Demangeat, C

M'Passi-Mabiala, B

Meza-Aguilar, S

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Available at: http://www.ictp.trieste.it/~pub off IC/2001/84United Nations Educational Scientic and Cultural OrganizationandInternational Atomic Energy AgencyTHE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICSA FERROMAGNETIC GROUND STATE FOR Mn-CoSURFACE ORDERED ALLOY ON Co(001) SUBSTRATEB. M'Passi{MabialaDepartement de Physique, Universite Marien NGouabi,Laboratoire des Materiaux et Energies, BP 69, Brazzaville, CongoandThe Abdus Salam International Centre for Theoretical Physics, Trieste, Italy,S. Meza{AguilarEscuela de Ciencias Fisico Matematicas, Universidad Autonoma de Sinaloa,Bldv. de las Americas y Universitarios, Ciudad Universitaria,Culiacan Sinaloa, CP 80010, MexicoandThe Abdus Salam International Centre for Theoretical Physics, Trieste, ItalyandC. DemangeatInstitut de Physique et Chimie des Materiaux de Strasbourg,23 rue du Loess F-63037 Strasbourg, France.MIRAMARE { TRIESTEJuly 2001Regular Associate of the Abdus Salam ICTP.AbstractRecent Low-energy electron diraction experiments concerning submonolayer Mn coverage onCo/Cu(001) substrates displayed a well-dened Mn0:5Co0:5surface ordered alloy. Through theMagneto-optic Kerr eect and X-ray magnetic circular dichroism a ferromagnetic coupling be-tween Mn and Co was obtained. Ab initio density functional theory within generalized gradientapproximation is able to explain these results.2Since the work of O'Brien and Tonner1,2it is well known that the magnetic moments of theultrathin Mn layers grown on-top on the Co/Cu(001) substrates is coupled ferromagnetically toCo. However, Noguera et al3, using a tight-binding Hamiltonian, were unable to obtain this ferro-magnetic coupling between Mn and Co for a perfect Mn monolayer epitaxially grown on Co(001).Later on both Choi et al4and O'Brien and Tonner5within careful Low-energy electron diraction(LEED), Magneto-optic Kerr eect (MOKE) and X-ray magnetic circular dichroism (XMCD) wereable to conrm the Mn-Co ferromagnetic coupling. The discrepancy between experimental andtheoretical investigations was clearly related to the appearance of a well dened Mn-Co surfaceordered alloy depicted via LEED. Recent Tight-binding Linear-MuÆn-Tin Orbital (TB-LMTO)calculations within the Local Density Approximation (LDA) by Meza et al6have shown that,indeed, the surface ordered Mn0:5Co0:5alloy is more stable than the perfect Mn monolayer onCo(001). Moreover a ferromagnetic conguration was one of the magnetic congurations obtainedwithin this LDA approach. However, this solution was found marginally unstable as compared tothe solution presenting an antiferromagnetic coupling. This discrepancy may originate from theeect of Oxygen on Mn5,7. However, as shown by Yoshiki et al7, the antiferromagnetic couplingbetween Mn and Co is clearly linked to the presence of Oxygen. Without Oxygen, the Mn-Cocoupling is clearly ferromagnetic at odd with the recent results of Meza et al6.From the point of view of its structural and magnetic properties, Mn can be considered asthe most complex of all metallic elements8and simple density functional theory (DFT) is of nouse in this case. Hobbs and Hafner8have investigated all known polymorphs of Mn using thegeneralized spin-density functional theory based on the unconstrained vector-eld description ofthe magnetization density. Also Hoshino et al9have depicted magnetic energy anomalies for Mnimpurities in noble metals. It is therefore clear that a simple LDA approach will be most probablyunable to explain the experimental results. Following the work of Blugel10where it was shownthat the formation energy for the Mn/Cu alloy changes sign when going from LDA to GeneralizedGradient Approximation (GGA), we have used here the GGA approaches of Langreth et al11and Perdew et al12. The supercell used has been described by Meza et al6whereas Izquierdoand Demangeat13have discussed the suitability of the Langreth-Mehl-Hu functional. Thus thedescription of the theoretical model is restricted to the minimum.We have used a scalar-relativistic version of the k-space TB-LMTOmethod14with atomic sphereapproximation. This method is based on the density functional theory15.3In this approach we have rst determinated the lattice parameter for fcc Co bulk by energyminimization of the total energy using dierent functionals, the von Barth-Hedin16(LSDA-vBH),Langreth-Mehl-Hu11(GGA-LMH) and Perdew et al12(GGA-PW91), and the dierent values ob-tained are shown in the Table I. In this work we have used the GGA-PW91 functionals. TheGGA{PW91 is known to reproduce correctly the magnetic properties of Mn as shown by Asadaand Terakura17.The overlayer-surface is modeled using the repeated slab geometry18. We take nine metalliclayers separated by ve layers of empty spheres (cf Fig. 1 of Meza et al6). This is suÆcient toprevent interaction between the slabs19, which is controlled through vanishing dispersion in thedirection perpendicular to the slab, and the vanishing charge in the central layer of the emptyspheres. The calculations are performed using an increasing number of k points, until nal con-vergence is obtained for at least 338 k points in the irreducible Brillouin zone (IBZ). We restrictourselves to two inequivalent atoms per layer.We report here the results of calculations done on the Mn monolayer and the 2D Mn0:5Co0:5surface alloy on fcc Co(001) substrate in the nonmagnetic as well as in the magnetic cases. Wehave calculated the formation energy E (cf. Table IV) following the Blugel formula10:E = EMn Co=Co(001)  1=2(ECo=Co(001)+EMn=Co(001))where EMn Co=Co(001), ECo=Co(001)and EMn=Co(001)are the total energies of the Mn-Co surfacealloy on Co(001), Co(001) slab and Mn monolayer on Co(001) substrate, respectively.For the Mn monolayer on Co(001) the following magnetic congurations have been consideredas input: p(1  1) ", p(1  1) # and c(2  2). The converged congurations obtained (cf. TableII) show that the antiferromagnetic c(2 2) remains in the ground state in agreement with LSDAresults6and in disagreement with experimental results1,2.Calculations done on nonmagnetic Mn monolayer and 2D Mn0:5Co0:5surface alloy on Co(001)have shown that the surface alloy is more stable than the Mn monolayer. A formation energy of -5.86 mRy has been found. Following this trend, which is in agreement with the experimental resultsof Choi et al4, we have investigated the magnetic case of the surface alloy. We have considered thecase of 2D Mn0:5Co0:5surface ordered alloy (1ML{thick) in the surface plane. This has been donein relation with the results of Choi et al4displaying surface alloy for Mn concentrations from 0.3to 0.8 equivalent to ML. Four types of magnetic congurations (Mn#Co#, Mn"Co#, Mn"Co" and4Mn#Co") corresponding to all possible directions of magnetization of Mn and Co surface atoms havebeen considered. Only two congurations (Mn#Co" and Mn"Co") remain after the convergence(Table III), namely the one where the Mn atom is coupled antiferromagneticaly with the Cosurface atom and the other with ferromagnetic coupling as in Meza's work6. The congurationwith ferromagnetic coupling between the Mn surface atoms and the Co atoms is the ground statein agreement with the experimental results4.The formation energy in the magnetic calculations, reported in the Table IV, is in agreementwith the trends found in the nonmagnetic case i.e. a stabilization of the Mn0:5Co0:5conguration.The total energies of all the magnetic congurations reported here are lower than the correspondingnonmagnetic one. However it is worthy to point out that contrary to the results reported withinLDA by Meza et al6where the formation energy decreases when going from nonmagnetic case tothe magnetic one, here, within GGA the opposite is true.We have found, within GGA, that the c(2  2) antiferromagnetic coupling between the Mnsurface atoms for the Mn monolayer on fcc Co(001) remains in the ground state in agreement withMeza et al6theoretical results but in disagreement with the experiments. Total energy obtainedwithin spin{polarisation calculations as a function of the magnetic congurations performed on theMn monolayer and the 2D ordered Mn0:5Co0:5surface alloy on Co(001) using TB{LMTO{ASA inthe GGA{PW91 approximation have shown that, as well as in previous LSDA calculations6, the 2Dordered Mn0:5Co0:5surface ordered alloy is the ground state conguration. A ferromagnetic groundstate is however found within GGA for the 2D ordered Mn0:5Co0:5surface alloy in agreement withexperimental results4.ACKNOWLEDGMENTSB. M'Passi{Mabiala and S. Meza{Aguilar wish to acknowledge the Abdus Salam Interna-tional Centre for Theoretical Physics (ICTP) and Swedish International Development CooperationAgency (SIDA) for the nancial support. Many thanks to J.A.C. Bland who pushes us to get aferromagnetic ground state in agreement with his MOKE results.This work was done within the framework of the Associateship Scheme of the Abdus SalamICTP, Trieste, Italy.5REFERENCES1W. L. O'Brien, and B. P. Tonner, Phys. Rev. B 50, 2963 (1994).2W. L. O'Brien, and B. P. Tonner, Phys. Rev. B 51, 617 (1995).3A. Noguera, S. Bouarab, A. Mokrani, C. Demangeat and H. Dreysse, J. Magn. Magn. Mater.156, 21 (1996).4B.-Ch. Choi, J. P. Bode, and J. A. C. Bland, Phys. Rev. B 58, 5166 (1998); B.-Ch. Choi, J. P.Bode, and J. A. C. Bland, J. Appl. Phys. 85, 5063 (1999).5W. L. O'Brien, and B. P. Tonner, Phys. Rev. B 58, 3191 (1998).6S. Meza Aguilar, O. Elmouhsinne, H. Dreysse, C. Demangeat, Phys. Rev. B 63, 64421 (2001).7Yoshiki Yonamoto, Toshihiko Yokoyama, Kenta Amemiya, Daiju Matsumura, and ToshiakiOhta, Phys. Rev. B 63, 214406 (2001).8D. Hobbs and J. Hafner, J. Phys. Condens. Matter 13, L681 (2001).9T. Hoshino, R. Zeller, P. H. Dederichs and M. Weinert, Europhys. Lett. 24, 495 (1993).10S. Blugel, Appl. Phys. A Mater. Sci. Process. A63 595 (1996).11D. C. Langreth and M. J. Mehl, Phys. Rev Lett. 47, 446 (1981); C.D. Hu and D.C. Langreth,Phys. Scr. 32, 391 (1985).12J.P. Perdew, Y. Wang, and E. Engel, Phys. Rev. Lett. 66, 508 (1991).13J. Izquierdo and C. Demangeat, Phys. Rev. B 62, 12287 (2000).14O. K. Andersen and O. Jepsen, Phys. Rev. Lett 53, 2571 (1984); O.K. Andersen, Z. Pawlowska,and O. Jepsen, Phys. Rev. B 34, 5253 (1986). The standard TB-LMTO-ASA code (version 47)developed by O.K. Andersen et al at M.P.I. Stuttgart, Germany, was used.15P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964); W. Kohn and L. J. Sham, Phys.Rev. 140, A1133 (1965).16U. von Barth and L. Hedin, J. Phys. C 5 1629 (1972).17T. Asada, K. Terakura, Phys. Rev. B 47, 15992 (1993).18M. A. Khan, J. Phys. Soc. Jpn. 62, 1682 (1993).19O. Elmouhssine, Ph.D Thesis, Strasbourg, France, 1998.6TABLE I: Lattice parameter (in a:u:) and magnetic moments of Co atom in (B) for the dierentsapproximations.Approximation Lattice magneticparameter momentLSDA-vBH 6.54 1.56GGA-LMH 6.64 1.64GGA-PW91 6.81 1.69TABLE II: Magnetic moments (in B) for Mn/Co(001) and dierences of total energies per cell(in mRy) with the Perdew-Wang 91 approximation. The ground state is indicated by 0Input c(22) p(11)" p(11)#Energy 0.0 46 159Atom Moments Moments MomentsMnb 3.22 3.53 -3.26Mna -3.51 3.53 -3.26Co4b 1.15 1.55 1.17Co4a 1.14 1.55 1.17Co3b 1.75 1.77 1.74Co3a 1.79 1.77 1.74Co2b 1.71 1.70 1.71Co2a 1.71 1.70 1.71Co1b 1.71 1.70 1.70Co1a 1.71 1.70 1.707TABLE III: Magnetic moments (in B) for Mn-Co/Co(001) and dierence of total energies per cell(in mRy) with GGA-PW-91 approximation. The ground state is indicated by 0.Input Mn#Co# Mn"Co#Mn#Co" Mn"Co"Energy 36 0Atom Moments MomentsMn -3.79 3.67Co5 0.82 1.73Co4b 1.33 1.59Co4a 1.33 1.59Co3b 1.77 1.76Co3a 1.71 1.73Co2b 1.71 1.70Co2a 1.71 1.70Co1b 1.70 1.70Co1a 1.71 1.70TABLE IV: Formation energies in nonmagnetic and magnetic cases with the two dierent approx-imations (in mRy).Approximation Formation FormationEnergy Energynonmagnetic magneticLSDA6-20.00 -5.00GGA-PW-91 -5.86 -9.778

A ferromagnetic ground state for Mn-Co surface ordered alloy on Co(001) substrate

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