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Magnetically stabilized Mn–Co surface alloys on Co(001)
Surface Science 454–456 (2000) 900–903 www.elsevier.nl/locate/susc
Magnetically stabilized Mn–Co surface alloys on Co(001) S. Meza-Aguilar *, O. Elmouhssine, H. Dreysse´, C. Demangeat Institut de Physique et Chimie des Mate´riaux de Strasbourg, 23, rue du Loess, 63037 Strasbourg, France
Abstract Choi et al. (Phys. Rev. B 58 (1998) 5166) using low-energy electron diffraction recently displayed an ordered Mn– Co alloy at the surface of Co for a 0.3–0.8 equivalent monolayer of Mn on Co(001). From magneto optic Kerr effect and X-ray magnetic circular dichroism experiments it was concluded that the coupling between Mn and Co in these surface alloys is ferromagnetic in type. Using the tight binding linear muffin tin orbitals scheme within an atomic sphere approximation and an local density approximation (LDA) in the film geometry we conclude that Mn in the ordered 1 ML thick Mn Co surface alloy is in a high spin state of ca. 3.2 m . Both ferromagnetic and 0.5 0.5 B antiferromagnetic couplings between Mn and Co are obtained but the antiferromagnetic coupling seems to be the preferred type. Going beyond LDA and considering a slightly disordered surface alloy should, therefore, be worthwhile. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Cobalt; Density functional calculations; Magnetic surfaces; Manganese; Metal–metal interfaces
1. Introduction It is now well recognized that the initial growth of a metal onto another starts generally with the place exchange between adatoms and substrate atoms. The best example remains the ordered twodimensional magnetic alloy. They consist of a 1 ML thick alloy film of CuMn (NiMn) with a checkerboard structure of Mn and Cu(Ni) sites [1–4]. The c(2×2) CuMn/Cu(001) ordered surface alloy displays some unusual properties. Usually ordered bulk alloys often are disordered at the surface due to surface segregation; but here it is the other way around and the ordered-surfacealloy structure forms although there is no ordered bulk CuMn phase. * Corresponding author. Fax: +33-388-10-72-49. E-mail address: [email protected] (S. Meza-Aguilar)
Blu¨gel [5] reported recently on these magnetically stabilized surface alloys within a full-potential linearized augmented plane wave ( FLAPW ) method in film geometry. In this paper he concentrated on the stability of the c(2×2) surface alloy against interdiffusion into the substrate and cluster formation. Calculations were performed for 3d transition metal monolayers on Cu(100). Later on Elmouhssine et al. [6,7] showed that the Mn monolayer on top of Ag(100) is unstable at room temperature. A MnAg superficial alloy is formed in the top two atomic layers, immediately after Mn deposition. Moreover, the Mn incorporation in the second plane is thermally activated, and an inverted Mn layer tends to be formed by mild annealing. These experimental findings are in line with electronic structure calculations [6,7] which show that the inverted Mn layer constitutes the energetically preferred state as compared to MnAg
0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 00 ) 0 01 0 1 -1
S. Meza-Aguilar et al. / Surface Science 454–456 (2000) 900–903
alloy formation or to a Mn monolayer on top of Ag(100). Before these ab initio calculations Hergert et al. [8], within a semi-empirical tight-binding scheme have shown that an ordered monolayer (ML) of Ag Rh on the Ag(001) substrate does not 0.5 0.5 display a magnetic moment. This result is in agreement with previous magneto optic Kerr effect (MOKE ) experiments by Mulhollan et al. [9]. Moreover, Turek et al. [10] within coherent-potential approximation (CPA) in the tight binding linear muffin tin orbitals ( TB-LMTO) method have displayed cancellation of the magnetization in disordered Rh–Ag alloys at the surface of Ag(100). All these previous considerations were restricted to the study of surface alloys between a 3d (or 4d ) element on top of a noble metal. More complicated are the study of the interdiffusion between two magnetic elements. In this communication we present the first study of the Mn–Co interface. Experimentally the Mn/Co/Cu(001) structure is such a model system which is well suited to the study of the magnetic interaction between Mn and the ferromagnetic Co. Experimentally O’Brien and Tonner [11] used X-ray magnetic circular dichroism ( XMCD) and found that a single Mn monolayer is ferromagnetically aligned with respect to fcc Co(001). On the contrary, a competition between an in-plane antiferromagnetically ordered c(2×2) configuration and one in which a ferromagnetic Mn monolayer is antiferromagnetically coupled to the Co is predicted by tight-binding model calculations [12]. This discrepancy was first linked to a possible uncertainty of the parameters used in the TB calculation. To sort out this suspicion an ab initio TB-LMTO calculation was performed and the c(2×2) antiferromagnetic configuration was confirmed to be the ground state [13,14] and the difference of the total energy with metastable configurations was considerable. The configuration used to perform this calculation was that of a perfect Mn monolayer on Co(001). O’Brien and Tonner [15] suspected the instability of the perfect Mn monolayer on Co(001) and proposed that the formation of a Mn–Co surface alloy, which is consistent with free-energy arguments, may explain this disagreement in the theo-
901
retical and experimental exchange coupling between Mn and Co. This proposal of a twodimensional ordered surface alloy was confirmed by in situ MOKE and low energy electron diffraction (LEED) by Choi et al. [16,17]. In this communication we compare the stability of the perfect Mn monolayer on Co(001) versus the surface ordered alloy. It has already been shown [14] that, in the paramagnetic case the Mn monolayer on top of Co(001) is unstable. In the present communication we have investigated the effect of the magnetization on the stability of the two-dimensional surface ordered alloy Mn Co on Co(001). The method used is the 0.5 0.5 TB-LMTO approach.
2. Magnetic configurations of a 1 ML thick Mn Co ordered alloy on Co(001) 0.5 0.5 The supercell used in this calculation consists of a slab of nine layers of metallic layers and five layers of empty spheres. The number of empty spheres are adjusted in order to find in the middle of the empty spheres no dispersion relation perpendicular to the metallic slab and no charge in the central spheres. Metallic slabs consist of seven layers of Co and two layers of Mn Co ordered 0.5 0.5 alloy on each side of the seven layers film of Co. Convergency with increasing number of k points is tested. Details can be found in Meza-Aguilar’s thesis [18]. For bulk Co, with one atom per unit cell total energy calculation leads to a magnetic moment of 1.63 m and a lattice parameter of B ˚ . The supercell 3.46 A of nine layers of Co and five layers of empty spheres with the bulk lattice parameter of Co leads to a magnetic moment at the surface of 1.78 m . B The ground state magnetic configuration of a Mn monolayer on Co(001) has been already performed. One monolayer of Mn is added at each side of a slab of 7 ML of Co. This slab of nine metallic monolayers is separated by five layers of empty spheres. A c(2×2) antiferromagnetic ground state is obtained [13,14]. Another calculation considered an Mn Co surface ordered 0.5 0.5 alloy on Co(001). This supercell consists of 1 ML of Mn Co on each side of a slab of 7 ML of 0.5 0.5
902
S. Meza-Aguilar et al. / Surface Science 454–456 (2000) 900–903 Table 1 Magnetic moments and total energy of the ordered alloy (Mn Co )/Co(001); the supercell used for the calculations is 0.5 0.5 reported in Fig. 1 and the values are in Bohr magnetons (m ) B and the energy in Ry per cell (2Mn, 16Co) Magnetic configuration Energy
AF −49157.659
F −49157.653
Atom
moments
moments
Mn Co5 Co4b Co4a Co3b Co3a Co2b Co2a Co1b Co1a
Fig. 1. Unit cell of the superlattice used to determine the magnetic configuration of the two-dimensional 1 ML thick ordered Mn Co alloy on Co(001). Co is in the center of the slab 0.5 0.5 1 of nine metallic monolayers and five layers of empty spheres (we display here only the upper part of the metallic layers of the supercell used; the lower part is symmetric versus the plane containing the Co atoms). 1
Co ( Fig. 1). A separation by 5 ML of empty spheres is used. Two input solutions are used: 1. Mn parallel to Co; and 2. Mn opposite to Co. Two converged solutions are obtained ( Table 1) noted AF for Mn moment antiparallel to the Co subsurface and F for Mn parallel to the Co subsurface. In the AF solution the magnetic moments of the Co atoms in the surface and in the subsurface are strongly reduced in comparison to bulk Co. However, in the F solution there is no significant reduction of those Co moments. Therefore, these two solutions present a very different magnetic behavior. The stability of the two-dimensional ordered Mn Co 1 ML thick on Co(001) is given, 0.5 0.5 following Blu¨gel [5] by comparison with Mn/Co(001) and the Co(001) film. A comparison
−3.18 0.44 1.04 1.04 1.58 1.52 1.62 1.62 1.61 1.60
3.21 1.39 1.39 1.39 1.65 1.61 1.61 1.61 1.60 1.60
of the total energy is needed to compute the different chemical configurations with the same number of inequivalent atoms, the same irreductible part of the Brillouin zone and the same number of k-points. A comparison of the total energy of the ground state of Mn Co /Co(001) versus Co 0.5 0.5 film and Mn/Co(001) displayed a gain of energy of 20 mRy. Therefore we can argue that the ordered Mn Co is stable in agreement with 0.5 0.5 previous experiments [15–17]. However, the antiferromagnetic coupling between Mn and Co appears to be the ground state contrary to that is expected from both MOKE [16,17] and XMCD [15]. Let us comment on this particular point. First it is clear that the magnetic moment of Mn is high and that the difference of total energy between ferromagnetic and antiferromagnetic configurations is small (5 mRy). Second it is well known that LDA may have problems with highly correlated bands. Therefore going beyond LDA, that is, introducing generalized gradient approximation (GGA) may be worthwhile. Third, it is not clear that this well-ordered two-dimensional surface alloy represents the ultimate version of the LEED results. Some kind of disorder may be present which could preclude a direct comparison between our calculations and the experimental results.
S. Meza-Aguilar et al. / Surface Science 454–456 (2000) 900–903
903
3. Conclusion and outlook
References
We have tentatively discussed the results obtained by O’Brien and Tonner [11,15] and Choi et al. [16,17] by performing a TB-LMTO calculation for the determination of the magnetic map of the two-dimensional ordered Mn Co surface 0.5 0.5 alloy on Co(001). This calculation was performed in the ASA with LDA. A magnetic configuration with a Mn in a high moment state (3.2 m ) and B ferromagnetically coupled to Co is obtained in agreement with recent MOKE [16,17] and XMCD [11] experiments. However, this is a metastable solution with total energy slightly higher than the ground state energy displaying an antiferromagnetic coupling between Mn and Co. To resolve this discrepancy we are presently solving the problem within a GGA approach. Moreover it should be proven that there is no disorder state with lower energy.
[1] T. Flores, M. Hansen, M. Wuttig, Surf. Sci. 279 (1992) 251. [2] M. Wuttig, Y. Gauthier, S. Blu¨gel, Phys. Rev. Lett. 70 (1993) 3619. [3] M. Wuttig, T. Flores, C.C. Knight, Phys. Rev. B 48 (1993) 12 082. [4] M. Wuttig, C.C. Knight, T. Flores, Y. Gauthier, Surf. Sci. 292 (1993) 189. [5] S. Blu¨gel, Appl. Phys. A 63 (1996) 595. [6 ] O. Elmouhssine, G. Moraitis, J.C. Parlesbas, C. Demangeat, P. Schieffer, M.C. Hanf, C. Krembel, G. Gewinner, Comp. Mater. Sci. 10 (1998) 260. [7] O. Elmouhssine, G. Moraitis, J.C. Parlesbas, C. Demangeat, P. Schieffer, M.C. Hanf, C. Krembel, G. Gewinner, J. Appl. Phys. 83 (1998) 7013. [8] W. Hergert, P. Rennert, C. Demangeat, H. Dreysse´, Surf. Rev. Lett. 2 (1995) 203. [9] G.A. Mulhollan, R.L. Fink, J.I. Erskine, Phys. Rev. B 44 (1991) 2393. [10] I. Turek, J. Kudrnovsky, M. Sob, V. Drchal, P. Weinberger, Phys. Rev. Lett. 74 (1995) 2551. [11] W.L. O’Brien, B.P. Tonner, Phys. Rev. B 50 (1994) 2963. [12] A. Noguera, S. Bouarab, A. Mokrani, C. Demangeat, H. Dreysse´, J. Magn. Magn. Mater. 156 (1996) 21. [13] O. Elmouhssine, Structure e´lectronique et magne´tique de surfaces et d’interfaces de syste`mes a` base de me´taux de transition, PhD Thesis, Strasbourg, 1998. [14] S. Meza-Aguilar, O. Elmouhssine, H. Dreysse´, C. Demangeat, Comp. Mater. Sci. (2000) (in press). [15] W.L. O’Brien, B.P. Tonner, Phys. Rev. B 58 (1998) 3191. [16 ] B.-Ch. Choi, P.J. Bode, J.A.C. Bland, Phys. Rev. B 58 (1998) 5166. [17] B.-Ch. Choi, P.J. Bode, J.A.C. Bland, Phys. Rev. B 59 (1999) 7029. [18] S. Meza-Aguilar, Proprie´te´s magne´tiques de films minces et d’alliages de surface de me´taux de transition sur substrates me´talliques par TB-LMTO, PhD Thesis, Strasbourg, 2000.
Acknowledgements S. Meza-Aguilar was supported by a Grant from the Mexican Government. C. Demangeat acknowledges the bilateral Alliance program (No. 95039) for partial support and J.A.C. Bland for helpful discussions. The authors would like to thank J.C. Parlebas and M.A. Khan for useful discussions.
Magnetically stabilized Mn–Co surface alloys on Co(001) S. Meza-Aguilar *, O. Elmouhssine, H. Dreysse´, C. Demangeat Institut de Physique et Chimie des Mate´riaux de Strasbourg, 23, rue du Loess, 63037 Strasbourg, France
Abstract Choi et al. (Phys. Rev. B 58 (1998) 5166) using low-energy electron diffraction recently displayed an ordered Mn– Co alloy at the surface of Co for a 0.3–0.8 equivalent monolayer of Mn on Co(001). From magneto optic Kerr effect and X-ray magnetic circular dichroism experiments it was concluded that the coupling between Mn and Co in these surface alloys is ferromagnetic in type. Using the tight binding linear muffin tin orbitals scheme within an atomic sphere approximation and an local density approximation (LDA) in the film geometry we conclude that Mn in the ordered 1 ML thick Mn Co surface alloy is in a high spin state of ca. 3.2 m . Both ferromagnetic and 0.5 0.5 B antiferromagnetic couplings between Mn and Co are obtained but the antiferromagnetic coupling seems to be the preferred type. Going beyond LDA and considering a slightly disordered surface alloy should, therefore, be worthwhile. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Cobalt; Density functional calculations; Magnetic surfaces; Manganese; Metal–metal interfaces
1. Introduction It is now well recognized that the initial growth of a metal onto another starts generally with the place exchange between adatoms and substrate atoms. The best example remains the ordered twodimensional magnetic alloy. They consist of a 1 ML thick alloy film of CuMn (NiMn) with a checkerboard structure of Mn and Cu(Ni) sites [1–4]. The c(2×2) CuMn/Cu(001) ordered surface alloy displays some unusual properties. Usually ordered bulk alloys often are disordered at the surface due to surface segregation; but here it is the other way around and the ordered-surfacealloy structure forms although there is no ordered bulk CuMn phase. * Corresponding author. Fax: +33-388-10-72-49. E-mail address: [email protected] (S. Meza-Aguilar)
Blu¨gel [5] reported recently on these magnetically stabilized surface alloys within a full-potential linearized augmented plane wave ( FLAPW ) method in film geometry. In this paper he concentrated on the stability of the c(2×2) surface alloy against interdiffusion into the substrate and cluster formation. Calculations were performed for 3d transition metal monolayers on Cu(100). Later on Elmouhssine et al. [6,7] showed that the Mn monolayer on top of Ag(100) is unstable at room temperature. A MnAg superficial alloy is formed in the top two atomic layers, immediately after Mn deposition. Moreover, the Mn incorporation in the second plane is thermally activated, and an inverted Mn layer tends to be formed by mild annealing. These experimental findings are in line with electronic structure calculations [6,7] which show that the inverted Mn layer constitutes the energetically preferred state as compared to MnAg
0039-6028/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 0 39 - 6 0 28 ( 00 ) 0 01 0 1 -1
S. Meza-Aguilar et al. / Surface Science 454–456 (2000) 900–903
alloy formation or to a Mn monolayer on top of Ag(100). Before these ab initio calculations Hergert et al. [8], within a semi-empirical tight-binding scheme have shown that an ordered monolayer (ML) of Ag Rh on the Ag(001) substrate does not 0.5 0.5 display a magnetic moment. This result is in agreement with previous magneto optic Kerr effect (MOKE ) experiments by Mulhollan et al. [9]. Moreover, Turek et al. [10] within coherent-potential approximation (CPA) in the tight binding linear muffin tin orbitals ( TB-LMTO) method have displayed cancellation of the magnetization in disordered Rh–Ag alloys at the surface of Ag(100). All these previous considerations were restricted to the study of surface alloys between a 3d (or 4d ) element on top of a noble metal. More complicated are the study of the interdiffusion between two magnetic elements. In this communication we present the first study of the Mn–Co interface. Experimentally the Mn/Co/Cu(001) structure is such a model system which is well suited to the study of the magnetic interaction between Mn and the ferromagnetic Co. Experimentally O’Brien and Tonner [11] used X-ray magnetic circular dichroism ( XMCD) and found that a single Mn monolayer is ferromagnetically aligned with respect to fcc Co(001). On the contrary, a competition between an in-plane antiferromagnetically ordered c(2×2) configuration and one in which a ferromagnetic Mn monolayer is antiferromagnetically coupled to the Co is predicted by tight-binding model calculations [12]. This discrepancy was first linked to a possible uncertainty of the parameters used in the TB calculation. To sort out this suspicion an ab initio TB-LMTO calculation was performed and the c(2×2) antiferromagnetic configuration was confirmed to be the ground state [13,14] and the difference of the total energy with metastable configurations was considerable. The configuration used to perform this calculation was that of a perfect Mn monolayer on Co(001). O’Brien and Tonner [15] suspected the instability of the perfect Mn monolayer on Co(001) and proposed that the formation of a Mn–Co surface alloy, which is consistent with free-energy arguments, may explain this disagreement in the theo-
901
retical and experimental exchange coupling between Mn and Co. This proposal of a twodimensional ordered surface alloy was confirmed by in situ MOKE and low energy electron diffraction (LEED) by Choi et al. [16,17]. In this communication we compare the stability of the perfect Mn monolayer on Co(001) versus the surface ordered alloy. It has already been shown [14] that, in the paramagnetic case the Mn monolayer on top of Co(001) is unstable. In the present communication we have investigated the effect of the magnetization on the stability of the two-dimensional surface ordered alloy Mn Co on Co(001). The method used is the 0.5 0.5 TB-LMTO approach.
2. Magnetic configurations of a 1 ML thick Mn Co ordered alloy on Co(001) 0.5 0.5 The supercell used in this calculation consists of a slab of nine layers of metallic layers and five layers of empty spheres. The number of empty spheres are adjusted in order to find in the middle of the empty spheres no dispersion relation perpendicular to the metallic slab and no charge in the central spheres. Metallic slabs consist of seven layers of Co and two layers of Mn Co ordered 0.5 0.5 alloy on each side of the seven layers film of Co. Convergency with increasing number of k points is tested. Details can be found in Meza-Aguilar’s thesis [18]. For bulk Co, with one atom per unit cell total energy calculation leads to a magnetic moment of 1.63 m and a lattice parameter of B ˚ . The supercell 3.46 A of nine layers of Co and five layers of empty spheres with the bulk lattice parameter of Co leads to a magnetic moment at the surface of 1.78 m . B The ground state magnetic configuration of a Mn monolayer on Co(001) has been already performed. One monolayer of Mn is added at each side of a slab of 7 ML of Co. This slab of nine metallic monolayers is separated by five layers of empty spheres. A c(2×2) antiferromagnetic ground state is obtained [13,14]. Another calculation considered an Mn Co surface ordered 0.5 0.5 alloy on Co(001). This supercell consists of 1 ML of Mn Co on each side of a slab of 7 ML of 0.5 0.5
902
S. Meza-Aguilar et al. / Surface Science 454–456 (2000) 900–903 Table 1 Magnetic moments and total energy of the ordered alloy (Mn Co )/Co(001); the supercell used for the calculations is 0.5 0.5 reported in Fig. 1 and the values are in Bohr magnetons (m ) B and the energy in Ry per cell (2Mn, 16Co) Magnetic configuration Energy
AF −49157.659
F −49157.653
Atom
moments
moments
Mn Co5 Co4b Co4a Co3b Co3a Co2b Co2a Co1b Co1a
Fig. 1. Unit cell of the superlattice used to determine the magnetic configuration of the two-dimensional 1 ML thick ordered Mn Co alloy on Co(001). Co is in the center of the slab 0.5 0.5 1 of nine metallic monolayers and five layers of empty spheres (we display here only the upper part of the metallic layers of the supercell used; the lower part is symmetric versus the plane containing the Co atoms). 1
Co ( Fig. 1). A separation by 5 ML of empty spheres is used. Two input solutions are used: 1. Mn parallel to Co; and 2. Mn opposite to Co. Two converged solutions are obtained ( Table 1) noted AF for Mn moment antiparallel to the Co subsurface and F for Mn parallel to the Co subsurface. In the AF solution the magnetic moments of the Co atoms in the surface and in the subsurface are strongly reduced in comparison to bulk Co. However, in the F solution there is no significant reduction of those Co moments. Therefore, these two solutions present a very different magnetic behavior. The stability of the two-dimensional ordered Mn Co 1 ML thick on Co(001) is given, 0.5 0.5 following Blu¨gel [5] by comparison with Mn/Co(001) and the Co(001) film. A comparison
−3.18 0.44 1.04 1.04 1.58 1.52 1.62 1.62 1.61 1.60
3.21 1.39 1.39 1.39 1.65 1.61 1.61 1.61 1.60 1.60
of the total energy is needed to compute the different chemical configurations with the same number of inequivalent atoms, the same irreductible part of the Brillouin zone and the same number of k-points. A comparison of the total energy of the ground state of Mn Co /Co(001) versus Co 0.5 0.5 film and Mn/Co(001) displayed a gain of energy of 20 mRy. Therefore we can argue that the ordered Mn Co is stable in agreement with 0.5 0.5 previous experiments [15–17]. However, the antiferromagnetic coupling between Mn and Co appears to be the ground state contrary to that is expected from both MOKE [16,17] and XMCD [15]. Let us comment on this particular point. First it is clear that the magnetic moment of Mn is high and that the difference of total energy between ferromagnetic and antiferromagnetic configurations is small (5 mRy). Second it is well known that LDA may have problems with highly correlated bands. Therefore going beyond LDA, that is, introducing generalized gradient approximation (GGA) may be worthwhile. Third, it is not clear that this well-ordered two-dimensional surface alloy represents the ultimate version of the LEED results. Some kind of disorder may be present which could preclude a direct comparison between our calculations and the experimental results.
S. Meza-Aguilar et al. / Surface Science 454–456 (2000) 900–903
903
3. Conclusion and outlook
References
We have tentatively discussed the results obtained by O’Brien and Tonner [11,15] and Choi et al. [16,17] by performing a TB-LMTO calculation for the determination of the magnetic map of the two-dimensional ordered Mn Co surface 0.5 0.5 alloy on Co(001). This calculation was performed in the ASA with LDA. A magnetic configuration with a Mn in a high moment state (3.2 m ) and B ferromagnetically coupled to Co is obtained in agreement with recent MOKE [16,17] and XMCD [11] experiments. However, this is a metastable solution with total energy slightly higher than the ground state energy displaying an antiferromagnetic coupling between Mn and Co. To resolve this discrepancy we are presently solving the problem within a GGA approach. Moreover it should be proven that there is no disorder state with lower energy.
[1] T. Flores, M. Hansen, M. Wuttig, Surf. Sci. 279 (1992) 251. [2] M. Wuttig, Y. Gauthier, S. Blu¨gel, Phys. Rev. Lett. 70 (1993) 3619. [3] M. Wuttig, T. Flores, C.C. Knight, Phys. Rev. B 48 (1993) 12 082. [4] M. Wuttig, C.C. Knight, T. Flores, Y. Gauthier, Surf. Sci. 292 (1993) 189. [5] S. Blu¨gel, Appl. Phys. A 63 (1996) 595. [6 ] O. Elmouhssine, G. Moraitis, J.C. Parlesbas, C. Demangeat, P. Schieffer, M.C. Hanf, C. Krembel, G. Gewinner, Comp. Mater. Sci. 10 (1998) 260. [7] O. Elmouhssine, G. Moraitis, J.C. Parlesbas, C. Demangeat, P. Schieffer, M.C. Hanf, C. Krembel, G. Gewinner, J. Appl. Phys. 83 (1998) 7013. [8] W. Hergert, P. Rennert, C. Demangeat, H. Dreysse´, Surf. Rev. Lett. 2 (1995) 203. [9] G.A. Mulhollan, R.L. Fink, J.I. Erskine, Phys. Rev. B 44 (1991) 2393. [10] I. Turek, J. Kudrnovsky, M. Sob, V. Drchal, P. Weinberger, Phys. Rev. Lett. 74 (1995) 2551. [11] W.L. O’Brien, B.P. Tonner, Phys. Rev. B 50 (1994) 2963. [12] A. Noguera, S. Bouarab, A. Mokrani, C. Demangeat, H. Dreysse´, J. Magn. Magn. Mater. 156 (1996) 21. [13] O. Elmouhssine, Structure e´lectronique et magne´tique de surfaces et d’interfaces de syste`mes a` base de me´taux de transition, PhD Thesis, Strasbourg, 1998. [14] S. Meza-Aguilar, O. Elmouhssine, H. Dreysse´, C. Demangeat, Comp. Mater. Sci. (2000) (in press). [15] W.L. O’Brien, B.P. Tonner, Phys. Rev. B 58 (1998) 3191. [16 ] B.-Ch. Choi, P.J. Bode, J.A.C. Bland, Phys. Rev. B 58 (1998) 5166. [17] B.-Ch. Choi, P.J. Bode, J.A.C. Bland, Phys. Rev. B 59 (1999) 7029. [18] S. Meza-Aguilar, Proprie´te´s magne´tiques de films minces et d’alliages de surface de me´taux de transition sur substrates me´talliques par TB-LMTO, PhD Thesis, Strasbourg, 2000.
Acknowledgements S. Meza-Aguilar was supported by a Grant from the Mexican Government. C. Demangeat acknowledges the bilateral Alliance program (No. 95039) for partial support and J.A.C. Bland for helpful discussions. The authors would like to thank J.C. Parlebas and M.A. Khan for useful discussions.