same lattice constant a 2.935 Å. We other hand, due to limitations of the LSDA, calculations per- have found that the Fe-Cr interface planes couple antiferro- formed using the lattice constant listed in columns two and magnetically, and that the magnetic moment of the Cr sites at three of Tables I and II yield magnetic moments for bulk bcc the Cr/Fe interface, is substantially enhanced in comparison Cr which are close to zero. Therefore, as in the case of the with the bulk Cr value. The magnetic moment of the inter- trilayer, the presence of Fe in the Fe2 /Cr3(001) and facial Cr sites is larger for n 1 (mCr 1.66 B) when they Fe3 /Cr3(001) superlattices leads, in all cases, to an enhance- are surrounded by Fe layers on both sides, and decreases to ment of the Cr moments relative to its pure bulk value ob- mCr 1.10 B when the Cr layer has seven atomic planes. tained with the same lattice parameter . We have seen that The moment of the central-plane sites Cr1 is also en- the moment of Cr is extremely sensitive to changes in the hanced, but it decreases as the distance to the Fe-Cr interface lattice parameter and it is interesting to investigate the effect increases, approaching the bulk-Cr value for sufficiently of these changes on the local moments at the Cr sites in large Cr layer thicknesses. Fe/Cr/Fe 001 sandwiches. Since the lattice parameter of Fe It is interesting to compare our results with others found is somewhat smaller than that of Cr, one would expect the Cr in the literature4,39 for Fe/Cr 001 multilayers with similar Cr layer lattice spacing to be slightly reduced in spacer layer thicknesses. Our calculation for the Fe/Crn /Fe(001) sandwiches, particularly for thin Cr layers. Fe/Cr3 /Fe(001) sandwich see Fig. 1 b give values of mCr To investigate the effect of such compression, we have con- which are greater than the experimentally observed bulk Cr sidered the Fe/Cr7 /Fe(001) system and calculated the mag- value (mCr 0.6 B) for all Cr sites. However, previous cal- netic moments at all inequivalent Cr sites, for different val- culations for Fe2 /Cr3(001)4 and Fe3 /Cr3(001) Ref. 39 su- ues of the lattice parameter. The calculated results are shown percells have found smaller values of mCr , apparently indi- in Table III for the central Cr1 and subsequent Cr atomic cating that the presence of the Fe layers reduces the Cr planes Cr2 and Cr3 , as well as for the interfacial Fe-Cr magnetic moments in these systems. Sandwiches and super- planes Fe1 and Cr4 , as a function of lattice parameter. The lattices have different geometries, but the tendencies ob- local moment of the Fe sites Fe1 does not change much tained for the Cr moments in the presence of Fe at an ideal when the lattice parameter is varied, but the Cr local mo- Fe-Cr interface should be similar, and the origin of this ap- ments are substantially reduced as the lattice parameter de- parent discrepancy must be investigated. In Tables I and II, creases. The Cr1 magnetic moment is reduced from mCr we present RS-LMTO-ASA results for the Fe2 /Cr3(001) 0.81 B for a 2.935 Å to mCr 0.25 B when the ex- and Fe3 /Cr3(001) systems, considering different values of perimental lattice constant of bcc Fe (aFe 2.861 Å) is used. the lattice constant. It is clear that the RS-LMTO-ASA cal- As in the case of the superlattices considered in Tables I and culations agree with those of Refs. 4 and 39, provide the II, the Cr moments in Fe/Crn /Fe(001) sandwiches can be same lattice constant is used in both ccalculations. On the TABLE II. Magnetic moment profiles in Fe3 /Cr3(001) super- lattices, calculated with different lattice parameters: column one with a1 2.935 Å; columns 2 and 3 with an unit cell whose lengths along the 100 and 001 directions are a2 2.829 Å and a3 2.875 Å, respectively. For comparison, we also show earlier ASW augmented spherical waves results. All magnetic moments in units of B . RS-LMTO-ASA ASW Ref. 39 a1 a2 ,a3 a2 ,a3 Fe1 2.22 1.94 1.80 Fe2 2.57 2.48 2.45 Cr2 0.89 0.48 0.35 FIG. 2. Schematic representation of the two layers Cr1 0.64 0.30 0.25 (Cr25%Fe75%)(Cr75%Fe25%) rough Fe-Cr interfaces, used in the sys- tem Fem /Crn(001). Each site is identified by numbers. PRB 60 MAGNETIC BEHAVIOR OF THIN Cr LAYERS . . . 3425 FIG. 3. Magnetic moment distribution for the a Fe3 /Cr1(001), b Fe3 /Cr3(001), and c Fe3 /Cr5(001) superlattices with a 2.935 Å, along the three lines representative of the inequivalent sites as explained in the text. The dashed dotted line shows bulk Fe Cr moments for the lattice parameter used in the calculations. smaller than 0.59 B . However, for perfect interfaces, and tigate the combined effects of compression and interface when the Fe layers are ferromagnetically aligned, they are mixing on the local moments at the Cr sites. always enhanced relative to the Cr bulk value which, in turn, The interfacial Cr-Fe mixing produces a disordered alloy can be drastically reduced under pressure. For the smaller which can extend over a few atomic planes beyond the Fe/Cr lattice constant considered in Table III, the moment of the interface. Such random mixing generates frustrations of Cr1 sites in Fe/Crn /Fe(001) sandwiches tends to zero as n magnetic character, which may induce intricate non-collinear increases, because this is the bulk-Cr value for aCr spin alignments. Presently, however, it would be computa- 2.861 Å . tionally prohibitive to include all these degrees of freedom in our first-principles calculation. Often simpler models can be IV. Fe/Cr 001... SUPERLATTICES IN THE PRESENCE used to understand the behavior of more complex systems, OF INTERFACE MIXING and here, to illustrate the effect of compression in the pres- Ideal interfaces are difficult to obtain experimentally and ence of interface mixing, we restrict our calculations to the some degree of mixing between adjacent Fe-Cr planes at the interfacially ordered compounds and collinear spin arrange- interface is usually present in real systems. Therefore it is ments. important to consider deviations from perfect interfaces. Fe/ To simulate the Fe-Cr superlattices, we have used super- Cr 001 superlattices with several degrees of interface mix- cells consisting of (Cr25%Fe75%) (Cr75%Fe25%)/Crn / ing have been studied by Stoeffler et al.16 using a param- (Cr75%Fe25%) (Cr25%Fe75%)/Fe3 with n 1, 3, 5, and 7, to etrized electronic structure approach. It was found that the generate large clusters of up to 6000 atoms which were used introduction of interfacial ordered compounds to simulating in the calculations. The potential parameters for all inequiva- a mixing of 25% at the interface can lead to strong reduc- lent atoms in the supercell were obtained self-consistently tions of local moments in the Cr layers. We have seen that a and the Fermi level was determined by filling the available compression of the Cr lattice can also cause a reduction of states with the correct number of valence electrons in the the Cr moments in Fe/Cr 001 superlattices and sandwiches. system. Due to interface mixing there are three inequivalent In this section we use the RS-LMTO-ASA method to inves- atoms in each of the 001 planes of the bcc structure and our 3426 KLAUTAU, LEGOAS, MUNIZ, AND FROTA-PESSO A PRB 60 systems: the Cr atoms in the mixed (Cr25%Fe75%) planes have moments around 0.8 B , enhanced relative to that of bcc Cr due to the presence of the Fe neighbors, while those in (Cr75%Fe25%) planes show moments of around 0.4 B . As expected,10 the local moments at the unmixed Cr planes are drastically reduced by interface mixing. The moments at Cr sites of the central plane in the Crn layer increase as n is increased, and should tend to the value for bcc Cr in the asymptotic limit of n large. Our results confirm the general behavior first described by the parametrized tight-binding calculations of Stoeffler et al.16 The qualitative agreement between the first-principles calculations and the parametrized results of the literature is not surprising. One can show that a sound parametrization and the use of approximate charge neutrality are expected to give a good description of the elec- tronic structure of transition metal systems.25,40 To investigate the combined effects of compression and interface mixing in Fe/Cr 001 superlattices, we have per- formed RS-LMTO-ASA calculations for the system with n 7, taking a 2.861 Å, the experimentally observed lattice constant of bcc Fe. In Fig. 4 we show results for the local moments at Cr sites for two different values of the lattice parameter: a 2.935 Å Fig. 4 a and a 2.861 Å Fig. 4 b . The notation is the same as in Fig. 3, but to better represent the small Cr moments, the larger Fe moments were not included. The calculated moment for Cr in the commen- surate antiferromagnetic state is close to this value for a 2.935 Å, but goes to zero for a 2.861 Å. Comparing FIG. 4. Magnetic moment distribution for the Fe3 /Cr7(001) su- the values in Figs. 4 a and 4 b , we see that a compression perlattices with a a 2.935 Å and b a 2.861 Å, along the of the Cr lattice can further suppress the moments at the Cr three lines I, II, and III representative of the inequivalent sites, as sites. The Cr atoms at the mixed Fe-Cr planes sustain con- specified in Fig. 3. The dotted line (0.59 B) indicates the experi- siderable local moments see box 4 b III even under com- mentally observed value in bcc Cr. pression, but the moments of Cr located in the Cr7 layer are already extremely small, below 0.1 results will be plotted following the lines of sites designated B . Furthermore, the Cr moment in the central Cr plane should tend asymptotically to by 1 two degenerate branches , 2, or 3 in the schematic zero the bulk value for the compressed lattice as the num- representation of the mixed interface planes of Fig. 2. ber of planes in the Cr layer is increased; as long as the In Fig. 3 we show results for Fe/Cr 001 superlattices lattice remains compressed, the Cr moments in the Cr with n 1 a , 3 b and 5 c , obtained using a lattice con- n layer should remain under 0.1 stant a 2.935 Å, which should represent well the magnetic B for n greater than seven. Such small moments may be difficult to detect experimentally. behavior of unstrained Cr layers. Values for the Cr moments Based on our results, we suggest that the combined effect of in the case of n 7 are shown in Fig. 4 a . Three sets of interface mixing and compression of the Cr lattice due to the boxes I, II, and III are shown in each case. In the first box presence of Fe layers could be responsible for the experi- I we show the behavior of the moments along the line of mentally observed19,23 paramagnetic behavior of the thin Cr sites designated by 1 in Fig. 2. The two degenerate paths of layers in Fe-Cr sandwiches. this type go through majority sites at the interface: Fe atoms in mixed (Cr25%Fe75%) planes and Cr atoms in mixed (Cr75%Fe25%) planes. In the second box II , we show mo- V. CONCLUSIONS ments along line 2, which pass through Fe atoms in all mixed planes, while in the third box III , we show results for the We have used the first-principles RS-LMTO-ASA scheme line 3 which passes through Cr atoms in these same planes. to study the magnetic behavior of extremely thin Cr layers in We see that the local moments at the central plane of the thin Fe-Cr sandwiches and superlattices. The effect of compres- Fe3 layer are slightly increased when compared to bulk val- sion of the Cr layer in these systems was also investigated. ues, while the moment at the minority Fe sites in the mixed The calculations, some performed for large supercells of 76 planes see box II is slightly decreased. These variations are atoms, illustrate the application of this order-N real-space rather small, and our results agree with the experimental approach to the study of the electronic structure and mag- observations,19 which indicates that the magnetism of the Fe netic behavior of complex metallic systems. is not significantly affected by the presence of Cr neighbors. We have considered Fe/Crn /Fe(001) sandwiches, con- The local moments of Cr atoms in the mixed planes box sisting of n atomic planes of Cr embedded in Fe along the III , with the same number of Fe neighbors, have similar 001 direction, and have obtained results for very thin Cr values of magnetic moments in the different Fe/Crn(001) layers with n 1, 3, 5, and 7. In all cases, the local moments PRB 60 MAGNETIC BEHAVIOR OF THIN Cr LAYERS . . . 3427 at the Cr sites were larger than 0.59 B , the experimentally the local moments at the Cr sites are significantly reduced by observed value in bcc Cr, being enhanced due to the pres- compression. ence of the Fe layers. A similar tendency was obtained for Cr Finally, we have presented RS-LMTO-ASA calculations moments in Fe for Fe/Cr 3 /Cr3(001) and Fe2 /Cr3(001) superlattices. n(001) superlattices, with n 1, 3, 5, and 7, in the By comparing the superlattice results with those of other first presence of interface mixing. Our results for the unstrained principle approaches in the literature, we have shown that, Cr lattice are in qualitative agreement with those of Ref. 16, due to the sensibility of the Cr moment to small variations of showing that interface mixing can substantially reduce the moments of the Cr layers. We have also investigated the role the lattice parameter, when investigating the behavior of bcc of compression of the Cr lattice in the presence of interface Cr layers in the presence of other elements, extra care must mixing in Fe/Cr 001 superlattices. Our results suggest that be taken to isolate the effect of compression from other ef- the combined effects of interface mixing and compression of fects. When performing first-principle calculations in these the Cr lattice could be responsible for the paramagnetic be- systems it is important, as a consistency check, to calculate havior observed for thin Cr layers19,23 in Fe/Cr 001 systems. bcc Cr under the same conditions and with the same method. Since the lattice parameter of bcc Fe is slightly smaller ACKNOWLEDGMENTS than that of bcc Cr, it is interesting to investigate the mag- We acknowledge profitable discussions with Dr. Marek netic behavior of Fe-Cr sandwiches under compression. Here Przybylski regarding the experimental aspects of the prob- we have performed RS-LMTO-ASA calculations for lem. This work was partially supported by FAPESP, CAPES, Fe/Cr7 /Fe(001) sandwiches, as a function of lattice param- and CNPq. Some of the calculations were performed using eter. 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