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Electronic and magnetic properties of ring-like Fe6 and Fe6@Si12 clusters
Physics Letters A 341 (2005) 256–260 www.elsevier.com/locate/pla
Electronic and magnetic properties of ring-like Fe6 and Fe6@Si12 clusters M. Samah ∗ , M.A. Belkhir Laboratoire de Physique Théorique, Groupe de Physique du Solide (GPS), Département de Physique, Université Abderahmane Mira, route Targua Ouzemour, 06000 Bejaia, Algeria Received 15 March 2005; accepted 15 April 2005 Available online 29 April 2005 Communicated by V.M. Agranovich
Abstract Novel structures based on Fe atoms encapsulated within a Si12 cluster are studied. Electronic and magnetic properties of ring-like Fe6 and Fe6 @Si12 were investigated using the frame work of density functional theory (DFT). We have demonstrated that Si12 cluster can be stabilized by encapsulating transition metal atoms (TMAs), Fe atoms. The magnetic moment of free Fe6 cluster is of 3.67µB , when that of encapsulated Fe6 ring within Si12 cluster spread from 2.9µB to 3.1µB . This decrease is explained by hybridization phenomenon. 2005 Published by Elsevier B.V. PACS: 61.46.+w; 31.15.Ar; 36.40.Mr Keywords: Fe6 ; Fe6 @Si12 ; Magnetic; Ab initio; DFT; Cluster
1. Introduction The study of atomic clusters has become one of the most active areas of research over the last decade. The main reasons for such an intense interest can be stated as follows: (i) fundamental importance of understanding properties of materials with increasing size, especially the transition molecule to cluster to bulk; (ii) experimental techniques for production and * Corresponding author.
E-mail address: [email protected] (M. Samah). 0375-9601/$ – see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.physleta.2005.04.053
analysis of clusters has improved dramatically, providing new data about their electronic, chemical, and structural properties; (iii) crucial role of clusters in a number of industrial applications such as catalysis or in a development of new semiconducting/magnetic devices. The physics of magnetic transition-metal TM clusters is still an intriguing and challenging topic both from an experimental and theoretical point of view. Although certain properties of the clusters can be explored directly, like the bond lengths [1], the vibrational frequencies of free clusters from resonance Raman spectroscopy [2], the dependence of the magnetic moments of the free clusters on size and temperature
M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
using a Stern–Gerlach magnet and time-of-flight mass spectrometer [3]. There are some further interesting works which we would like to mention. A recent implementation of the density functional based self-consistent charge tight-binding method allowing to addressing larger TM clusters is discussed in [4]. Different aspects of magnetism of small clusters have also been discussed on the basis of the Hubbard model allowing to deal with correlation effects [5–7] or on the basis of the Heisenberg model showing novel quantum effects for the case of antiferromagnetic exchange [8]. We finally notice that the magnetic moments of TM clusters, which for the free clusters are usually larger than corresponding bulk values, can significantly change for the case that clusters are supported [9,10] or embedded [11,12]. Clusters based on pure Si as well as metal-doped Si have drawn much interest from researchers in the area of both chemistry and solid state physics. The main reason for this is that metal-doped Si structures have found many technological applications and appear to be powerful candidates for numerous new applications in nanoelectronics. It should be noted that even though Si is isovalent to the C atom in the periodic table, heir behaviour in forming chemical bonds can be very different. The remarkable stability of closed carbon cages can be attributed to the sp2 affinity for the C atom. In contrast, Si cages are unstable [13] due to the fact that sp2 hybridization is highly unfavourable for Si. A possible way to stabilize a Si cage is to introduce a guest atom inside the cage, as suggested by recent experimental and theoretical works [14–18]. These studies have demonstrated that the encapsulation of TM atoms (TMAs) leads to stable Si cage whose structure depends on many factors. Among these, the most important ones were found to be filling factor of the d-band of the encapsulated TMA, the number and the symmetry of the encapsulated TMA cluster, and the size of the Si cage [17,18]. Computationally, much works has been done in this field of research Hiura et al. [14] also provided theoretical support for their experimental findings by performing ab initio calculations for a WSi12 cluster. Following this work, Kumar and Kawazoe reported results of metal encapsulated Si cage clusters from ab initio pseudopotential plane wave calculations using density functional theory in the generalized gra-
257
dient approximation for the exchange-correlation energy [15]. Depending upon the size of the metal atom, they found that silicon forms fullerene-like M@Si16 , M = Hf, Zr, and cubic M@Si14 , M = Fe, Ru, Os cage clusters. Additionally, they reported stable clusters of Sin M type (n = 14–17, M = Cr, Mo, W) in the cubic, fullerene-like, decahedral and Frank–Kasper polyhedron type geometry [16]. The theoretical calculations of Andriotis et al. suggested that the type of ground state geometry of these clusters is sensitively dependent on the d-band filling factor of the encapsulated TMA rather than its size [17,18]. More recently, it was also shown that the Si60 cage can also be stabilized by including within it as endohedral units, small magic number clusters such as Al12 X (X = Si, Ge, Sn, Pb) and Ba@Si20 [19]. An interesting feature of the TMA-encapsulated Si clusters was reported recently by Andriotis and coworkers [17,18]. In particular, they showed that Si nanotubes (NTs) can be stabilized by the encapsulation of a linear chain o TMAs. The most interesting feature of their work is the profound effect of the type of TMA on the symmetry of the Si-NT and the reduction in the magnetic moment of the TMA cluster upon encapsulation by Si cage. A similar results can be consulted in Refs. [20,21]. In the present Letter, we report results of our detailed investigation of structural, electronic and magnetic properties of ring-like Fe6 and Fe6 @Si12 . These structures do not been studied elsewhere, in our knowledge. For this study, we have used an ab initio pseudopotential atomic orbitals (PAO) calculations using density functional theory in the generalized gradient approximation for the exchangecorrelation energy, using the S IESTA simulation package [22]. For exchange correlation functional we chose a form proposed by Perdew, Burke and Ernzerhof (PBE) [23]. For all clusters, the chosen supercell is a cube of size 123 Å3 which is large enough to ensure that the interaction of clusters with their images is negligible. The k-sampling is sensitively equal to one thousand points. For the structural optimization a conjugate gradient molecular dynamic (CGDM) was run, with a maximum force tolerance equal to 0.04 eV/Å (eV per angstrom) and maximum atomic displacement in each CGDM step equal to 0.1 Å.
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The initial structures are constructed as follows. For ring-like Fe6 , the six Fe atoms are located on the vertexes of an equilateral hexagon inscribed in a circle with 2.34 Å as radius. The Fe–Fe distance is taken as 2.34 Å, also. Fe6 @Si12 structure is created by imbricate the ring-like Fe6 in a similar ring-like Si12 with a radius averaging 5.43 Å.
2. Results The optimized structure of ring-like Fe6 is represented on Fig. 1. The first aspect observed is that the ring-like structure was swollen. The interatomic distance (2.33 Å) in the initial structure becomes equal to 4.42 Å in the relaxed one. This effect is explained by the way to minimizing the overlapping energy of 4s and 3d orbitals. The structure preserves its symmetry that consists on six order axis and inversion centre. All Fe atoms locate at equilateral hexagon. The Fermi energy is equal to EF = −2.00 eV. All atoms are equally magnetized. The magnetic moment average 3.67µB . This value is higher than the bulk value of 2.2µB , but less bellow the moment of 4µB of the free Fe atom. This high magnetic moment value is not reported elsewhere. Ballone and Jones, who performed the first ab initio study on a capped trigonal bipyramid Fe6 cluster, obtained a value of 3.33µB . The interatomic lengths vary from 2.24 to 2.61 Å [24]. Gustev and Bauschlicher suggested a value of 2.32 to 2.72 Å [25]. The magnetic moment results essentially from the d-band, especially 3dxy , 3dyz , 3dz2 , 3dxz and 3dx 2 –y 2 orbitals.
Fig. 1. Optimized configuration of as ring-like Fe6 clusters.
On Fig. 2, we have represented the optimized configurations of Fe6 @Si12 and Si12 structures. The ringlike Si12 cluster atoms, are located on vertexes of an irregular dodecagon inscribed in an ellipse with for great and little half-axes the values of 4.50 and 4.27 Å, respectively. The interatomic distances spread from 4.5 to 4.6 Å. These distances seem to be great, comparatively with silicon bulk ones, but similar values are obtained elsewhere [26]. For the Fe6 @Si12 structure, the lowest energy configuration is shown on Fig. 2. One can notice that Fe atom positions do not shift but those of Si, rearrange thus forming a perfect circle where the Si atoms are inscribed within a dodecagon. Analysis of the structure gives a equitable distribution: four Si–Si distances
Fig. 2. Lowest energy structure of Si12 and Fe6 @Si12 rings.
M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
259
Fig. 3. DOS (density of states) of Fe6 and Fe6 @Si12 clusters.
equal to 2.23 Å, four other equal to 4.42 Å and finally four equal to 6.54 Å. The symmetry of this configuration exhibits a centre of inversion and a two order axis. In this Letter we have demonstrated that a Fe6 @Si12 cluster is more stable than the Fe6 one strengthened by several results done on different structure configuration of encapsulated TMA within silicon clusters [27]. The DOS calculations are summarized on Fig. 3. We note, firstly, that the Fermi level of the Fe6 @Si12 ring-like cluster is much lower that the Fe6 one. It is equal to 5.55 eV. The spin-up curves for both
structures reveals that the very intense peak shift slightly to lower energy and increase of the DOS at Fermi level by more than a factor of 2. This effect can easily explained by the hybridization phenomenon. The same report can be lead with the down spin, expect the splitting of the highest intense peak into two peaks for Fe6 @Si12 cluster. The magnetic moment of Fe atoms are of 3.1µB for four atoms and 2.9µB for the two last ones. We note here that Fe atoms in the region where Si–Si distance equal to 2.23 Å, exhibit the highest magnetic moment.
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M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
The total spin of structure comes partially from the p orbitals of the Si atoms. For Si1, Si7 atoms, the orbital contributions on magnetic moment are as 75% for 3py and 3pz , and 25% for 3s. This situation is inversed for other Si atoms. The dx 2 orbital of Fe again plays a major role in the bonding and is combined with the spy hybridized orbital of each Si. The bonding molecular orbitals are formed by hybridized 3dx 2 and 3dyz orbitals of Fe combined with s, py , pz , or hybridized spy pz orbitals of each Si atom.
3. Conclusion In this Letter we have lead with new clusters structures of free and encapsulated TMAs within as ringlike silicon clusters. The first result is the possibility of stabilize Si clusters by encapsulating Fe atoms. The magnetic moment taken by each Fe atom in the free Fe6 cluster is of 3.6µB . The encapsulated Fe atoms exhibit two different values: 3.1µB and 2.9µB . The bonding molecular orbitals are formed by hybridized 3dx 2 and 3dyz orbitals of Fe combined with s, py , pz , or hybridized spy pz orbitals of each Si atom. References [1] H. Purdum, P.A. Montano, G.K. Shenoy, T. Morrison, Phys. Rev. B 25 (1982) 4412. [2] T.L. Haslett, K.A. Bosnick, S. Fedrigo, M. Maskovits, J. Chem. Phys. 111 (1999) 6456. [3] I.M.L. Billas, J.A. Becker, A. Châtelain, W.A. de Heer, Phys. Rev. Lett. 71 (1993) 4067. [4] P. Bobadova-Parvanova, K.A. Jackson, S. Srinivas, M. Horoi, C. Kohler, G. Seifert, J. Chem. Phys. 116 (2002) 3576.
[5] F. Lopez-Urias, G.M. Pastor, Eur. Phys. J. D 9 (1999) 495. [6] M.A. Ojeda, J. Dorantes-Davila, G.M. Pastor, Phys. Rev. B 60 (1999) 6121. [7] F. Lopez-Urias, G.M. Pastor, K.H. Bennemann, J. Appl. Phys. 87 (2000) 4909. [8] J.B. Parkinson, J. Temonen, J. Phys.: Condens. Matter 12 (2000) 8669. [9] S. Pick, V.S. Stepanyuk, A.N. Baranov, W. Hergert, P. Bruno, Phys. Rev. B 68 (2003) 104410. [10] Z. Šljivanˇcanin, A. Pasquarello, Phys. Rev. Lett. 90 (2003) 247202. [11] R. Robles, R.C. Longo, A. Vega, C. Rey, V. Stepanyuk, L.J. Gallego, Phys. Rev. B 66 (2002) 064410. [12] Y. Xie, J.A. Blakman, Phys. Rev. B 66 (2002) 085410. [13] M. Menon, K.R. Subbaswamy, Chem. Phys. Lett. 219 (1994) 219. [14] H. Hiura, T. Miyazaki, T. Kanayama, Phys. Rev. Lett. 86 (2001) 1733. [15] V. Kumar, Y. Kawazoe, Phys. Rev. Lett. 87 (2001) 045503. [16] V. Kumar, Y. Kawazoe, Phys. Rev. B 87 (2002) 073404. [17] M. Menon, A.N. Andriotis, G. Froudakis, Nanoletters 2 (2002) 301. [18] A.N. Andriotis, G. Mpourmpakis, G. Froudakis, M. Menon, New J. Phys. 4 (2002) 78. [19] Q. Sun, Q. Wang, P. Jena, B.K. Rao, Y. Kawazoe, Phys. Rev. Lett. 90 (2003) 135503. [20] U. Landman, R.N. Barnett, A.G. Scherbakov, A. Avouris, Phys. Rev. Lett. 85 (2000) 1958. [21] B.X. Li, P.L. Cao, R.Q. Zhang, S.T. Lee, Phys. Rev. B 65 (2002) 125305. [22] J.M. Soler, E. Artacho, J.D. Gale, A. García, J. Junguera, P. Ordejón, D. Sánchez-Portal, J. Phys.: Condens. Matter 14 (2002) 2745. [23] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [24] P. Ballone, R.O. Jones, Chem. Phys. B 49 (1994) 11842. [25] G.L. Gustev, C.W. Bauschlicher, J. Phys. Chem. A 107 (2003) 7013. [26] D.Y. Zhang, D. Bégué, C. Pouchan, Chem. Phys. Lett. 398 (2004) 283. [27] G. Mpourmpakis, G. Froudakis, A.N. Andriotis, M. Menon, Phys. Rev. B 68 (2003) 125407.
Electronic and magnetic properties of ring-like Fe6 and Fe6@Si12 clusters M. Samah ∗ , M.A. Belkhir Laboratoire de Physique Théorique, Groupe de Physique du Solide (GPS), Département de Physique, Université Abderahmane Mira, route Targua Ouzemour, 06000 Bejaia, Algeria Received 15 March 2005; accepted 15 April 2005 Available online 29 April 2005 Communicated by V.M. Agranovich
Abstract Novel structures based on Fe atoms encapsulated within a Si12 cluster are studied. Electronic and magnetic properties of ring-like Fe6 and Fe6 @Si12 were investigated using the frame work of density functional theory (DFT). We have demonstrated that Si12 cluster can be stabilized by encapsulating transition metal atoms (TMAs), Fe atoms. The magnetic moment of free Fe6 cluster is of 3.67µB , when that of encapsulated Fe6 ring within Si12 cluster spread from 2.9µB to 3.1µB . This decrease is explained by hybridization phenomenon. 2005 Published by Elsevier B.V. PACS: 61.46.+w; 31.15.Ar; 36.40.Mr Keywords: Fe6 ; Fe6 @Si12 ; Magnetic; Ab initio; DFT; Cluster
1. Introduction The study of atomic clusters has become one of the most active areas of research over the last decade. The main reasons for such an intense interest can be stated as follows: (i) fundamental importance of understanding properties of materials with increasing size, especially the transition molecule to cluster to bulk; (ii) experimental techniques for production and * Corresponding author.
E-mail address: [email protected] (M. Samah). 0375-9601/$ – see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.physleta.2005.04.053
analysis of clusters has improved dramatically, providing new data about their electronic, chemical, and structural properties; (iii) crucial role of clusters in a number of industrial applications such as catalysis or in a development of new semiconducting/magnetic devices. The physics of magnetic transition-metal TM clusters is still an intriguing and challenging topic both from an experimental and theoretical point of view. Although certain properties of the clusters can be explored directly, like the bond lengths [1], the vibrational frequencies of free clusters from resonance Raman spectroscopy [2], the dependence of the magnetic moments of the free clusters on size and temperature
M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
using a Stern–Gerlach magnet and time-of-flight mass spectrometer [3]. There are some further interesting works which we would like to mention. A recent implementation of the density functional based self-consistent charge tight-binding method allowing to addressing larger TM clusters is discussed in [4]. Different aspects of magnetism of small clusters have also been discussed on the basis of the Hubbard model allowing to deal with correlation effects [5–7] or on the basis of the Heisenberg model showing novel quantum effects for the case of antiferromagnetic exchange [8]. We finally notice that the magnetic moments of TM clusters, which for the free clusters are usually larger than corresponding bulk values, can significantly change for the case that clusters are supported [9,10] or embedded [11,12]. Clusters based on pure Si as well as metal-doped Si have drawn much interest from researchers in the area of both chemistry and solid state physics. The main reason for this is that metal-doped Si structures have found many technological applications and appear to be powerful candidates for numerous new applications in nanoelectronics. It should be noted that even though Si is isovalent to the C atom in the periodic table, heir behaviour in forming chemical bonds can be very different. The remarkable stability of closed carbon cages can be attributed to the sp2 affinity for the C atom. In contrast, Si cages are unstable [13] due to the fact that sp2 hybridization is highly unfavourable for Si. A possible way to stabilize a Si cage is to introduce a guest atom inside the cage, as suggested by recent experimental and theoretical works [14–18]. These studies have demonstrated that the encapsulation of TM atoms (TMAs) leads to stable Si cage whose structure depends on many factors. Among these, the most important ones were found to be filling factor of the d-band of the encapsulated TMA, the number and the symmetry of the encapsulated TMA cluster, and the size of the Si cage [17,18]. Computationally, much works has been done in this field of research Hiura et al. [14] also provided theoretical support for their experimental findings by performing ab initio calculations for a WSi12 cluster. Following this work, Kumar and Kawazoe reported results of metal encapsulated Si cage clusters from ab initio pseudopotential plane wave calculations using density functional theory in the generalized gra-
257
dient approximation for the exchange-correlation energy [15]. Depending upon the size of the metal atom, they found that silicon forms fullerene-like M@Si16 , M = Hf, Zr, and cubic M@Si14 , M = Fe, Ru, Os cage clusters. Additionally, they reported stable clusters of Sin M type (n = 14–17, M = Cr, Mo, W) in the cubic, fullerene-like, decahedral and Frank–Kasper polyhedron type geometry [16]. The theoretical calculations of Andriotis et al. suggested that the type of ground state geometry of these clusters is sensitively dependent on the d-band filling factor of the encapsulated TMA rather than its size [17,18]. More recently, it was also shown that the Si60 cage can also be stabilized by including within it as endohedral units, small magic number clusters such as Al12 X (X = Si, Ge, Sn, Pb) and Ba@Si20 [19]. An interesting feature of the TMA-encapsulated Si clusters was reported recently by Andriotis and coworkers [17,18]. In particular, they showed that Si nanotubes (NTs) can be stabilized by the encapsulation of a linear chain o TMAs. The most interesting feature of their work is the profound effect of the type of TMA on the symmetry of the Si-NT and the reduction in the magnetic moment of the TMA cluster upon encapsulation by Si cage. A similar results can be consulted in Refs. [20,21]. In the present Letter, we report results of our detailed investigation of structural, electronic and magnetic properties of ring-like Fe6 and Fe6 @Si12 . These structures do not been studied elsewhere, in our knowledge. For this study, we have used an ab initio pseudopotential atomic orbitals (PAO) calculations using density functional theory in the generalized gradient approximation for the exchangecorrelation energy, using the S IESTA simulation package [22]. For exchange correlation functional we chose a form proposed by Perdew, Burke and Ernzerhof (PBE) [23]. For all clusters, the chosen supercell is a cube of size 123 Å3 which is large enough to ensure that the interaction of clusters with their images is negligible. The k-sampling is sensitively equal to one thousand points. For the structural optimization a conjugate gradient molecular dynamic (CGDM) was run, with a maximum force tolerance equal to 0.04 eV/Å (eV per angstrom) and maximum atomic displacement in each CGDM step equal to 0.1 Å.
258
M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
The initial structures are constructed as follows. For ring-like Fe6 , the six Fe atoms are located on the vertexes of an equilateral hexagon inscribed in a circle with 2.34 Å as radius. The Fe–Fe distance is taken as 2.34 Å, also. Fe6 @Si12 structure is created by imbricate the ring-like Fe6 in a similar ring-like Si12 with a radius averaging 5.43 Å.
2. Results The optimized structure of ring-like Fe6 is represented on Fig. 1. The first aspect observed is that the ring-like structure was swollen. The interatomic distance (2.33 Å) in the initial structure becomes equal to 4.42 Å in the relaxed one. This effect is explained by the way to minimizing the overlapping energy of 4s and 3d orbitals. The structure preserves its symmetry that consists on six order axis and inversion centre. All Fe atoms locate at equilateral hexagon. The Fermi energy is equal to EF = −2.00 eV. All atoms are equally magnetized. The magnetic moment average 3.67µB . This value is higher than the bulk value of 2.2µB , but less bellow the moment of 4µB of the free Fe atom. This high magnetic moment value is not reported elsewhere. Ballone and Jones, who performed the first ab initio study on a capped trigonal bipyramid Fe6 cluster, obtained a value of 3.33µB . The interatomic lengths vary from 2.24 to 2.61 Å [24]. Gustev and Bauschlicher suggested a value of 2.32 to 2.72 Å [25]. The magnetic moment results essentially from the d-band, especially 3dxy , 3dyz , 3dz2 , 3dxz and 3dx 2 –y 2 orbitals.
Fig. 1. Optimized configuration of as ring-like Fe6 clusters.
On Fig. 2, we have represented the optimized configurations of Fe6 @Si12 and Si12 structures. The ringlike Si12 cluster atoms, are located on vertexes of an irregular dodecagon inscribed in an ellipse with for great and little half-axes the values of 4.50 and 4.27 Å, respectively. The interatomic distances spread from 4.5 to 4.6 Å. These distances seem to be great, comparatively with silicon bulk ones, but similar values are obtained elsewhere [26]. For the Fe6 @Si12 structure, the lowest energy configuration is shown on Fig. 2. One can notice that Fe atom positions do not shift but those of Si, rearrange thus forming a perfect circle where the Si atoms are inscribed within a dodecagon. Analysis of the structure gives a equitable distribution: four Si–Si distances
Fig. 2. Lowest energy structure of Si12 and Fe6 @Si12 rings.
M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
259
Fig. 3. DOS (density of states) of Fe6 and Fe6 @Si12 clusters.
equal to 2.23 Å, four other equal to 4.42 Å and finally four equal to 6.54 Å. The symmetry of this configuration exhibits a centre of inversion and a two order axis. In this Letter we have demonstrated that a Fe6 @Si12 cluster is more stable than the Fe6 one strengthened by several results done on different structure configuration of encapsulated TMA within silicon clusters [27]. The DOS calculations are summarized on Fig. 3. We note, firstly, that the Fermi level of the Fe6 @Si12 ring-like cluster is much lower that the Fe6 one. It is equal to 5.55 eV. The spin-up curves for both
structures reveals that the very intense peak shift slightly to lower energy and increase of the DOS at Fermi level by more than a factor of 2. This effect can easily explained by the hybridization phenomenon. The same report can be lead with the down spin, expect the splitting of the highest intense peak into two peaks for Fe6 @Si12 cluster. The magnetic moment of Fe atoms are of 3.1µB for four atoms and 2.9µB for the two last ones. We note here that Fe atoms in the region where Si–Si distance equal to 2.23 Å, exhibit the highest magnetic moment.
260
M. Samah, M.A. Belkhir / Physics Letters A 341 (2005) 256–260
The total spin of structure comes partially from the p orbitals of the Si atoms. For Si1, Si7 atoms, the orbital contributions on magnetic moment are as 75% for 3py and 3pz , and 25% for 3s. This situation is inversed for other Si atoms. The dx 2 orbital of Fe again plays a major role in the bonding and is combined with the spy hybridized orbital of each Si. The bonding molecular orbitals are formed by hybridized 3dx 2 and 3dyz orbitals of Fe combined with s, py , pz , or hybridized spy pz orbitals of each Si atom.
3. Conclusion In this Letter we have lead with new clusters structures of free and encapsulated TMAs within as ringlike silicon clusters. The first result is the possibility of stabilize Si clusters by encapsulating Fe atoms. The magnetic moment taken by each Fe atom in the free Fe6 cluster is of 3.6µB . The encapsulated Fe atoms exhibit two different values: 3.1µB and 2.9µB . The bonding molecular orbitals are formed by hybridized 3dx 2 and 3dyz orbitals of Fe combined with s, py , pz , or hybridized spy pz orbitals of each Si atom. References [1] H. Purdum, P.A. Montano, G.K. Shenoy, T. Morrison, Phys. Rev. B 25 (1982) 4412. [2] T.L. Haslett, K.A. Bosnick, S. Fedrigo, M. Maskovits, J. Chem. Phys. 111 (1999) 6456. [3] I.M.L. Billas, J.A. Becker, A. Châtelain, W.A. de Heer, Phys. Rev. Lett. 71 (1993) 4067. [4] P. Bobadova-Parvanova, K.A. Jackson, S. Srinivas, M. Horoi, C. Kohler, G. Seifert, J. Chem. Phys. 116 (2002) 3576.
[5] F. Lopez-Urias, G.M. Pastor, Eur. Phys. J. D 9 (1999) 495. [6] M.A. Ojeda, J. Dorantes-Davila, G.M. Pastor, Phys. Rev. B 60 (1999) 6121. [7] F. Lopez-Urias, G.M. Pastor, K.H. Bennemann, J. Appl. Phys. 87 (2000) 4909. [8] J.B. Parkinson, J. Temonen, J. Phys.: Condens. Matter 12 (2000) 8669. [9] S. Pick, V.S. Stepanyuk, A.N. Baranov, W. Hergert, P. Bruno, Phys. Rev. B 68 (2003) 104410. [10] Z. Šljivanˇcanin, A. Pasquarello, Phys. Rev. Lett. 90 (2003) 247202. [11] R. Robles, R.C. Longo, A. Vega, C. Rey, V. Stepanyuk, L.J. Gallego, Phys. Rev. B 66 (2002) 064410. [12] Y. Xie, J.A. Blakman, Phys. Rev. B 66 (2002) 085410. [13] M. Menon, K.R. Subbaswamy, Chem. Phys. Lett. 219 (1994) 219. [14] H. Hiura, T. Miyazaki, T. Kanayama, Phys. Rev. Lett. 86 (2001) 1733. [15] V. Kumar, Y. Kawazoe, Phys. Rev. Lett. 87 (2001) 045503. [16] V. Kumar, Y. Kawazoe, Phys. Rev. B 87 (2002) 073404. [17] M. Menon, A.N. Andriotis, G. Froudakis, Nanoletters 2 (2002) 301. [18] A.N. Andriotis, G. Mpourmpakis, G. Froudakis, M. Menon, New J. Phys. 4 (2002) 78. [19] Q. Sun, Q. Wang, P. Jena, B.K. Rao, Y. Kawazoe, Phys. Rev. Lett. 90 (2003) 135503. [20] U. Landman, R.N. Barnett, A.G. Scherbakov, A. Avouris, Phys. Rev. Lett. 85 (2000) 1958. [21] B.X. Li, P.L. Cao, R.Q. Zhang, S.T. Lee, Phys. Rev. B 65 (2002) 125305. [22] J.M. Soler, E. Artacho, J.D. Gale, A. García, J. Junguera, P. Ordejón, D. Sánchez-Portal, J. Phys.: Condens. Matter 14 (2002) 2745. [23] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [24] P. Ballone, R.O. Jones, Chem. Phys. B 49 (1994) 11842. [25] G.L. Gustev, C.W. Bauschlicher, J. Phys. Chem. A 107 (2003) 7013. [26] D.Y. Zhang, D. Bégué, C. Pouchan, Chem. Phys. Lett. 398 (2004) 283. [27] G. Mpourmpakis, G. Froudakis, A.N. Andriotis, M. Menon, Phys. Rev. B 68 (2003) 125407.