Eur. Phys. J. B 9, 149­157 (1999) THE EUROPEAN PHYSICAL JOURNAL B EDP Sciences c Societ a Italiana di Fisica Springer-Verlag 1999 Surface dependence of the magnetic configurations of the ordered B2 FeCr alloy F. Amalou1, M. Benakki1, A. Mokrani2, and C. Demangeat3,a 1 Institut de Physique, Universit´e Mouloud Mammeri, 15000 Tizi-ouzou, Algeria 2 LPME, EA1153 DS4, 2, Rue de la Houssini ere, 44072 Nantes, France 3 IPCMS-GEMME, 23, rue du Loess, F-67037 Strasbourg Cedex, France Received 23 March 1998 Abstract. Tight-binding linear muffin tin orbitals calculations with generalized gradient approximation were carried out for the magnetic configurations at the surface of the ferromagnetic ordered B2 FeCr alloys. For both (001) and (111) crystallographic phases, non ferromagnetic configurations are shown to be more stable than the ferromagnetic configuration of the bulk alloy. For (001) surface we display a c(2 × 2) ground state for either Cr or Fe at the surface. For Cr top layer the magnetic moments are 700% larger than in the bulk B2 FeCr while they are slightly enhanced for Fe top layer. For (111) surface an antiferromagnetic coupling between surface and subsurface is always obtained i.e. for either Fe or Cr at the surface. This change of coupling between Fe and Cr (from ferromagnetic to antiferromagnetic) is expected to be fundamental to any explanation of the experimental results obtained for the interface alloying at the Fe/Cr interfaces. PACS. 75.30.Pd Surface magnetism ­ 75.10.Lp Band and itinerant models ­ 75.50.Bb Fe and its alloys 1 Introduction ments in Fe/Cr/Fe sandwiches with pinhole defects. The distribution of the moments inside the pinhole is simi- The angular resolved Auger spectroscopy (ARAES) [1­3], lar to the Fe clusters embedded into a Cr matrix [10]. the scanning tunneling microscopy (STM) [4] and proton Uzdin et al. [11] have explained recent results of Cr over- induced Auger electron spectroscopy [5] have shown that layers on Fe surface by means of magnetic linear dichro- the formation of the Fe/Cr (001) interface is far more com- ism in the angular distribution and spin-resolved core level plicated than expected. The above studies revealed very photoemission within the framework of periodic Anderson clearly that the Cr undergoes interfaces mixing when the model. Comparison of experimental spectra and theoreti- substrate temperature is adjusted for optimum growth. cal dependencies, obtained for the different surface rough- However, the quantitative conclusions based on the STM ness, leads to conclusions about the microscopic structure technique differ significantly from those based on Auger of Cr overlayers. spectroscopy [6]. Kulikov and Demangeat [12] have performed self- Pizzagalli et al. [7] have shown that contradictory ex- consistent calculations of the spin polarized electronic perimental data on magnetic moments and spin-order at structure of disordered FeCr alloy. The moments coupling Fe/Cr interfaces can be explained by structural irregu- is a function of the alloy concentration and for iron-rich larities at the interfaces. The spin polarized electronic alloys this coupling changes from parallel (ferromagnetic) charge distribution was calculated by using a self consis- to antiparallel (antiferromagnetic). It is therefore obvious tent tight-binding model combined with a real space recur- that, in order to explain the magnetic profiles at the Fe/Cr sion method. It was used to interpret the total magnetic interfaces it is necessary to consider both coupling between moment of Cr (001) films and of Cr/Fe (001) sandwiches Fe and Cr i.e. ferromagnetic as in the B2 (FeCr) alloy MBE grown on Fe (001) from in situ measurements with [13­15] whereas for Fe an alternating gradient magnetometer during film growth. nCrm superlattices for n > 1 the coupling is believed to be of antiferromagnetic type With the same model as Pizzagalli et al.; Bouzar et al. [8] [16­18]. have investigated the magnetic reconstruction at the sur- face of B2 FeCr alloy. Up to now, calculations concerning FenCrm superlat- Uzdin and Demangeat [9] have studied within periodic tices for n > 1 have been numerous and the conclusion Anderson model (PAM) the distribution of magnetic mo- reached is that the coupling between Fe and Cr is antipar- allel (or antiferromagnetic). Recently, Mora¨itis et al. [19] a e-mail: claude@belenus.u-strasbg.fr have shown within a tight-binding linear muffin tin 150 The European Physical Journal B Surface layer for (001) and (111) crystallographic configurations at the surface of B2 FeCr alloy. In Section 2 we present briefly the TB-LMTO calculation model applied to the surface. We will discuss more precisely two points: i) the effect Fe of the number of k points on the values of the magnetic moments and on the stability of the ground state config- Cr uration, and ii) the effect of the thickness of the supercell slab on the magnetic reconstruction at the surface of the B2 FeCr alloy. Section 3 presents the results obtained for (a) B2 FeCr bulk within generalized gradient approximation. These results are discussed and compared to previous cal- culations. In Section 4 we present our results concerning the different magnetic configurations converged for (001) surface. The results for the (111) surface are presented in Section 5. Finally, Section 6 is devoted to the conclu- sion. It will be especially shown that the self consistent procedure does not converge easily, in particular for the (011) surface so that those last results will appear in a forthcoming publication. (b) 2 Calculation model In this paper, we report the magnetic structure at the surface of B2 FeCr alloy, using a scalar-relativistic ver- sion of the k space tight-binding linear muffin-tin orbital method [20] in the atomic sphere approximation (TB- LMTO ASA). This method has given pertinent results (c) in the case of one Mn monolayer on Fe(001) [21], for the relative stability of an on-top and an inverted Mn mono- layer an Ag (001) [22] as well as for 3d transition metal Fig. 1. Schematic view of three magnetic configurations at monolayers on graphite [23]. Suitable results have been the surface of B2 FeCr with Fe (dark circles) at the surface: also obtained for FenVm superlattices [24] and for Vm (a) c(2 × 2), (b) p(1 × 1) and (c) p(1 × 1) . In dashed lines we thin films (m = 1, 4) on Fe (001), the magnetic moment of have represented the unit cell which is used to reproduce the the V monolayer being equal to 0.7µB whereas Handschuh semi-infinite environment for all these configurations. and Bl¨ugel [25] within full potential linearized augmented plane waves method (FLAPW) have obtained a value of 0.6µB. orbitals (TB-LMTO) approach in local density approxi- In the work of Bouzar et al. [8] only ferromagnetic mation (LDA), that for the B2 FeCr alloy, a slight increase i.e. p(1 × 1) and p(1 × 1) configurations for the sur- of the lattice parameter leads to a change of the interfacial face layer were considered. Here, we include also the well- coupling between Fe and Cr. It may be worthwhile to re- known c(2 × 2) magnetic configuration which has been member that this alloy may be viewed as alternating (001) shown to be the ground state for Mn on Fe (001) [21]. In layers of Fe and Cr, thus forming the low thickness limit the case of (111) surface, antiferromagnetic configurations in the FenCrm multilayer family (FeCr is FenCrm super- are frustrated due to the triangular geometry. Therefore, lattice for n = 1 and m = 1). It is therefore necessary to as discussed by Kr¨uger et al. [23] various magnetic config- explain why the coupling at the Fe/Cr interface in FenCrm urations (if we restrict to constrained collinear solutions) multilayers depends on n, the number of Fe layers! We [19] should be tested. Here we restrict to the most simplest row have already shown that the coupling depends strongly on by row (noted here p(2 × 1)) and displayed in Figure 1a the lattice parameter. This point has been confirmed re- of [23]. To be able to compare between the total ener- cently by Qiu et al. [15] within the augmented spherical gies of all these configurations we have chosen the same waves (ASW) approach. This coupling between Fe and Cr unit cell in real space (as shown in Fig. 1 for the (001) depends more generally on the Fe concentration as shown crystallographic surface) and also the same number of k- in disordered FeCr alloys [12]. points in the irreducible Brillouin zone has been used. In In the present communication we want to assert the our TB-LMTO approach, in the atomic sphere approxi- precision of the semi-empirical calculations of Bouzar mation, we used the general gradient approximation with et al. [8] displaying a transition from ferromagnetic to anti- the Langreth-Mehl-Hu functional [26]. The model consists ferromagnetic coupling when one goes from bulk B2 FeCr of slabs that are superposition of alternating Fe and Cr alloy to the surface. In this article we present electronic- monolayers. Atomic layers are in general separated by five structure calculation of different magnetic configurations layers of empty spheres. This number (five) is found to F. Amalou et al.: Surface magnetism of B2 FeCr alloy 151 z be sufficient to obtain well separated noninteracting slabs [21,22], that is charge vanishing in the central layer of E7 E8 empty spheres and no dispersion along the z-axis direc- tion. However, for the specific case of B2 FeCr, we have E5 E6 found that five layers was not sufficient, so we will use in all the calculations seven layers in order to reach the above E3 E4 conditions. Empty spheres consist of pseudo atoms with no core states. They are located alternatively at the Fe E1 E2 and Cr sites. Their role is double: (i) reproduce the sym- metry along the z-axis broken for a semi infinite system, Cr5 Cr6 thus allowing us to calculate electronic structure using a method operating in the k-space, (ii) break the bonds for Fe5 Fe6 the atoms of the top layer of the slab thus creating the surface. Cr3 Cr4 We have optimized the number of k-points in order to get accurate solutions with a reasonable time of calcula- Fe3 Fe4 tion. A typical set of 6×6×2 special k-points mesh (which a2 yield 32 points in the irreducible first Brillouin zone) is Cr1 Cr2 therefore used to perform Brillouin zone sampling. Also we have investigated the effect of the thickness of the slab on: y i) the stability of the magnetic surface reconstruction i.e. Fe1 Fe2 that a particular ground state should not depend on the x thickness of the slab used; Cr1 Cr2 ii) the values of the magnetic moments at the surface should not vary over 10-2µB. Fe3 Fe4 Taking into account these two conditions we have shown that reasonable thicknesses of the slabs are 11 monolayers Cr3 Cr4 (ML) for (001) surface (Fig. 2) and 9 ML for (111) surface. Fe5 Fe6 3 Bulk FeCr Cr5 Cr6 We have computed the total energy versus lattice parame- E1 ter for bulk B2 FeCr alloy (Fig. 3a) for Langreth-Mehl-Hu E2 functional. The equilibrium lattice constant in bcc mag- E3 E4 netic B2 FeCr is found to be 5.36 a.u. In Figure 3b we can see that the magnetic moments varies slowly over the entire range of lattice parameter around the ground state E5 E6 and shows parallel coupling between Fe and Cr magnetic moments. A transition from ferromagnetic configuration a1 E7 E8 to antiferromagnetic configuration is observed for an in- a1 crease of the lattice parameter by 3%. This is in qualitative agreement with the LDA results of Mora¨itis et al. [19]. : Fe For the lattice parameter corresponding to the ground state we have obtained 1.51µ : Cr B for Fe and 0.37µB for Cr. These values are different from those obtained within : Empty spheres LMTO-LDA [14] i.e. 1.10µB and 0.68µB and TB-LMTO- LDA [19] i.e. 0.98µB and 0.68µB. They are in reasonable agreement with the GGA results of Singh i.e. 1.21 or 1.36 Fig. 2. Calculation model for (001) surface with Cr on top layer. This model, shown in the left side of the figure, consists for Fe depending on the lattice parameter used. It is not at of supercell slab with 11 (alternating Fe and Cr) atomic layers all clear why GGA and LDA leads to such discrepancies. and 7 layers of empty spheres (Ei). In each layer we consider Some clues can be found in Table 1 of the paper of Moroni a pattern of two atoms that we distinguish by different indices and Jarlborg [14] where it is shown that different results as shown in the right side of the figure (which is a projection are obtained i.e. from 0 to 1.2µB for bulk Cr depending of the slab on the yz-plane), i.e. in the center of the slab we on the functional used. The Perdew-Wang functional [27] distinguish the two iron sites by Fe1 and Fe2. These atoms are overestimates the lattice parameter of the ground state as inequivalent in the c(2 × 2) configuration and equivalent in the discussed by Amalou et al. [28]. Moreover this functional p(1 × 1) and p(1 × 1) configurations. Lattice parameters are: leads to a value of 1.2µB for bulk Cr [14] which is twice the a1 = 2 × a and a2 = 8 × a, "a" is the lattice parameter of experimental value. Also in the case of TB-LMTO method the B2 structure of FeCr corresponding to the ground state. used here with the Perdew-Wang functional a moment of 152 The European Physical Journal B to obtain well separated supercells and to reduce charge transfers in the central layers, we have been constrained to take here seven layers of empty spheres. In order to verify the validity of our model we have studied the effect of varying the number of atomic layers. We have found no fundamental effect so that relative stability of the differ- ent magnetic configurations is not altered. We have also studied the effect of increasing the number of k points in the irreducible Brillouin zone. Energies are found to be quantitatively the same: a difference 10-2 mRy/at be- tween a set of 6 × 6 × 2 and a set of 12 × 12 × 4 k-points is obtained. For Cr at the (001) surface we have obtained 3 con- verged solutions i.e. c(2 × 2), p(1 × 1) and p(1 × 1) . Results are reported respectively in Figures 4a, 4b and 4c and summarized in Figures 5a, 5b, 5c. As displayed in Figure 6a, the c(2 × 2) antiferromagnetic configuration is shown to be the ground state. The magnetic moments of Cr are about 3µB which is an increase of about 700% as compared to bulk B2 FeCr. For the metastable solution p(1×1) we recover quickly the bulk values for Fe and Cr. For the ground state i.e. the c(2 × 2) like configuration we obtain for the Cr sur- face values of -2.93 and 2.74 whereas for S-2 also the Cr magnetic moments are deeply modified i.e. the moments are 0.07 and 0.61. For p(1 × 1) we observe an increase of the Fe magnetic moment for S-3 and S-5 whereas a strong decrease of the Cr moment is observed for S-4. Mean magnetic moment per atom is not very different from zero for Cr at the surface i.e. -0.1µB for the ground state c(2 × 2) configuration. This is in perfect agreement with recent "in situ measurements with an alternating gradient magnetometer during film growth" of Miethaner and Bayreuther [7,29,30]. In this experiment Cr layer is grown on Fe. As discussed by Heinrich [3], Davies [4] and Pfandzelter [5], alloying is formed at the surface. There- fore, if this alloy is of B2 FeCr type, then the magnetic moment at the surface is roughly zero which is the result Fig. 3. Total energy (a) and magnetic moments (b) ver- obtained by Miethaner. sus lattice parameter with Langreth-Mehl-Hu functional for For Fe at the (001) surface we have obtained 2 con- Fe(squares) and Cr(circles) for B2 FeCr around the minimum verged solutions, namely c(2 × 2) and p(1 × 1) . As for of energy E0 obtained for a lattice parameter a0 = 5.36 a.u. Cr at the surface, the c(2 × 2) configuration is the ground A transition from ferromagnetic to antiferromagnetic coupling state with a difference of energy of 1.7 [mRy/at] between between Fe and Cr is obtained at a0 = 5.49 a.u. the two configurations. A small increase of the magnetic moments of Fe is obtained. Mean magnetic moments of Fe 1.4µ are also not very different from zero i.e. in agreement with B has been obtained. On the other hand, with the Langreth-Mehl-Hu functional a moment of 0.6µ Miethaner's results [7,30] where Fe monolayers, deposited B is ob- tained for bulk Cr, which is in clear agreement with the on a Cr substrate, displays a roughly zero total magnetic experimental result. Thus in the present work, and for the moment. particular case of B2 FeCr, we have chosen the Langreth- As summary, for both Cr or Fe at the (001) crystallo- Mehl-Hu functional. graphic surface of B2 FeCr the c(2 × 2) configuration is shown to be the ground state. These results may explain the recent results of Miethaner et al. [7,29,30]. 4 Magnetic configurations at the (001) surface 5 Magnetic configurations at the (111) surface In this part we will consider two cases, namely: i) when Cr is on top layer and ii) for Fe at the surface. Calculation As for the (001) surface we will consider here the two model for both systems is shown in Figure 2. However, cases of Fe and Cr at the (111) surface. Since we have F. Amalou et al.: Surface magnetism of B2 FeCr alloy 153 Fig. 4. Magnetic moments at the (001) FeCr surface with Cr on top layer (dark circles) in a c(2 × 2) (a), an antiferromagnetic p(1 × 1) (b) and a ferromagnetic p(1 × 1) (c) configuration. The case of Fe (hollow circles) on top layer is shown in a c(2 × 2) (d) and an antiferromagnetic p(1 × 1) (e) configuration. found numerical difficulties to converge the magnetic con- results of Turtur and Bayreuther [31] if one considers that figurations on this surface, we have been constrained to the Fe surface is highly faceted with a non negligible num- reduce the number of atomic layers, so that the supercell ber of (111) domains [32]. contains in this study 9 alternating Fe and Cr layers, and 7 layers of empty spheres. For Fe at the (111) surface, three converged magnetic configurations are obtained: p(2×1)p(2×1), p(1×1) and For Cr at the (111) surface we have obtained two con- p(1 × 1) p(1 × 1) . As shown for Cr at the (111) surface, verged solutions i.e. p(2×1)p(2×1)p(2×1) and p(1×1) . we have also a long range coupling. The p(2 × 1)p(2 × 1) Results are shown in Figures 7a, 7b and summarized in notation indicates a p(2 × 1) antiferromagnetic coupling Figures 8a, 8b. Here we have used different notations than between the surface and the subsurface. The p(1×1) p(1× those used for the (001) surface to indicate the long range 1) solution, obtained starting the self-consistent proce- coupling of the atomic layers. The p(2×1)p(2×1)p(2×1) dure with a ferromagnetic coupling overall the atomic lay- notation indicates a p(2 × 1) antiferromagnetic coupling ers, displays an antiferromagnetic coupling between the between the three top most layers. The p(1×1) configura- two top most layers. Magnetic moments are shown in Fig- tion is shown to be the ground state contrary to what was ures 7c, 7d, 7e and summarized in Figures 8c, 8d, 8e. As obtained for the (001) surface. Energy difference between for Cr at the (111) surface, the p(1 × 1) configuration is the two converged configurations is about 0.7 [mRy/at]. shown to be the ground state. Relative energies are shown The antiferromagnetic p(1 × 1) coupling at the surface, in Figure 6. Mean magnetic moment at the surface layer with a mean magnetic moment of -3µB, can explain the is -2.66µB. 154 The European Physical Journal B Fig. 5. Magnetic moments in the atomic layers taken from the surface [S] in the (001) crystallographic orientation. In each atomic layer we have considered two inequivalent sites represented here by the two columns in each graduation. In (a), (b) and (c) we have represented the different magnetic configurations at the surface with Cr on top layer in respectively a c(2 × 2), p(1 × 1) and p(1 × 1) configurations. The case of Fe on top layer is displayed in (d) and (e). We note that for Fe the p(1 × 1) configuration does not exist. F. Amalou et al.: Surface magnetism of B2 FeCr alloy 155 Fig. 6. Relative stability of different magnetic configurations for the (001) surface with Cr on the top layer(a) and (111) surface with Fe on the top layer (b). E0 is the energy of the ground state. Fig. 7. Magnetic moments at the (111) FeCr surface with Cr on top layer (dark circles) in (a) a p(2 × 1)p(2 × 1)p(2 × 1) and (b) an antiferromagnetic p(1 × 1) configuration. The case of Fe (hollow circles) on top layer is shown in a p(2 × 1)p(2 × 1) (c), an antiferromagnetic p(1 × 1) (d) and a p(1 × 1) p(1 × 1) (e) configuration. Our results show clearly the fundamental effect of the are antiferromagnetically coupled contrary to the (001) crystallographic orientation on the stability of the mag- surface where the ground state is shown to be c(2 × 2). netic configurations at the surface. For the (111) surface, Therefore the mean magnetic moment is roughly zero for the magnetic moments at the surface and at the subsurface the (001) surface and about -3µB for (111) surface. 156 The European Physical Journal B Fig. 8. Magnetic moments in the atomic layers taken from the surface [S] in the (111) crystallographic orientation. In each atomic layer we have considered two inequivalent sites represented here by the two columns in each graduation. In (a) and (b) we have represented the different magnetic configurations at the surface with Cr on top layer in respectively a p(2×1)p(2×1)p(2×1) and p(1 × 1) configuration. For Fe at the surface, magnetic configurations are shown in (c) in p(2 × 1)p(2 × 1) (d) p(1 × 1) and (e) p(1 × 1) p(1 × 1) configurations. We note that for Cr at the surface the p(1 × 1) configuration does not exist. F. Amalou et al.: Surface magnetism of B2 FeCr alloy 157 6 Conclusion and outlook Schneider, K. Myrtle, J. Magn. Magn. Mater. 156, 215 (1996). In this communication we have displayed magnetic surface 4. A. Davies, J.A. Stroscio, D.T. Pierce, R.J. Celotta, Phys. reconstruction at the B2 FeCr bulk ferromagnet. This is Rev. Lett. 76, 4175 (1996). the first gradient corrected ab initio calculation on this 5. R. Pfandzelter, T. Igel, H. Winter, Phys. Rev. B 54, 1 subject. It confirms the previous semi-empirical calcula- (1996). tions of Bouzar et al. [8]. The main results are: i) for the 6. B. Heinrich, J.F. Cochran, T. Monchesky, K. Myrtle, J. (001) surface and for Cr or Fe at the surface, a c(2 × 2) Appl. Phys. 81, 4350 (1997). reconstruction is shown to be the ground state; ii) for the 7. L. Pizzagalli, M. Freyss, G. Mora¨itis, D. Stoeffler, (111) surface a p(1 × 1) magnetic configuration is shown C. Demangeat, H. Dreyss´e, A. Vega, S. Miethaner, to be the ground state. G. Bayreuther, J. Appl. Phys. 81, 4347 (1997). From the experimental side [1­7,11] a convinced pic- 8. H. Bouzar, M. Benakki, M. Zemirli, A. Mokrani, C. De- mangeat, H. Dreyss´e, Surf. Sci. 381, 117 (1997). ture has now appeared: alloying is present at the Fe/Cr 9. V. Uzdin, C. Demangeat, J. Magn. Magn. Mater. 156, interfaces and lead to drastic changes in the interpretation 458 (1997). of the results. It is not trivial to handle this problem the- 10. M.S. Borczuch, V.M. Uzdin, J. Magn. Magn. Mater. 172, oretically because of the lack of detailed structural infor- 110 (1997). mations arising from experiments. Freyss et al. [33] have 11. V.M. Uzdin, D. Knabben, F.U. Hillebrecht, E. Kisker, taken into account Cr diffusion into Fe substrate by con- Phys. Rev. B 59, 1214 (1999). sidering a two-layer alloy near the Fe substrate. The rate 12. N.I. Kulikov, C. Demangeat, Phys. Rev. B 55, 3533 (1997). of interdiffusion in such a model is found to play an im- 13. D.J. Singh, J. Appl. Phys. 76, 6688 (1994). portant role when the growth mode is far from being layer 14. E.G. Moroni, T.J. Jarlborg, Phys. Rev. B 47, 3255 (1993). by layer. However this calculation [33] was based on semi- 15. S.L. Qiu, P.M. Marcus, V.L. Moruzzi, Phys. Rev. 58, empirical tight-binding model and the parameters used 2651 (1998). should be very sensitive to the coordination number of 16. A. Vega et al., J. Appl. Phys. 69, 4544 (1991). the Cr atom. Also, Uzdin et al. [11] have combined semi- 17. F. Herman, J. Sticht, M.V. Schilfgaarde, J. Appl. Phys. empirical Periodic Anderson Model together with mag- 69, 4789 (1991). netic dichroism and spin-resolved photoemission to probe 18. D. Stoeffler, F. Gautier, Phys. Rev. B 44, 10389 (1991). interdiffusion at the Fe/Cr interfaces. Wille et al. [34] have 19. G. Mora¨itis, M.A. Khan, H. Dreyss´e, C. Demangeat, J. recently discussed the growth mode of Cr on Fe(001) by Magn. Magn. Mater. 156, 250 (1996). using Effective Cluster Interactions (ECI) which are ob- 20. O.K. Andersen, O. Jepsen, Phys. Rev. Lett. 53, tained by a KKR-Green's function in the dilute limit [35]. 2571 (1984). 21. O. Elmouhssine, G. Mora¨itis, C. Demangeat, J.C. These parameters are then used in a Monte-Carlo simu- Parlebas, Phys. Rev. B 55, 7410 (1997). lation of deposition and diffusion. These parameters are, 22. O. Elmouhssine. G. Mora¨itis, J.C. Parlebas, C. as shown in the present communication, highly dependent Demangeat, P. Schieffer, M.C. Hanf, C. Krembel, G. on the coordination of the Cr atom. Moreover it has been Gewinner, Comp. Mat. Sci. 10, 260 (1998). shown that Fe can be not only in the usual ferromagnetic 23. P. Kr¨uger, A. Rakotomahevitra, J.C. Parlebas, C. configuration but also in a c(2×2) antiferromagnetic state. Demangeat, Phys. Rev. B 57, 5276 (1998). It is therefore necessary, in any modelling of the growth 24. J. Izquierdo, A. Vega, O. Elmouhssine, H. Dreyss´e, C. process, to take into account not only of the isolated im- Demangeat, Philos. Mag. B 78, 469 (1998). purity limit [35] but also other concentrations (like the B2 25. S. Handschuh, S. Bl¨ugel, Solid. St. Comm. 10, 633 (1998). FeCr). Work in this direction is in progress. 26. D.C. Langreth, M.J. Mehl, Phys. Rev. Lett. 47, 446 (1981). 27. J.P. Perdew, Y. Wang, E. Engel, Phys. Rev. Lett. 66, 508 F.A. would like to thank the IPCMS-GEMME group for (1991). their kind hospitality. The Institut de Physique et Chimie des 28. F. Amalou, H. Bouzar, M. Benakki, A. Mokrani, C. mat´eriaux de Strasbourg is "Unit´e Mixte Associ´ee au CNRS Demangeat, G. Mora¨itis, Comp. Mat. Sci. 10, 273 (1998). No 7504". This work was partly supported by the European 29. S. Miethaner, G. Bayreuther, J. Magn. Magn. Mater. 148, Community Human Capital and Mobility Program trough con- 42 (1995). tract No CHRX-CT93-0369, and by a collaborative program 30. S. Miethaner, Ph.D. thesis, Regensburg, 1998 (unpub- between France and Algeria (93MEN222). lished). 31. C. Turtur, G. Bayreuther, Phys. Rev. Lett. 72, 1557 (1994). 32. G. Bayreuther, 1997 (private communication). References 33. M. Freyss, D. Stoeffler, S. Miethaner, G. Bayreuther, H. Dreyss´e, in Current Problems in Condensed Matter, edited by Moran-Lopez (Plenum Press, New York, 1998), p.209. 1. B. Heinrich, J.F. Cochran, D. Venus, K. Totland, D. Atlan, 34. L.T. Wille, B. Nonas, P.H. Dederichs, H. Dreyss´e, Philos. S. Kovorkov, K. Myrtle, J. Appl. Phys. 79, 4518 (1996). Mag. B 78, 643 (1998). 2. D. Venus, B. Heinrich, Phys. Rev. B 53, 1733 (1996). 35. B. Nonas, K. Wildberger, R. Zeller, P.H. Dederichs, Phys. 3. B. Heinrich, J.F. Cochran, D. Venus, K. Totland, C. Rev. Lett. 80, 4574 (1998).