Fe encapsulation by silicon clusters: Ab initio

PHYSICAL REVIEW B 68, 125407 共2003兲

Fe encapsulation by silicon clusters: Ab initio electronic structure calculations Giannis Mpourmpakis and George E. Froudakis* Department of Chemistry, University of Crete, P.O. Box 1470, Heraklio, Crete, Greece 71409

Antonis N. Andriotis† Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, P.O. Box 1527, 71110 Heraklio, Crete, Greece

Madhu Menon‡ Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506-0055, USA and Center for Computational Sciences, University of Kentucky, Lexington, Kentucky 40506-0045, USA 共Received 28 May 2003; published 12 September 2003兲 Ab initio electronic structure calculations based on density functional theory are performed for Sin Fe clusters to determine stable structures. Our results show that these clusters can form the building block for Feencapsulated Si-nanotubes. The Si10Fe and Si12Fe clusters are found to be very stable, exhibiting large charge transfer, and can lead to Si-based nanotubes of the types Si5n Fen⫺1 and Si6n Fen⫺1 , respectively. The effect of Si encapsulation on the magnetic properties of the Fe atom is also investigated. DOI: 10.1103/PhysRevB.68.125407

PACS number共s兲: 61.46.⫹w, 31.15.Ar, 82.30.Nr, 36.40.Mr

I. INTRODUCTION

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, their behavior in forming chemical bonds can be very different. Carbon is well known to form stable caged clusters known as fullerenes. The remarkable stability of closed carbon cages can be attributed to the s p 2 affinity for the C atom. In contrast, Si cages are unstable1 due to the fact that s p 2 hybridization is highly unfavorable for Si. A possible way to stabilize a Si cage is to introduce a guest atom inside the cage, as suggested by recent experimental2 and theoretical works.2– 6 These studies have demonstrated that the encapsulation of transition metal atoms 共TMAs兲 leads to stable Si cages whose structure depends on many factors. Among these, the most important ones were found to be the 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 共i.e., the number of the Si atoms兲.5,6 The filling factor of the d band of the TMA seems to be responsible for the symmetry of the ground state structure formed by the metal-encapsulated Si cage.6 Computationally, much work has been done in this field of research. Hiura et al.2 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 for metal encapsulated Si cage clusters from ab initio pseudopotential plane wave calculations using density functional theory in the generalized gradient approximation for the exchange-correlation energy.3 0163-1829/2003/68共12兲/125407共5兲/$20.00

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兲 in the cubic, fullerenelike, decahedral and FrankKasper-polyhedron type of geometry.4 The theoretical calculations of Andriotis et al, however, 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 to its size.5,6 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 Al12X(X⫽Si, Ge, Sn, Pb兲 and Ba@Si20 . 7 An interesting feature of the TMA-encapsulated Si clusters was reported recently by Andriotis and co-workers.5,6 In particular, they showed that Si nanotubes 共NTs兲 can be stabilized by the encapsulation of a linear chain of TMAs. The most interesting feature of their work is the profound effect of the type of TMA on the symmetry of the Si-NT. Specifically, it was shown that a chain of TMAs of the late 3d series 共e.g., a chain of Ni atoms兲 stabilizes a Si-NT with a C 5 v symmetry, while a chain of TMAs belonging to early 3d series 共e.g., a chain of V atoms兲 stabilizes a Si-NT in the C 6 v symmetry. It is worth noting that in both these cases the Si-NTs exhibit small energy gaps at the Fermi energy E F , which become vanishingly small as the length of the tube becomes infinite. A similar length dependence was also found in subsequent investigations.8,9 A detailed analysis of the electron density of states 共DOS兲 of these systems has revealed that the contribution of the d orbitals to the electron DOS at the Fermi energy, ␳ (E F ), is vanishingly small in the case of the encapsulated Ni chain but quite pronounced in the case of the V chain. Another interesting feature of the encapsulation process, namely, the reduction in the magnetic moment of the TMA cluster upon encapsulation by a Si or C cage, was also reported by us recently.10

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MPOURMPAKIS, FROUDAKIS, ANDRIOTIS, AND MENON

FIG. 1. Minimum energy structures for the trimer Si2 Fe with distances given in Å.

In the present work, we report results of our detailed investigations of structural and magnetic properties on FeSin , n⫽1, 2, 5, 6, 10, 12, and 14, using ab initio calculations. Fe-encapsulated Si cages appear to be the ideal systems for justifying the conclusions of our previous investigations dealing with Ni and V encapsulated Si cages. This is because Fe belongs close to the middle of the 3d series in the Periodic Table and, therefore, is expected to show tendencies to form clusters either with C 5 v or C 6 v symmetry. Our calculations were performed using the density functional theory at the B3LYP level of approximation and the LANL2DZ basis sets using the Gaussian program package.11 All the clusters were fully relaxed with no symmetry constraints. II. RESULTS A. Sin Fe clusters

SiFe and Si 2 Fe clusters: The SiFe dimer is found to be stable, having a spin multiplicity of 5 and is well separated from states of lower multiplicity. The binding energy 共BE兲共Ref. 20兲 is ⫺1.93 eV and the highest occupied molecular orbital—lowest unoccupied molecular orbital gap 共HLg兲 is found to be 1.63 eV. At the equilibrium geometry the Fe-Si bond length is 2.33 Å. For the Si2 Fe trimmer, we performed structural optimizations to determine all possible minimum energy configurations 共Fig. 1兲. The ground state is a triangle of C 2 v symmetry having the Fe-Si bond distances all equal 关Fig. 1共a兲兴. The multiplicity of the system is 3 and is almost isoenergetic to the state of multiplicity 5 (⌬E⫽0.0005 eV). The HLg is ⫹1.5 eV and the binding energy per atom 共BE/atom兲共Ref. 21兲 is ⫺1.83 eV. Noting that the isomers shown in Figs. 1共a兲, 1共c兲, and 1共d兲 have the Fe atom bonded to two Si atoms and each of the Si2 Fe cluster has the same spin multiplicity (2S⫹1⫽3), we performed an orbital analysis to see if there are any differences in their bonding. We find that in the closed triangular structure 关Fig. 1共a兲兴 which is the ground state, the bonds between Fe and the Si atoms are formed between the d z 2 orbital of Fe and either the s, p z or the s p z hybridized orbital of each Si.22 The total spin of the system derives its contribution mainly from the d xz , d yz , and d xy orbitals of Fe. Another stable open triangular structure with a binding energy only 0.75 eV higher is shown in Fig. 1共b兲. The linear

FIG. 2. Lowest energy structures for Si5 Fe. Structure 共b兲 lies 0.2 eV higher than the ground state 共a兲.

structure 关Fig. 1共c兲兴, which is a transition state, has bonding features similar to that of the ground state and is higher in energy 共by 3.01 eV兲 when compared with the ground state. The d z 2 orbital of Fe again plays a major role in the bonding and is combined with the sp z hybridized orbital of each Si. Contrary to the structure in Fig. 1共a兲, the total spin of the structure in Fig. 1共c兲 comes mainly from the p orbitals of the Si atoms 共75% p y , 25% p x orbitals of Si atoms兲. In the open triangular structure shown in Fig. 1共d兲, which lies very high in energy 共by 1.99 eV compared to the ground state兲, the character of d z 2 orbital decreases in forming the bond, while those of d x 2 ⫺y 2 and d yz increase. The bonding molecular orbitals are formed by hybridized d z 2 , d x 2 ⫺y 2 and d yz orbitals of Fe combined with s, p x , p z , or hybridized sp x p z orbitals of each Si. Once again, the total spin comes mainly from the p orbitals of the Si atoms (p x , p y and p z ). In these C 2 v symmetry systems the magnetic moments of the Si atoms are aligned anti-ferromagnetically with respect to that of the TMA.10 These results are in agreement with our previous work,6,12 where it was demonstrated that the symmetry and the magnetic moment of the ground state structure of the Si based cages and TMA encapsulated Si NT’s depend strongly on the filling factor of the d band of the TMA. Figure 1共e兲 shows another stable structure that lies 1.61 eV/atom higher in energy compared to the ground state. Si 5 Fe and Si 6 Fe clusters: For the Si5 Fe cluster, the starting configuration with C 5 v symmetry resulted in the two structures shown in Fig. 2 on relaxation. The ground state is a rhombic bipyramid with the Fe atom on top. The spin state of the ground state is a triplet with a HLg of more than 2 eV and BE/atom⫽⫺2.9 eV. For the Si6 Fe system we performed relaxation on the initial geometry with C 6 v symmetry. Two possible minimum energy structures were obtained as shown in Figs. 3共a兲 and 3共b兲. The ground state obtained is an armchair structure having the Fe atom on top 关Fig. 3共a兲兴. This system has a spin multiplicity of 3 with a HLg of more than 2 eV and BE/atom⫽⫺2.5 eV. The remarkable stability of this structure provides evidence that stable Si nanotubes can be constructed by combining layers of armchair like Si structures with a TM included between them. Xiao et al.13 performed similar calculations using the B3LYP density functional method in the Si6 Cu system. They found that the ground state of that system was similar to the structure shown in Fig. 3共b兲 with the Cu atom replacing Fe. We also obtained an

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Fe ENCAPSULATION BY SILICON CLUSTERS . . .

FIG. 3. Lowest energy structures for Si6 Fe. The 共b兲 and 共c兲 structures lie 0.7 and 1.6 eV higher, respectively, when compared to the ground state 共a兲.

octahedral structure to be a local minimum for the Si6 Fe cluster 关Fig. 3共c兲兴. B. Fe-encapsulated Si cage clusters

Si 10Fe, Si 12Fe clusters: Si10Fe is a strong candidate for constructing a stable nanotube. Using initial geometries of D 5h and D 5d symmetry, two possible relaxed structures were obtained. The ground state 关shown in Fig. 4共a兲兴 is of D 5h symmetry having two Si pentagons in eclipsed positions with respect to each other and encapsulating the Fe atom. The spin multiplicity of this structure is 5, the HLg is more than 1 eV, and the BE/atom⫽⫺2.82 eV. In a recently reported work, Lu and Nagase14 using the same method and basis set, found this system to have a magnetic moment of 2 ␮ B 共the spin multiplicity is 3兲, a HLg of 0.25 eV 共calculated using the non hybrid BLYP functional兲, a binding energy with values similar to ours, and a charge transfer towards the Fe atom of 0.80 兩 e 兩 . The differences in the multiplicity values between our result and that in Ref. 14 may be attributed to the different values of the distances between Fe atom and the pentagons. This can lead to different stationary points and, therefore, a more accurate relaxation process is necessary in order to locate the ground state. The structure shown in Fig. 4共b兲 is a symmetric one, which illustrates the tendency of an Fe atom to bond with even more Si atoms in order to form a closed cage structure. The ground state of Si10Fe is the first structure in which strong charge transfer is observed. In all previous structures investigated, the charge transfer was negligible. In this system the Fe atom gains almost four electrons from the two pentagons 共two from each兲. The case of Si12Fe cluster provides additional support for stable Fe encapsulated Si nanotubes. Using initial geometries with D 6h , D 6d , D 5h , and D 5d symmetries, obtained by cap-

FIG. 4. Lowest energy structures for Si10Fe. Structure 共b兲 lies 1.1 eV higher in energy when compared to the ground state 共a兲.

FIG. 5. Lowest energy structures for Si12Fe. Structure 共b兲 lies 1.2 eV higher than the ground state 共a兲.

ping each of the Si pentagons in Fig. 4 by a Si atom, we obtained two relaxed structures. The ground state structure 关shown in Fig. 5共a兲兴 has D 6h symmetry with two Si hexagons in eclipsed positions relative to each other and encapsulating the Fe atom. The spin state of the system is found to be a triplet, the HLg is 1.1 eV and the BE/n is ⫺2.93 eV. The structure shown in Fig. 5共b兲 is an asymmetric one, showing an affinity to form two pentagons by pushing out the two Si atoms. A significant charge transfer is also observed when compared with the case of Si10Fe cluster, with the Fe atom gaining 2.7 electrons. Si 14Fe cluster: Our final investigation involves the study of the Si14Fe cluster. The initial geometry used for this system had D 6h and D 6d symmetries with two Si hexagons facing each other in eclipsed and staggered configurations and each hexagon capped with a Si atom. These initial conditions resulted in three possible minima, as illustrated in Fig. 6. The ground state is a symmetric structure which contains mainly Si pentagons and a rhombic base encapsulating the Fe atom. The spin multiplicity of this system is 3 but the singlet spin state lies only 0.08 eV higher in energy. The HLg is 1.3 eV and the BE/atom is ⫺2.93 eV. The second possible structure is 0.6 eV higher in energy. The orientation of the Si atoms surrounding the Fe atom is the same as the ground state of the WSi14 system reported by Lu and Nagase.14 The third structure, which is a symmetric body-centered-cubic packing, lies 1.6 eV higher in energy. This structure was predicted to be the ground state by Kumar and Kawazoe3 using pseudopotential plane wave calculations making use of generalized gradient approximation for the exchange correlation energy. By contrast, we found two additional relaxed structures that are lower in energy.

FIG. 6. Lowest energy structures for Si14Fe. The 共b兲 and 共c兲 structures lie, respectively, 0.6 and 1.6 eV higher than the ground state 共a兲.

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MPOURMPAKIS, FROUDAKIS, ANDRIOTIS, AND MENON III. DISCUSSION AND CONCLUSIONS

We have presented results of our detailed investigations of structural and magnetic properties on FeSin clusters. The results presented can be summarized through the following salient points. 共i兲

共ii兲共iii兲

共iv兲

Encapsulation of Fe by Si leads to Fe-encapsulated cage clusters with both C 5 (D 5 ) and C 6 (D 6 ) symmetries provided the number of Si atoms is large enough. The smallest Fe encapsulated Si cage cluster is determined to be Si10Fe and stable Sin Fe clusters will always have Fe encapsulated for n⬎10. The spin-multiplicity 共and, therefore, the effective magnetic moment兲 of the system decreases as the total number of Si atoms of the system increases. Si ‘‘gives’’ electron density to Fe. Charge transfer increases as the number of Si atoms increases. The strongest charge transfer is observed in the cases of Si10Fe, Si12Fe and Si14Fe clusters due to the fact that the coordination number of the Fe atom is large and electron density can be gained easily. All observed clusters are stable; they all have a HLg larger than 1 eV.

Not surprisingly, since Fe lies near the center of the 3d series in the Periodic table, Fe-encapsulated Si cages show a tendency to form structures with both C 5 and C 6 symmetries. This result provides further support to our previous conclusions, according to which the d-band filling factor plays a dominant role in the stability, the symmetry and the magnetic configuration of Si cages encapsulating transition metal atoms. This is mainly due to the symmetry dependence of the hybridization process and—based on this—to the type of bonds that become available due to the degree of filling these orbitals. A small d-band filling can lead to strong ␴ and ␲ type of bonds between Fe and the surrounding Si atoms. A large d-band filling, on the other hand, usually leads to weaker ␦ type of bonding. We, thus, see a delicate interplay between the attainable symmetry and the d-band filling factor of the TMA in the process of forming stable TMencapsulating Si cages. The outcome of this process has a significant effect on the magnetic properties of these clusters.

ACKNOWLEDGMENTS

The present work was supported through grants by EUGROWTH research Project No. AMMARE 共G5RD-CT2001-00478兲, NSF Grant No. 共NER-0165121, ITR0221916兲, DOE Grant No. 共00-63857兲, NASA Grant No. 共00-463937兲, and the Kentucky Science and Technology Corporation.

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*Electronic address: [email protected] †

As shown by us,15 the relative orientation between the magnetic moments of the encapsulated TMA and those of its neighboring Si atoms exhibits an antiferromagnetic alignment if the TMA belongs to the early 3d series; it shows a ferromagnetic alignment if the TMA belongs to the late 3d series. As a result, the effective value of the magnetic moment of the encapsulated TMA may appear to be enhanced or reduced. This is clearly justified in the case of Si10Fe and Si12Fe clusters where we find a ferromagnetic alignment in the former (C 5 symmetry兲 and an antiferromagnetic alignment in the latter (C 6 symmetry兲. It may be argued that the enhancement or the reduction of the magnetic moment of the encapsulated TMA is due solely to its dependence on symmetry, and consequently the result of the spin-orbit 共SO兲 interaction.16 –19 The small contribution of the SO interaction in the case of the 3d elements, however, seems to advocate this effect in favor of the d-band filling factor. The SO interaction may have an additional but of less importance contribution. It should also be noted that as the number of Si atoms increases, the energy difference between the states of various spin multiplicity decreases. This necessitates a detailed search of the configuration space in order to locate the true ground state of these clusters, as shown in the case of the Si14Fe cluster for which a new ground state energetically more favorable 共by 1.6 eV兲 than previously reported3 was found in the present work. The present results also indicate that Fe-encapsulated Sibased nanotubes may be stabilized in a way analogous to that described in the case of encapsulated V and Ni atomic chains.5,6 In particular, the Si10Fe and Si12Fe clusters can be used as building blocks to form nanotubes of the types Si5n Fen⫺1 and Si6n Fen⫺1 , respectively.

Electronic address: [email protected] ‡ Electronic address: [email protected] 1 M. Menon and K.R. Subbaswamy Chem. Phys. Lett. 219, 219 共1994兲. 2 H. Hiura, T. Miyazaki, and T. Kanayama, Phys. Rev. Lett. 86, 1733 共2001兲. 3 V. Kumar and Y. Kawazoe, Phys. Rev. Lett. 87, 045503 共2001兲. 4 V. Kumar and Y. Kawazoe, Phys. Rev. B 65, 073404 共2002兲. 5 M. Menon, A.N. Andriotis, and G. Froudakis, Nanoletters 2, 301 共2002兲. 6 A. N. Andriotis, G. Mpourmpakis, G. Froudakis, and M. Menon, New J. Phys. 4, 78 共2002兲. 7 Q. Sun, Q. Wang, P. Jena, B.K. Rao, and Y. Kawazoe, Phys. Rev. Lett. 90, 135503 共2003兲.

U. Landman, R.N. Barnett, A.G. Scherbakov, and P. Avouris, Phys. Rev. Lett. 85, 1958 共2000兲. 9 B.X. Li, P.L. Cao, R.Q. Zhang, and S.T. Lee, Phys. Rev. B 65, 125305 共2002兲. 10 G. Mpourmpakis, G. Froudakis, A. N. Andriotis, and M. Menon 共unpublished兲. 11 M.J. Frisch et al., Gaussian 98 共Revision A.11兲共1998兲. 12 G. Mpourmpakis, A. N. Andriotis, G. Froudakis, and M. Menon 共unpublished兲. 13 I.V. Ovcharenko, W.A.L. Jr., C. Xiao, and F. Hagelberg, J. Chem. Phys. 114, 9028 共2001兲. 14 J. Lu and S. Nagase, Phys. Rev. Lett. 90, 115506 共2003兲. 15 A.N. Andriotis, G. Mpourmpakis, G. Froudakis, and M. Menon 共unpublished兲.

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Fe ENCAPSULATION BY SILICON CLUSTERS . . . 16

S.H. Baker, C. Binns, K.W. Edmonds, M.J. Maher, S.C. Thornton, S. Louch, and S.S. Dhesi, J. Magn. Magn. Mater. 247, 19 共2002兲. 17 C. Binns, S. Louch, S.H. Baker, K.W. Edmonds, M.J. Maher, and S.C. Thornton, The Magnetic Recording Conference 共Minnesota兲共August 2001兲. 18 Y. Xie and J.A. Blackman, Phys. Rev. B 66, 155417 共2002兲.

S. Dennler, J. Morillo, and G. M. Pastor 共unpublished兲. We define the binding energy 共BE兲 for a Sin Fe cluster as E(Sin Fe)-n*E(Si)-E(Fe). 21 The BE/atom for a Sin Fe cluster is defined as BE/(n⫹1). 22 The z axis has been taken along the line bisecting the angle SiFe-Si. 19 20

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