Density-functional study of the CO adsorption on ferromagnetic Co(0 0 0 1) and Co(1 1 1) surfaces

Density-functional study of the CO adsorption on ferromagnetic Co(0 0 0 1) and Co(1 1 1) surfaces

Available online at www.sciencedirect.com Surface Science 601 (2007) 5571–5575 www.elsevier.com/locate/susc Density-functional study of the CO adsor...

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Available online at www.sciencedirect.com

Surface Science 601 (2007) 5571–5575 www.elsevier.com/locate/susc

Density-functional study of the CO adsorption on ferromagnetic Co(0 0 0 1) and Co(1 1 1) surfaces Sˇteˇpa´n Pick

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J. Heyrovsky´ Institute of Physical Chemistry of the Academy of Sciences of the Czech Republic, v.v.i., Dolejsˇkova 3, CZ-182 23 Prague 8, Czech Republic Received 31 May 2007; accepted for publication 18 September 2007 Available online 25 September 2007

Abstract The regular CO overlayers at coverage h = 1/3 adsorbed on the (0 0 0 1) surface of hcp Co and (1 1 1) surface of fcc Co are studied by first-principles density-functional theory with the exchange–correlation component in the PBE form. Adsorption in atop, bridge, and three-fold hcp or fcc position are considered. The adsorption energies, CO stretching frequencies, geometry, work function, and local magnetic moments are studied, and, when possible, compared with experimental or theoretical data. Particularly, we show that the recently proposed correction to adsorption energy of CO prefers correctly the atop adsorption site, whereas the remaining sites are almost degenerate in energy. The CO molecule lowers magnetization on neighbouring Co atoms, and the effect decreases with the adsorption site coordination. We show, however, that this trend is not the result of the different C–Co separation at different adsorption sites. A very small magnetic moment appears on CO that couples antiferromagnetically to Co. Most results are very similar for the Co(0 0 0 1) and Co(1 1 1) surfaces. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Density-functional calculations; Chemisorption; Magnetic films; Cobalt; Carbon monoxide

1. Introduction Adsorption of carbon monoxide at transition-metal surfaces belongs to most frequently studied chemisorption systems. Yet, there remain a number of open questions. The analysis can turn difficult at CO high coverage because of the presence of non-equivalent adsorption sites, for coadsorption of another species, etc. A specific problem is, however, the tendency to overestimate stability of highlycoordinated adsorption sites (overbonding problem) in first-priniciples density-functional theory (DFT) calculations that lead even to wrong predictions of the groundstate geometry in some cases. In a very detailed computational study [1] of CO adsorption on Pt(1 1 1) it has been shown that it is an intrinsic problem of commonly-used solid-state DFT theories. Later, another detailed calculation

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[2] considering CO adsorption at various d-electron metal surfaces and at different adsorption sites together with methodical aspects of the calculation has appeared. In the studies [3,4], the overbonding flaw was related to the inaccuracy in describing the empty 2p CO states (HOMO–LUMO separation, singlet–triplet excitation) originating from forms of the exchange–correlation functional that are used for extended systems. In the paper [4], where the Perdew–Burke–Ernzerhof (PBE) form of the density-functional [5] together with norm-conserving pseudopotentials [6] were employed, a simple correction, based on the analysis of the singlet–triplet excitation error, was proposed. Hopefully, this correction might reduce the overbonding error and improve the adsorption energy values. Its validity has been corroborated by recent calculations [7], where the revised form [8] of the PBE functional (RPBE) and ultrasoft Vanderbilt [9] pseudopotentials were applied. Presently, numerous theoretical data on geometry, vibrational frequencies and adsorption energies on CO adsorbed on transition-metal surfaces are

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available (cf. Refs. [2,4,7] and references given therein). These data include also CO deposition upon magnetic systems. Calculation of CO effect upon surface magnetization has been published for Fe [10,11] and Ni [12–16]. Let us turn now to the CO adsorption on ferromagnetic hcp (0 0 0 1) and fcc (1 1 1) surfaces. At low-coverage (up to about pffiffiffi 1/3), pffiffiffi CO adsorbs at atop sites on Co(0 0 0 1). It forms ð 3  3ÞR30 overlayer, properties of which have been studied experimentally [17–19]. It is interesting that coadsorbed K moves CO molecules to three-fold fcc and hcp sites [20]. For higher CO coverage, new adsorption sites become occupied and complicated overlayer phases are formed [17,18,21], geometry of which is not completely clarified. In the realm of thin-film magnetism, the CO adsorption on Co (especially in Co(1 1 1)) is of special interest because of its ability to switch the magnetization orientation [22–24]. The conclusions arrived at in the last cited study are especially involved since they relate the spin reorientation to the presence/absence of weakly adsorbed CO in the bridge position. For low-coverage CO adsorption at Co(0 0 0 1), several first-principles calculations are available. The extensive analysis based on the popular gradient-corrected Perdew–Wang (PW91) [25] form of the density-functional (cf. also refs. [26,27]) confirms the presence of the overbonding error that does not allow to correctly predict the most stable adsorption site. In the paper [7], where the RPBE functional is used, a (semi)empirical correction to the adsorption energy was used to tackle the problem. For the fcc Co(1 1 1) surface, similar calculations seem to be missing although most results are likely to resemble the hcp case. Strange enough, however, theoretical analysis of the effect of the CO molecule upon magnetic properties of Co surfaces on the first-principle level is completely lacking. It was performed [28] only at the semi-empirical level for atop and bridge CO positions above Co(0 0 0 1) in not optimized geometries. The calculation predicts that CO molecule adsorbed at atop position drastically reduces magnetic moment of its Co nearest-neighbour, whereas the effect is very small for adsorption in the bridge position. In the present short paper, we show the results of firstprinciples calculation performed for regular CO structures at coverage 1/3 on the (0 0 0 1) surface of hcp Co film or on the analogous (1 1 1) surface of fcc Co film. We address three simple issues: (1) We check the influence of CO adsorbed in various symmetric adsorption sites on the magnetization of cobalt surface atoms. Particularly, we rule out the logical hypothesis that the trend arrived at might result essentially from the difference in the Co–C separation. (2) Since in the calculations of other authors for Co surfaces, PW91 and RPBE forms of exchange–correlation functionals were used, we perform calculations with the PBE functional to enable a comparison. Particularly, we calculate the surface optimized geometries, CO stretching vibrational frequencies and adsorption energies for various adsorption sites (these data overlap with the literature findings for Co(0 0 0 1)) and surface work function values. We

check also the result of the (semi)empirical energy-correction mentioned above. We suppose that an extensive set of data obtained by using another form of the density functional than in other authors studies might be useful in further development of simple corrections to the overbonding error. Besides that, calculations with this choice of functional match the important paper [4]. (3) We check to what extent the results for hcp and fcc Co films, respectively, are similar. 2. Model and the method of calculation Because, in dependence on experimental conditions, both hcp and fcc Co films can be prepared, (0 0 0 1) the surface of hcp film as well as the (1 1 1) surface of fcc film are considered. For coverage up to about h = 1/3, the experiment finds [17,18] pffiffiffi CO pffiffiffi adsorbed upright in atop positions forming the ð 3  3ÞR30 overlayer on Co(0 0 0 1). Together with pffiffiffi p ffiffiffi this geometry, we consider also the structure ð 3  3ÞR30 formed by upright standing CO molecules in bridge (two-fold), three-fold fcc and three-fold hcp sites (Fig. 1) at Co(0 0 0 1) or Co(1 1 1) surfaces. It is known that relaxations at closely packed Co surfaces are moderate and magnetization perturbation due to the CO at magnetic surfaces is highly localized. We model the systems by five-layer Co slabs with CO adsorbed on the upper surface. The two upper slab surfaces and CO molecule are the subject of geometry optimalization. The remaining Co–Co distances are fixed at a value found from independent optimalization for the bulk structures (see below). Supercells (periodically alternating solid and vacuum slabs) are used with the vac˚. uum width about 14 A We use the code DACAPO [8,29], which enables DFT electronic-structure calculations of periodic systems. It employs plane-wave basis and ultrasoft pseudopotentials. The calculation settings are similar to those used by other authors for analogous systems, see, e.g. Ref. [2]. The energy cut-off is 450 eV and we use the ð4  4  1Þ Monkhorst– Pack sampling of the Brillouin zone. A dipole layer is added to compensate for the work function jump when going through the slab. The geometry optimalization is

f a

b

h Fig. 1. Various adsorption sites ( a = atop, b = bridge, f = three-fold fcc, h = three-fold hcp) above the Co(0 0 0 1) or Co(1 1 1) surface (top view). Co atoms are represented by circles; surface (subsurface) atoms are distinguished by full (dotted) lines.

Sˇ. Pick / Surface Science 601 (2007) 5571–5575

done via conjugate–gradient method, and CO stretching frequency is calculated similarly as in the Ref. [7]. The PBE form of the exchange–correlation functional is used that, to the best of our knowledge, has not been applied to CO on cobalt before. For Co, the PBE pseudopotential was constructed with the aid of Vanderbilt’s package [30] and with input settings (also including the nonlinear core–valence exchange–correlation correction with the cut-off radius 0.90 a.u.) as for the PW91 form [31]. For C and O, pseudopotentials from Ref. [32] were used. For the CO molecule, we find that the equilibrium bond ˚ and length and stretching frequency are 1.142 A 1 2135 cm , respectively, which almost coincide with the calculations of Ref. [2], and can be compared with the ˚ and 2145 cm1. For hcp/fcc experimental values 1.128 A crystals we derive the Co–Co nearest-neighbour distance ˚ /2.490 A ˚ and magnetic moment as 1.56 l /1.58 as 2.495 A B lB per Co atom. For nonhomogeneous slabs, magnetic mo˚ ments within spheres with bulk Wigner–Seitz radius 1.38 A are evaluated for Co atoms. For C and O moments, the va˚ close to C and O literature covalent radii is used. lue 0.75 A The value of adsorbate magnetic moments is not sensitive to reasonable radius changes. This is probably due to the fact that the delocalized electrons, that dominate near the limiting sphere, are only weakly magnetically polarized (cf. Fig. 4 of Ref. [40]). In this respect, the definition of local magnetic moments seems to be essentially less sensitive to a scheme chosen than the definition of the atomic charge (ionicity). We have also checked the accuracy of the slab approximation pffiffiffi pby ffiffiffi repeating the calculations for Co(0 0 0 1) and ð 3  3ÞR30 -CO(atop)/Co(0 0 0 1) systems with 10 Co layers. The relaxed atomic coordinates in the surface region ˚ , the work function values by about differ by about 0.003 A 0.006 eV and the CO adsorption energy is by 0.01 eV/molecule lower for the 10-layer slab. 3. Results and discussion In Table 1, we present the calculated structure and energy data. For CO on the Co(0 0 0 1) surface, they were calculated also by other authors who used the PW91 [2,27,26] and RPBE [7] forms of the exchange–correlation potential. Our results resemble the PW91 calculations, although we obtained perhaps a slightly better agreement with the experimental value 2012 cm1 [33] of the CO stretching frequency for CO in atop position above Co(0 0 0 1). The RPBE stretching frequencies of CO are elevated as compared with the PW91 and our PBE values. The corrected adsorption energy [4,7] Ead is calculated from the formula Ead ¼ Ead  A þ B  m;

ð1Þ 1

where B = 0.0008 eV cm is an (approximately) universal coefficient according to the analysis of Refs. [4,7], and A = 1.996 eV was fitted to reproduce the experimental energy from Ref. [17]; m is the calculated CO stretching frequency. Thus we get the correct stabilization of the atop

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Table 1 pffiffiffi pffiffiffi Calculated properties of ð 3  3ÞR30 -CO overlayer with admolecules placed at various sites (a = atop, b = bridge, h = three-fold hcp, f = threefold fcc) above Co(0 0 0 1) or Co(1 1 1) surface Site

Surface

d(CO)

d(Co–C)

h

Ead

Ead

a b h f

Co(0 0 0 1)

1.166 1.185 1.192 1.191

1.75 1.91 1.98 1.99

1.75 1.45 1.36 1.37

1.71 1.63 1.69 1.69

1.33 1.10 1.11 1.12

a b h f

Co(1 1 1)

1.165 1.185 1.191 1.190

1.74 1.91 1.98 1.98

1.74 1.45 1.37 1.37

1.70 1.64 1.70 1.70

1.31 1.10 1.13 1.14

m a

2017 1841 1770 1783 2005 1842 1785 1803

Molecule length d(CO), distance of C from the nearest Co atom d(Co–C) and vertical separation h of C from the Co surface defined by the nearest ˚ . Ead (in eV, positive value means energy gain) is Co atom(s) is given in A the adsorption energy per molecule, Ead stands for energy including the empirical correction (see the text). m (in cm1) is the CO stretching-mode frequency. a Fitted to the experiment [17].

adsorption site. Let us note that its energetical preference as compared with other adsorption sites is a bit higher than in Ref. [7]. The remaining adsorption sites are almost degenerate in the energy. The results for the fcc Co(1 1 1) surface are almost the same; an exception is somewhat higher m’s for three-fold adsorption sites on Co(1 1 1) than on Co(0 0 0 1). The calculated C–O bond length for CO in the atop position agrees with the LEED result for the Co(0 0 0 1) surface [18], whereas we get slightly shorter Co–C separation ˚ derived for adsorption above than the value 1.78 ± 0.06 A the (0 0 0 1) [18] and (1 1 1) [24] surface, respectively. According to the experiment [20], K co-adsorption moves CO to three-fold fcc and hcp sites above Co(0 0 0 1). The measured Co–C distance is very close to the calculated one (Table 1, for surface without any K), whereas the ˚ can experimental average C–O bond length 1.22 ± 0.1 A reflect the K-induced bond weakening. The geometry of cobalt carbonyls in crystalline salts Cs2[Co6(CO)15] Æ 3H2O [35] and K4[Co6(CO)14] Æ 6H2O [36] was also analyzed experimentally. In the cesium salt, the C–O and Co–C distances for CO in atop, bridge and three-fold position above the Co6 cluster correlate quite well with the corresponding values in Table 1. For the second salt, some CO molecules ˚ from in three-fold sites have large separation 2.16–2.31 A Co [36]. It would be interesting to know whether the latter result has some relation to the large Co–C distance for the CO in bridge position above Co(1 1 1) claimed for the lowtemperature chemisorption phase in the Ref. [24]. Let us give, yet, a short comment on the relaxation at Co surfaces. For the clean surfaces, we find the relaxation of the surface – subsurface vertical distance by about 2% in accord with the measurements [34] for Co(0 0 0 1). For CO in two- and three-fold adsorption sites, this relaxation is reduced. For atop adsorption, we get only semiquantitative accord with the LEED analysis [18]: for Co(0 0 0 1) we obtain a rather marked surface buckling with surface – sub-

Sˇ. Pick / Surface Science 601 (2007) 5571–5575

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Table 2 pffiffiffi pffiffiffi Calculated properties of ð 3  3ÞR30 -CO overlayer with admolecules placed at various sites (a = atop, b = bridge, h = three-fold hcp, f = threefold fcc) above Co(0 0 0 1) or Co(1 1 1) surface Site

Surface

m (O)

m (C)

m (Co)

m (Co)*

/

0.03 0.04 0.03 0.03

0.02 0.03 0.04 0.04

1.71 0.72 1.21 1.33 1.37

0.72 1.03 1.13 1.17

5.00 5.98 6.42 6.51 6.44

0.03 0.04 0.04 0.03

0.02 0.04 0.04 0.04

1.68 0.72 1.22 1.34 1.38

0.72 1.04 1.13 1.15

5.03 5.99 6.44 6.52 6.46

Co(0 0 0 1) a b h f Co(1 1 1) a b h f

The lines without adsorption site specified describe the free relaxed Co slabs. Magnetic moments in lB on O, C and on the surface Co atom(s) lying closest to C are given; m(Co)* is the moment value for the Co–C ˚ for Co(0 0 0 1)/Co(1 1 1) (see the text). / (eV) is separation of 1.75/1.74 A the work function.

˚ for the Co atom below CO and surface distance 2.06 A ˚ 1.95 A for the remaining Co surface atoms. For Co(1 1 1), ˚ and 1.97 A ˚ , respectively. We also the two values are 2.05 A predict considerable increase of the work function due to adsorption (Table 2), which is most marked for non-atop chemisorption. The work function value for the free surfaces coincides with the experimental value 5.0 eV [37] for polycrystalline Co. For the adsorbate-free slabs, we find some enhancement of surface magnetism (Table 2) – a situation common for magnetic metal surfaces. The CO molecule lowers the magnetic moment on its nearest Co neighbour(s), the influence being less important at more distant atoms. The magnetization is reduced more than twice for atop adsorption, and the effect decreases with the admolecule coordination. An analogous finding was made in the first-principle calculation of Ref. [10] for CO on the Fe(0 0 1) surface. On semiquantitative level, the conclusion of the semi-empirical model [28] is thus confirmed. Since the Co–C separation increases with the CO coordination (Table 1), one might be tempted to relate together the magnetization and distance decrease. For this purpose, we have analyzed the situation with the Co–C distance fixed at the atop–adsorption value ˚ for hcp (fcc) slabs. (For the equilibrium 1.75 (1.74) A geometries of CO adsorbed in bridge or three-fold positions, we have simply shifted the molecule as a whole along the surface normal). The resulting moments displayed in Table 2 show clearly that the distance factor is not the main parameter controlling the magnetization. The CO molecule couples always antiferromagnetically to Co, although the induced magnetic moment is very small (cf. also Ref. [28]). The very same trend was arrived at for, e.g. CO at Ni surfaces [13,15], and was predicted also for some atomic adsorbates above ferromagnetic surfaces, see Refs. [38–41] and references given therein. An attempt to discuss the physical origin of such an antiferromagnetic coupling has been undertaken in Ref. [42].

4. Summary and conclusions In the present pffiffiffi study, pffiffiffi we have considered the properties of ordered ð 3  3ÞR30 -CO overlayers on ferromagnetic Co(0 0 0 1) and Co(1 1 1) surfaces by using the firstprinciples density-functional theory with the exchange–correlation energy part in the Perdew–Burke–Ernzerhof form – a choice, different from other calculations for Co surfaces. Atop, bridge, and three-fold fcc and hcp adsorption positions were considered. Thorough comparison with experimental and theoretical data was performed. We obtained the optimized adsorption geometries, first-principles and (semi)empirically corrected adsorption energies, C–O stretching vibrational frequencies, work function values and local C, O and Co magnetic moments. For the atop adsorption above Co(0 0 0 1), we get fair agreement with experiment for the CO stretching frequency, and quite reasonable but not complete accord for the geometry details. For CO above Co(0 0 0 1), our results are close to those obtained with the PW91 form of the exchange–correlation functional. Particularly, the overbonding error does not allow to predict the correct CO adsorption site, although for the Co(1 1 1) surface, the energies for atop and three-fold sites are practically the same. The application of the recently proposed correction to the adsorption energy of CO yields the correct answer, the remaining adsorption sites being almost degenerate in energy. The magnetic moments of Co atoms close to CO are lowered, and the effect increases markedly with decreasing admolecule coordination. We show clearly that such a behaviour is not due to the different Co–C separation at different adsorption sites. On the CO molecule, a very small magnetic moment is induced that couples antiferromagnetically to Co moments. This seems to be a rather general trend for adsorbates forming a strong (covalent) bond with a ferromagnetic metal surface. We verify that most results are very similar for the hcp Co(0 0 0 1) and fcc Co(1 1 1) surfaces. References [1] P.J. Feibelman, B. Hammer, J.K. Nørskov, F. Wagner, M. Scheffler, R. Stumpf, R. Watwe, J. Dumesic, J. Phys. Chem. B 105 (2001) 4018. [2] M. Gajdosˇ, A. Eichler, J. Hafner, J. Phys.: Condens. Matter 16 (2004) 1141. [3] G. Kresse, A. Gill, P. Sautet, Phys. Rev. B 68 (2003) 073401. [4] S.E. Mason, I. Grinberg, A.M. Rappe, Phys. Rev. B 69 (2004) 161401(R). [5] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [6] A.M. Rappe, K.M. Rabe, E. Kaxiras, J.D. Joannopoulos, Phys. Rev. B 41 (1990) 1227(R). [7] F. Abild-Pedersen, M.P. Andersson, Surf. Sci. 601 (2007) 1747. [8] B. Hammer, L.B. Hansen, J.K. Nørskov, Phys. Rev. B 46 (1999) 7413. [9] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892. [10] S.K. Nayak, M. Nooijen, S.L. Bernasek, P. Blaha, J. Phys. Chem. B 105 (2001) 164. [11] D. Spisˇa´k, J. Hafner, Phys. Rev. B 64 (2001) 094418. [12] G. Pacchioni, N. Ro¨sch, Acc. Chem. Res. 28 (1995) 390. [13] Q. Ge, S.J. Jenkins, D.A. King, Chem. Phys. Lett. 327 (2000) 125.

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