hcp surface: Density functional calculations

Surface Science 642 (2015) 39–44

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Magnetism of Mn single atom and dimer on Co(0001) hcp surface: Density functional calculations J.J. Molina-Duarte a, F.C. Delgado-Nieblas a, R.E. Félix-Medina a, M.A. Leyva-Lucero a, S. Meza-Aguilar a,⁎, C. Demangeat b,⁎ a b

Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Sinaloa, Blvd. de las Américas y Universitarios, Ciudad Universitaria, Culiacán Sinaloa, CP 80010, Mexico UFR de Physique et Ingénierie, 3, rue de l’Université, 67000 Strasbourg, France

a r t i c l e

i n f o

Article history: Received 18 March 2015 Accepted 3 August 2015 Available online 9 August 2015 Keywords: Manganese Cobalt Magnetic surface Density functional calculations Magnetic interface

a b s t r a c t Magnetism of Mn single atom and dimer on Co(0001) hcp surface is studied on the basis of density functional theory using Quantum Espresso code. The most stable geometry takes place when Mn is adsorbed in the most highly coordinated sites. Mn single atom couples ferromagnetically to the Co atoms and shows a high magnetic moment of 4.53 μB. Mn dimer also couples ferromagnetically to the Co atoms, shows a mean atomic magnetic moment of 4.45 μB, and increases its interatomic distance to minimize its energy. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Mn is really an element worth studying. It can be considered as one of the most complex of all 3d transition metal elements. Mn solid crystalline exists in at least five allotropic forms depending on its temperature and pressure [1]. If Mn bulk shows such a complicated behavior, it is rather natural to expect that in low-dimensional systems, Mn presents a more involved behavior because of the loss of spacial periodicity typical of this kind of systems. This difficulty is already evident for the Mn dimer, for which a theoretical discrepancy exists about whether it couples ferromagnetically[2–4] or antiferromagnetically[5]. An even more challenging behavior is to be expected from Mn-based bimetallic low-dimensional systems. The study of magnetic bimetallic low-dimensional systems represents a true challenge from a fundamental point of view because of the complexity in the behavior of their electronic, structural, and magnetic properties. Such complexity in the physical phenomena arises from the reciprocal interactions of the two components which can be themselves immersed in a very complicated local atomic environment. In particular, Mn nanostructures deposited on nonmagnetic [6–11] or magnetic[12–14] substrates have strongly attracted the attention of the researchers in the field, due to their unusual properties which are at the same time fascinating for scientists and highly relevant for technologists. Regarding Mn nanostructures deposited on nonmagnetic substrates, a very recent theoretical investigation of the adsorption of Mn single ⁎ Corresponding authors. E-mail address: [email protected] (S. Meza-Aguilar).

http://dx.doi.org/10.1016/j.susc.2015.08.002 0039-6028/© 2015 Elsevier B.V. All rights reserved.

atoms and dimers on the Cu(111), Ag(111), and Au(111) surfaces within the framework of the density functional theory has been reported by Francisco Muñoz et al [6]. They have found that the most stable configuration for each one of the three noble metals corresponds to the Mn atom chemisorbed in threefold coordinated sites. For the dimer, they have found that the lowest-energy configuration corresponds to both atoms chemisorbed in threefold coordinated sites, but with different local symmetry. They also found that the magnetic state with the lowest energy corresponds to the antiferromagnetic arrangement of Mn atoms with individual magnetic moments close to 5 μB. Regarding Mn nanostructures deposited on magnetic substrates, Lounis et al [12, 13] have studied the magnetic properties of Mn clusters deposited on Ni(001) and Ni(111) surfaces. They have identified two sources of noncollinear magnetism: (i) the competition between the coupling in the cluster and with the substrate, as in the case of the Mn dimer on Ni(001), and (ii) the triangular geometry of the substrate together with the intracluster interactions, as in the case of the Mn trimer on Ni(111). Additionally, Lounis et al [14] have found for Mn nanochains on Ni(001) that even-numbered nanochains always exhibit noncollinear magnetism, while odd-numbered wires can lead to a collinear ferromagnetic ground state. The study of magnetic properties of molecules adsorbed to surfaces is interesting not only from the fundamental point of view but from their potential technological applications, for example, magnetic recording media and spintronic devices. Despite the existence of several works on the magnetic properties of clusters deposited on magnetic or nonmagnetic substrates, to our knowledge, there is no any report about magnetism of Mn clusters deposited on Co substrates. Given the

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J.J. Molina-Duarte et al. / Surface Science 642 (2015) 39–44

importance of Co as one of the four ferromagnetic elementary metals, we think that such a study should be performed. In this paper, we intend to start addressing that issue by searching for answers to the following questions: (1) Which adsorption site does Mn single atom like to be located when it is deposited on Co substrates? (2) What kind of coupling to the Co substrate does Mn single atom prefer? (3) How are the magnetic states modified when we add a second Mn atom to form a dimer? The answers to these questions could provide a basis for understanding the magnetic behavior of larger Mn clusters on Co substrates. We have investigated these issues by performing density functional calculations for the magnetic, structural, and electronic properties of the Mn single and dimer atoms deposited on Co(0001) hcp substrate including total atomic relaxation. We have considered several adsorption sites with their corresponding magnetic states. We report the total energy differences with respect to the lowest-energy state, the atomic magnetic moments, as well as the atomic positions for the Mn and Co atoms. This paper is organized as follows. In Section 2, the theoretical model utilized for the calculations is briefly explained. In Section 3, the results obtained for the magnetic, structural, and electronic properties of the various systems are presented and discussed. Finally, in Section 4, we summarize the main conclusions.

(a) HCP Site

(b) FCC Site

(c) Bridge Site

(d) Atop Site

2. Computational details All calculations in the present paper have been performed by applying Quantum Espresso code [15], which is based on density functional theory [16], within the generalized gradient approximation of Perdew–Burke– Ernzerhof [17]. The pseudopotentials utilized are taken from Quantum Espresso Distribution [18]. These pseudopotentials are generated by using the Vanderbilt code [19]. The Co pseudopotential file is obtained by using the electronic configuration [Ar] 3d7 4 s2 with scalar relativistic calculations, exchange-correlation of Perdew–Burke–Ernzerhof [17], nonlinear core-corrections, semicore state d in valence, and ultrasoft pseudopotential of Rabe–Rappe–Kaxiras–Joannopoulos [20]. The Mn pseudopotential file is obtained by using the electronic configuration [Ar] 3d5 4 s2 with scalar relativistic calculations, exchange-correlation of Perdew–Burke–Ernzerhof [17], semicore states s and p in valence, and ultrasoft pseudopotential of Vanderbilt [19]. The unit cell used for the Mn single atom and dimer consisted of a slab with 5 planes of Co(0001) hcp with lattice parameters a = 2.51 Å and c = 1.622a with 12 atoms per plane with the Mn atom and dimer being deposited at each side of the slab [that is, we used a unit cell with p(3 × 4)], and seven planes of empty space to prevent the interaction between slabs. The lattice parameters for the unit cell are 7.53 × 15.21 × 26.46 Å. The mesh 8 × 8 × 1 is the k-points uniform mesh in the Brillouin zone, by Monkhorst and Pack. A cutoff energy of 35 Ry has been used for the plane waves expansion of the pseudowave functions (560 Ry for the charge density and potential). The criterion for the convergence for the total energy is that the differences of total energies are less than 1 × 10−8 Ryd/Cell (2.19 × 10−6 meV/(unit cell atom)). Finally, total relaxation has been considered until the total absolute force has been less than 0.001 Ryd/a.u. 3. Results obtained 3.1. Mn single atom on Co(0001) hcp surface In this subsection, we present and discuss the results for the magnetic, structural, and electronic properties of Mn single atom deposited on the Co(0001) hcp substrate. Fig. 1 shows a top view of the Mn single atom on Co(0001) hcp surface. There, we present four adsorption sites: (a) hcp site, (b) fcc site, (c) bridge site, and (d) atop site. The blue line represents the unit cell. The blue circles represent the Mn adatoms, the yellow circles represent the first nearest neighbors of the Mn adatom (located at the surface), the brown circles represent the

Fig. 1. Top view for the Mn single atom on Co(0001) hcp surface. Here we present the adsorption sites: (a) hcp site, (b) fcc site, (c) bridge site, and (d) atop site. The blue line represents the unit cell. The blue circles represent the Mn adatom, the yellow circles represent the first nearest neighbors of the Mn adatom (located at the surface), the brown circles represent the second nearest neighbors of the Mn adatom (located at the surface), the green circles represent the subsurface atoms, and blue zyan circles represent the surface atoms.

second nearest neighbors of the Mn adatom (located at the surface), the green circles represent the subsurface atoms, and the blue zyan circles represent the surface atoms. Table 1 reports the magnetic and structural properties of Mn single atom deposited on the Co(0001) hcp substrate. The differences of total energies (ΔE in meV/atom) with respect to the lowest energy state as well as the Mn and Co magnetic moments (in μB) in accordance with the Loewdin population analysis are given for each one of the adsorptions sites considered in this work (see Fig. 1) and their corresponding states: ferromagnetic and antiferromagnetic. In all cases, we have taken into account fully relaxing effects. The Co1 and Co2 rows correspond, respectively, to the first and second neighbors of Mn. Note that the information corresponding to the atop site is not shown in Table 1. This is because, as a consequence of the structural relaxation, the Mn

Table 1 Magnetic and structural properties of Mn single atom deposited on the Co(0001) hcp substrate. The differences of total energies (ΔE in meV/atom) with respect to the lowest energy state as well as the Mn and Co magnetic moments (in μB) in accordance with the Loewdin population analysis are given for each one of the adsorptions sites considered in this work (see Fig. 1) and their corresponding states: ferromagnetic and antiferromagnetic. In all cases, we have taken into account fully relaxing effects. The Co1 and Co2 rows correspond, respectively, to the first and second neighbors of Mn. I

II

III

IV

V

VI

VII

Site/ State

hcp/ FM

hcp/ AF

fcc/ FM

fcc/ AF

bridge/ FM

bridge/ AF

ΔE Mn Co1 Co2

0.57 4.50 1.63 1.79

5.53 −4.84 1.43 1.79

0.00 4.53 1.65 1.79

6.43 −4.89 1.46 1.79

0.61 4.53 1.61 1.73

6.75 −4.88 1.37 1.68

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atom moved from the atop site to the fcc site. Specifically, when initially in the ferromagnetic or antiferromagnetic states of the atop site, Mn atom moved to the ferromagnetic or antiferromagnetic states of the fcc site, respectively. Note that these displacements go from the lowest-coordination site (the atop site) to the highest-coordination site (fcc site). The atop site is the only energetically unstable site that we found. According to the results presented in Table 1, we can observe that the most stable geometries take place when the Mn single atom is adsorbed in the most highly coordinated sites. There is a correspondence between the order of energy preferences and the coordination number for each adsorption site of the Mn atom through the number of bonding for each of them: three for fcc and hcp sites, two for the bridge site, and only one for the atop site. Note that for all adsorption sites, the ferromagnetic state is the preferred one. Concretely, we have obtained that the adsorption site energetically preferred is the fcc site in the ferromagnetic state [ΔEFM fcc = 0.00], followed by the hcp site in the ferromagnetic state to which corresponds a total energy difference equal to ΔEFM hcp = 0.57 meV/atom, and by the bridge site in the ferromagnetic state with a total energy difference equal to ΔEFM bridge = 0.61 meV/ atom. Then there are the antiferromagnetic states, which belong in order of increasing energy, to the hcp site (ΔEAF hcp = 5.53 meV/atom), AF the fcc site (ΔEAF fcc = 6.43 meV/atom), and the bridge site (ΔEbridge = 6.75 meV/atom). Finally, the differences in total energies for nonmagnetic states (not shown in Table 1) are the following: hcp site (ΔENM hcp = 336.50 meV/atom), fcc site (ΔENM fcc = 341.02 meV/atom), and bridge site (ΔENM bridge = 341.04 meV/atom). We have obtained high magnetic moment values for the Mn atoms. In fact, the magnetic moments of the Mn single atoms deposited on Co(0001) hcp surfaces are larger than the magnetic moments of Mn atoms deposited on Ni(111) fcc as reported by Lounis et al. They reported 4.17 μB and −4.25 μB for the magnetic and antiferromagnetic, respectively. In the case of ferromagnetic coupling, we have obtained the FM following magnetic moments: μFM fcc = 4.53μB, for the fcc site; μhcp = = 4.53μ , for the bridge site. In the 4.50μB, for the hcp site; and μFM bridge B case of antiferromagnetic coupling, we have obtained in order of inAF creasing energy: μAF hcp = −4.84μB, for the hcp site; μfcc = −4.89μB, for = −4.88μ , for the bridge site. the fcc site; and μAF bridge B We can also observe that the magnetization of some of the Co atoms in the most superficial substrate layer is strongly affected by the hybridization with the Mn atom. This is particularly remarkable for the Co atoms that are first neighbors of Mn when the coupling is antiferromagAF netic. So we have μAF hcp(Co1) = 1.43μB and μfcc(Co1) = 1.46μB for the Co atoms which are first neighbors of Mn at the hcp and fcc sites, respectively; and μAF bridge(Co1) = 1.37μB for the Co atoms that are first neighbors of Mn at the bridge site. Regarding our results for the structural properties of the Mn single atom deposited on the Co(0001) hcp substrate, we point out that in the Co crystalline solid, the interlayer distance is equal to d = 2.03 Å. But as a consequence of the reduction of the dimensionality, the most superficial layer comes closer to the subsurface layer. Besides, not all the Co atoms belonging to a given layer are exactly at the same distance as in the Co bulk layers. To compare the role of the geometry of Co substrate, we have calculated the magnetic, structural, and electronic properties of Mn single atom deposited on the Co (001) fcc substrate for each one of the three adsorption sites here considered and the corresponding ferromagnetic and antiferromagnetic states. Fig. 2 shows a surface top view for the Mn adatom on Co(001) fcc. Here, we present the adsorption sites: (a) fcc site, (b) bridge site, and (c) atop site. The blue line represents the unit cell. The blue circles represent the Mn adatom, the yellow circles represent the first nearest neighbors of the Mn adatom (located at the surface), the brown circles represent the second nearest neighbors of the Mn adatom (located at the surface), the green circles represent the subsurface atoms, and blue zyan circles represent the surface atoms. Similar effects to those found for the Mn single atoms deposited

41

(a) FCC Site

(b) Bridge Site

(c) Atop Site Fig. 2. Surface top view for the Mn adatom on Co(001) fcc. Here we present the adsorption sites (a) fcc site, (b) bridge site, and (c) atop site. The blue line represents the unit cell. The blue circles represent the Mn adatom, the yellow circles represent the first nearest neighbors of the Mn adatom (located at the surface), the brown circles represent the second nearest neighbors of the Mn adatom (located at the surface), the green circles represent the subsurface atoms, and blue zyan circles represent the surface atoms.

on the Co(0001) hcp substrate are obtained here: the ferromagnetic coupling among the Mn atom and the Co substrate atoms, the energy preference for the most highly coordinated sites, the strong hybridization among the Mn atom and Co atoms that belong to the most superficial layer. This last feature is particularly remarkable for the first neighbor of the Mn atom in the atop site of the Co(001) fcc surface. In the following, we describe the quantitative aspects of these effects. Table 2 reports the magnetic and structural properties of Mn adatom deposited on the Co(001) fcc substrate. The differences of total energies ΔE (in meV/atom) with respect to the lowest energy state as well as the Mn and Co magnetic moments (in μB) in accordance with the Loewdin population analysis are given for each one of the adsorptions sites considered in this work (see Fig. 2) and their corresponding states: ferromagnetic and antiferromagnetic. In all cases, we have taken into account fully relaxing effects. The Co1 and Co2 rows correspond, respectively, to the first and second neighbors of Mn. According to the results

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Table 2 Magnetic and structural properties of Mn adatom deposited on the Co(001) fcc substrate. The differences of total energies (ΔE in meV/atom) with respect to the lowest energy state as well as the Mn and Co magnetic moments (in μB) in accordance with the Loewdin population analysis are given for each one of the adsorptions sites considered in this work (see Fig. 2) and their corresponding states: ferromagnetic and antiferromagnetic. In all cases, we have taken into account fully relaxing effects. The Co1 and Co2 rows correspond, respectively, to the first and second neighbors of Mn. I

II

III

IV

V

VI

VII

Site/ State

fcc/ FM

fcc/ AF

bridge/ FM

bridge/ AF

atop/ FM

atop/ AF

ΔE Mn Co1 Co2

0.00 4.30 1.75 1.90

7.09 −4.89 1.64 1.92

21.75 4.50 1.65 1.88

18.2 −4.92 1.40 1.89

26.26 4.75 1.50 1.87

29.08 −4.99 0.99 1.88

presented there, we can observe that the most stable geometry takes place when the Mn single atom is adsorbed in the most highly coordinated sites, and the abovementioned correspondence between this order of energy preferences and the coordination number for each adsorption site of the Mn atom through the number of bondings for each of them, being for this substrate: two for the most stable sites (fcc and bridge sites) and only one for the atop site. Note that for all the adsorption sites, the ferromagnetic state is preferred, with the exception of the bridge site. Concretely, the adsorption site energetically preferred is the fcc site in its ferromagnetic state [ΔEFM fcc = 0.00], followed by its antiferromagnetic state to which corresponds a total energy difference equal to ΔEAF fcc = 7.09 meV/atom. Then, it follows the bridge site in the antiferromagnetic and ferromagnetic states with a total energy diference equal FM to ΔEAF bridge = 18.2 meV/atom and ΔEbrigde = 21.75 meV/atom, respectively. Finally, there are the ferromagnetic and antiferromagnetic states for the atop sites with total energy differences equal to ΔEFM atop = 26.26 meV/atom and ΔEEF atop = 29.08 meV/atom, respectively. In summary, the Mn atom will prefer to be coupled antiferromagnetically to the Co(001) fcc substrate atoms at the fcc site before being located at the bridge site, and it will prefer to be coupled antiferromagnetically to the Co substrate atoms before being located at the atop site. This situation does not occur for Mn single atom deposited on the Co(0001) hcp substrate.

Although not so high like the Mn magnetic moments obtained for the Mn single atoms deposited on the Co(0001) hcp substrate because of the higher coordination of the Co(001) fcc substrate, here we also have obtained high magnetic moment values for the Mn atom. In fact, the magnetic moments of Mn single atoms deposited on Co(001) fcc are larger than the magnetic moments of Mn atoms deposited on Ni(001) fcc reported by Lounis et al [12]. They reported 4.09 μB, for the ferromagnetic coupling. In the case of ferromagnetic coupling, we have obtained the following Mn atomic magnetic moment values: FM FM μ FM fcc (Mn) = + 4.30μ B , μ bridge (Mn) = + 4.50μ B , and μ atop (Mn) = + 4.75μ B for the fcc, bridge, and atop sites, respectively. We can also compare our results with the experimental results of O'Brien and Tonner [21] and Choi et al [22]: they have found ferromagnetic coupling between Mn and Co atoms when Mn is grown with a thickness equal to 0.5 monolayer (ML) on Co(001) fcc substrate. Later, these experimental results were corroborated theoretically by M'Passi-Mabiala et al [23]. The strong hybridization among the Mn atom and the Co atoms in the most superficial layer also occurs here. The most remarkable case is for the atop site for which we have for the only Co atom that is first neighbor AF of Mn: μFM atop(Co1) = 1.50μB in the ferromagnetic state and μatop(Co1) = 0.99μB in the antiferromagnetic state. Fig. 3 (top) shows the d-component of the local density of states (LDOS) for the Mn adatom on Co(0001) hcp substrate. We present the LDOS for (a) HCP site, (b) FCC site, and (c) Bridge site, and Fig. 3 (bottom) shows the LDOS for the Mn adatom on Co(001) fcc substrate. We present the LDOS for (d) FCC site, (e) Bridge site, and (f) atop site. In both cases, the LDOS is the Mn adatom and Co nearest neighbors. The black continuous (dashed) line is for the Mn adatom spin up (down) and the red continuous (dashed) line is for Co spin up (down). The green line represents the Fermi level. The magnetic moment is calculated by Z μ¼

EF 

−∞

 ρ↑ ðEÞ−ρ↓ ðEÞ dE

ð1Þ

In Fig. 3, (a), (b), and (c) look very similar because of the similarity of the local atomic environment. In contrast, we can easily note that the value for the maximum of Mn local density of states increases from (d) to (f), that is, as the coordination number of the Mn atom

States/eV/Atom

6 4 2 0 -2 -4

(a) HCP Site

(b) FCC Site

(c) Bridge Site

(d) FCC Site

(e) Bridge Site

(f) Atop Site

States/eV/Atom

-6 6 4 2 0 -2 -4 -6 -6

-4

-2 0 2 E - EF (eV)

-6

-4

-2 0 2 E - EF (eV)

-6

-4

-2 0 2 E - EF (eV)

4

Fig. 3. (Top) The d-component of the local density of states (LDOS) for the Mn adatom on Co(0001) hcp substrate. We present the LDOS for (a) HCP site, (b) FCC site, and (c) bridge site. (Bottom) The LDOS for the Mn adatom on Co(001) fcc substrate. We present the LDOS for (d) FCC site, (e) bridge site, and (f) atop site. In both cases, the LDOS is the Mn adatom and Co nearest neighbors. The black continuous (dashed) line is for the Mn adatom spin up (down) and the red continuous (dashed) line is for Co spin up (down). The green line represents the Fermi level.

J.J. Molina-Duarte et al. / Surface Science 642 (2015) 39–44

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diminishes. In particular for the atop site (c), we can observe the coincidence about E − EF ≈ −3eV of the maximum in the Mn local density of states and the minimum of Co local density of states, which explains the high Mn magnetic moment (+4.75 μB) as well as the remarkable reduction of the Co magnetic moment (+1.50 μB) for this adsorption site. This reduction is less remarkable in the cases (d) and (e) because the number of Co atoms that are nearest neighbors to the Mn atom is greater, and consequently, in the transfer of electrons, there are more Co atoms involved.

3.2. Mn dimer atoms on Co(0001) hcp substrate

(a) HCP−HCP

(b) FCC−FCC

(c) HCP−FCC Fig. 4. Surface top view for the Mn dimer (MnA and MnB) at adsorption sites (a) hcp–hcp, (b) fcc–fcc, and (c) hcp–fcc sites on Co(0001) substrate. The blue line represents the unit cell. The blue circles represent the Mn atoms, the yellow circles represent the first nearest neighbors of the Mn dimer (Co1, located at the surface), the brown circles represent the second nearest neighbors of the Mn dimer (Co2, located at the surface), the pink circles represent the third nearest neighbors of the Mn dimer (Co3, located at the surface), the green circles represent the Co subsurface atoms, and blue zyan circles represent the Co surface atoms.

The results that we have presented and discussed in the previous subsection show that the Mn single atom deposited on the Co substrates prefers to be adsorbed in the most highly coordinated sites and coupled ferromagnetically to the Co atoms. But, what happens when we add a second Mn atom to form a dimer? More specifically, how are the magnetic states modified when we also have to take into account the interaction between two Mn atoms? To answer this question, we have calculated the magnetic properties of Mn dimers deposited on the Co(0001) hcp substrate. Fig. 4 shows a surface top view for the Mn dimer (MnA and MnB) at adsorption sites (a) hcp–hcp, (b) fcc–fcc, and (c) hcp–fcc sites on Co(0001) substrate. The blue line represents the unit cell. The blue circles represent the Mn atoms, the yellow circle represents the first nearest neighbors of the Mn dimer (Co1, located at the surface), the brown circles represent the second nearest neighbors of the Mn dimer (Co2, located at the surface), the pink circles represent the third nearest neighbors of the Mn dimer (Co3, located at the surface), the green circles represent the Co subsurface atoms, and blue zyan circles represent the Co surface atoms. From now on, we follow the nomenclature used by Lounis et al [14] to describe the possible Mn dimer magnetic states, namely, ferromagnetic (FM), for the moments of both Mn atoms pointing parallel to the Co substrate moments; antiferromagnetic (AF), for the moments of both Mn atoms pointing antiparallel to the Co substrate magnetic moments; and ferrimagnetic (FERRI), for the magnetic moment of one Mn atom pointing parallel to the Co substrate magnetic moments and the magnetic moment of the other Mn atom pointing antiparallel to the Co substrate magnetic moments. Besides the magnetic dimer state, we have specified the sites of the individual Mn atoms as well as the directions of their magnetic moments. So, for example, FERRI (hcp↓–fcc↑) means that the Mn dimer magnetic state is ferrimagnetic, with the Mn atom at hcp site coupled antiferromagnetically to the Co substrate and the other Mn atom at fcc site coupled ferromagnetically to the Co substrate. Table 3 shows the HCP, FCC, and HCP–FCC configurations of Mn dimer deposited on Co(0001) hcp substrate with the magnetic configurations ↑ ↑, ↑↓, and ↓↓. We report the differences of total energy (ΔE in meV/atom) with respect to the lowest energy state and the Mn and Co magnetic

Table 3 HCP, FCC, and HCP–FCC configurations of Mn dimer deposited on Co(0001) hcp substrate with the magnetic configurations ↑↑, ↑↓, and ↓↓. We report the differences of total energy (ΔE in meV/atom) with respect to the lowest energy state and the Mn and Co magnetic moments (in μB) in accordance with the Loewdin population analysis. The Co1, Co2, and Co3 rows represent, respectively, the first, second, and third nearest neighbors for the Mn dimer in the surface plane. HCP

FCC

HCP–FCC

↑↑

↑↓

↓↓

↑↑

↑↓

↓↓

↑↑

↑↓

↓↑

↓↓

ΔE MnA MnB Co1 Co2

1.51 4.42 4.42 1.56 1.61

13.39 −4.73 −4.73 1.10 1.38

0.79 4.45 4.45 1.59 1.61

0.0 4.43 4.46 1.55 1.63

3.08 4.48 −4.74 1.30 1.47

4.13 −4.77 4.44 1.29 1.64

1.66

1.48

1.68

4.90 4.46 −4.78 1.42 1.63 1.44 1.67 1.50

15.03 −4.76 −4.76 1.18 1.39

Co3

4.53 4.43 −4.47 1.37 1.62 1.43 1.65 1.48

1.51

1.65

1.66

1.50 1.49

12.74 −4.73 −4.77 0.97 1.45 1.46 1.48

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moments (in μB) in accordance with the Loewdin population analysis. The Co1, Co2, and Co3 rows represent, respectively, the first, second, and third nearest neighbors for the Mn dimer in the surface plane. These results can be classified in three groups of magnetic states according to their stability. In the first group, we have the ferromagnetic states: FM (hcp↑–fcc↑) with ΔE = 0.00 meV/atom, FM (fcc↑–fcc↑) with ΔE = 0.79 meV/atom, and FM (hcp↑–hcp↑) with ΔE = 1.51 meV/atom. In the second group, we have the ferrimagnetic states in the following order: FERRI (hcp↑–fcc↓) with ΔE = 3.08 meV/atom, FERRI (hcp↓–fcc↑) with ΔE = 4. 13 meV/atom, FERRI (hcp↑–hcp↓) with ΔE = 4.53 meV/atom, and FERRI (fcc↑–fcc↓) with ΔE = 4.90 meV/atom. Finally, in the third group, we have the antiferromagnetic states: AF (hcp↓–fcc↓) with ΔE = 12.74 meV/atom, AF (hcp↓–hcp↓) with ΔE = 13.39 meV/atom, and AF (fcc↓–fcc↓) with ΔE = 15.03 meV/atom. The Mn magnetic moment values for the dimers are high, although, naturally, not so high as the magnetic moments corresponding to the Mn single adatoms. For the ferromagnetic states, we have in order of increasing energy: 4.43 μB and 4.46μB for FM (hcp↑–fcc↑); 4.45 μB and 4.45 μB for FM (fcc↑–fcc↑), and 4.42 μB, and 4.42 μB for FM (hcp↑–hcp↑). We can also observe that the magnetization of some of the Co atoms in the most superficial substrate layer are strongly affected by the hybridization with the Mn atoms particularly in the cases of ferrimagnetic and antiferromagnetic states, this is when at least one of the Mn atom couples antiferromagnetically to the Co substrate atoms. So, for example, the magnetic moment values of Co atoms are 1.37 μB for the FERRI (hcp↑–hcp↓); 1.10 μB for the AF (hcp↓–hcp↓)(hcp↑–hcp↑); 1.42 μB for the FERRI (fcc↑– fcc↓); 1.18 μB for the AF (fcc↓–fcc↓); 1.30 μB for the FERRI (hcp↑–fcc↓); 1.29 μB for the FERRI(hcp↓–fcc↑); and 0.97 μB (the most remarkable case) for the AF (hcp↓–fcc↓). Regarding the structural properties, we make note that to minimize their energies, the interatomic Mn distances are significantly modified. Thus, when both Mn atoms are deposited at hcp sites with an initial Mn interatomic distance DI = 2.51 Å, we get the following final Mn interatomic distances DF = 2.91, DF = 2.76, and DF = 2.93 for the ferromagnetic, ferrimagnetic, and antiferromagnetic states, respectively. When both Mn atoms are deposited at fcc sites with also DI = 2.51 Å, we get DF = 2.90, DF = 2.77, and DF = 2.95 for the ferromagnetic, ferrimagnetic, and antiferromagnetic states, respectively. And when the Mn dimer is deposited at mixed sites with DI = 2.89 Å, we get DF = 2.98, DF = 2.81, DF = 2.80,and DF = 2.98 for the ferromagnetic, ferrimagnetic (hcp↑–fcc↓), ferrimagnetic (hcp↓–fcc↑), and antiferromagnetic states, respectively. From this, we can see that the most remarkable change in the Mn interatomic distance results for the ferromagnetic and for the antiferromagnetic states. 4. Conclusions In the present paper, we have studied Mn single atoms and dimers deposited on Co(0001) hcp substrates using Quantum Espresso code, which is based on the density functional theory. For Mn single atom deposited on the Co(0001) hcp substrate, we have studied four adsorption sites: hcp, fcc, bridge, and atop site. For each one of those sites, we have considered two magnetic states: ferromagnetic and antiferromagnetic states. For Mn dimer on the Co(0001) hcp surface, we have considered three magnetic configurations: ferromagnetic, antiferromagnetic, and ferrimagnetic. Our main conclusions are the following:

(i) Mn single atom couples ferromagnetically to the Co substrates; (ii) the most stable geometry takes place when Mn atom is adsorbed in the most highly coordinate sites; (iii) the Mn atomic magnetic moments are high: +4.53 μB and +4.30 for the lowest-energy states corresponding to the Co(0001) hcp and Co(001) fcc substrates, respectively; (iv) for Mn dimer deposited on Co(0001) hcp substrate, the lowest energy state is ferromagnetic with an increased Mn interatomic distance from 2.89 Å to 2.98 Å with Mn magnetic moments of +4.43 μB and +4.46 μB. Acknowledgments J.J. Molina-Duarte and F.C. Delgado-Nieblas wish to acknowledge CONACyT-México for the financial support. We acknowledge the support by the Universidad Autónoma de Sinaloa and SEP through Project PIFI 2005-25-06 UAS-ECFM, Project UAS-PROFAPI 2009/057, Project UAS-PROFAPI 2009/097, Project UAS-PROFAPI 2012/108 and CONACyT Project Number 99946. We also acknowledge the computational resources provided by the Facultad de Ciencias Físico- Matemáticas de la Universidad Autónoma de Sinaloa, México. Calculations in this work have been done using the Quantum Espresso code [15]. References [1] D. Hobbs, J. Hafner, D. Spisák, Phys. Rev. B 68 (2003) 014407; J. Hafner, D. Hobbs, Phys. Rev. B 68 (2003) 014408; J. Hafner, D. Spisák, Phys. Rev. B 72 (2005) 144420. [2] P. Bobadova-Parvanova, K.A. Jackson, S. Srinivas, M. Horoi, J. Chem. Phys. 122 (2005) 014310. [3] R.C. Longo, E.G. Noya, L.J. Gallego, Phys. Rev. B 72 (2005) 174409. [4] R.C. Longo, M.M.G. Alemany, J. Ferrer, A. Vega, L.J. Gallego, J. Chem. Phys. 128 (2008) 1143. [5] J. Meja-López, A.H. Romero, M.E. Garca, J.L. Morán-López, Phys. Rev. B 74 (2006) 140405. [6] Francisco Muñoz, Aldo H. Romero, José Meja-López, J.L. Morán-López, Phys. Rev. B 85 (2012) 115417. [7] Ph. Kurz, G. Bihlmayer, K. Hirai, S. Blügel, Phys. Rev. Lett. 86 (2001) 1106. [8] G. Bihlmayer, Ph. Kurz, S. Blügel, Phys. Rev. B 62 (2000) 4726. [9] W. Wulfhekel, C.L. Gao, J. Phys. Condens. Matter 22 (2010) 084021. [10] M.S. Ribeiro, G.B. Corrêa Jr., A. Bergman, L. Nordström, O. Eriksson, A.B. Klautau, Phys. Rev. B 83 (2011) 014406. [11] N.N. Negulyaev, V.S. Stepanyuk, W. Hergert, J. Kirschner, Phys. Rev. Lett. 106 (2011) 037202. [12] S. Lounis, Ph. Mavropoulos, P.H. Dederichs, S. Blügel, Phys. Rev. B 72 (2005) 224437. [13] S. Lounis, Phivos Mavropoulos, Rudolf Zeller, Peter H. Dederichs, Stefan Blügel, Phys. Rev. B 75 (2007) 174436. [14] S. Lounis, Peter H. Dederichs, Stefan Blügel, Phys. Rev. Lett. 101 (2008) 107204. [15] Paolo Giannozzi, Stefano Baroni, Nicola Bonini, Matteo Calandra, Roberto Car, Carlo Cavazzoni, Davide Ceresoli, Guido L. Chiarotti, Matteo Cococcioni, Ismaila Dabo, Andrea Dal Corso, Stefano de Gironcoli, Ralph Gebauer, Uwe Gerstmann, Christos Gougoussis, Anton Kokalj, Michele Lazzeri, Layla Martin Samos Colomer, Nicola Marzari, Francesco Mauri, Stefano Paolini, Alfredo Pasquarello, Lorenzo Paulatto, Carlo Sbraccia, Sandro Scandolo, Gabriele Sclauzero, Ari P. Seitsonen, Alexander Smogunov, Paolo Umari, Renata M. Wentzcovitch, J. Phys. Condens. Matter 21 (2009) 395502 (http://www.quantum-espressso.org.). [16] P. Hohenberg, W. Kohn, Phys. Rev. 136 (1964) B864. W. Kohn, L. J. Sham, Phys. Rev. 140, 1965, A1133. [17] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [18] The pseudopotentials used are Mn.pbe-sp-van.UPF and Co.pbe-nd-rrkjus.UPF; and these are taken from Quantum Espresso Distribution, http://www.quantum-espresso.org distribution. [19] http://www.physics.rutgers.edu/dhv/uspp/index.html. [20] A.M. Rappe, K.M. Rabe, E. Kaxiras, J.D. Joannopoulos, Phys. Rev. B 41 (1990) 1227. [21] W.L. O’Brien, B.P. Tonner, Phys. Rev. B 50 (1994) 2963; Phys. Rev. B 58 (1998) 3191. [22] B.Ch. Choi, J.P. Bode, J.A.C. Bland, Phys. Rev. B 58 (1998) 5166; Phys. Rev. B 59 (1999) 7029. [23] B. M’Passi-Mabiala, S. Meza-Aguilar, C. Demangeat, Phys. Rev. B 65 (2002) 012414.