Structure, bonding and magnetism in cobalt clusters
📝 Abstract
The structural, electronic and magnetic properties of Co $_n$ clusters ( $n=2- $20) have been investigated using density functional theory within the pseudopotential plane wave method. An unusual hexagonal growth pattern has been observed in the intermediate size range, $n=15- $20. The cobalt atoms are ferromagnetically ordered and the calculated magnetic moments are found to be higher than that of corresponding hcp bulk value, which are in good agreement with the recent Stern-Gerlach experiments. The average coordination number is found to dominate over the average bond length to determine the effective hybridization and consequently the cluster magnetic moment.
💡 Analysis
The structural, electronic and magnetic properties of Co $_n$ clusters ( $n=2- $20) have been investigated using density functional theory within the pseudopotential plane wave method. An unusual hexagonal growth pattern has been observed in the intermediate size range, $n=15- $20. The cobalt atoms are ferromagnetically ordered and the calculated magnetic moments are found to be higher than that of corresponding hcp bulk value, which are in good agreement with the recent Stern-Gerlach experiments. The average coordination number is found to dominate over the average bond length to determine the effective hybridization and consequently the cluster magnetic moment.
📄 Content
Study of finite size clusters is an important means of understanding how magnetic behavior evolves in reduced dimensionality. The 3d transition metal (TM) elements are characterized by their unfilled d-shell, which gives rise to their magnetism and many other interesting physical and chemical properties. Early transition metals are nonmagnetic in bulk solids, and only Fe, Co and Ni are known to be ferromagnetic among the 3d metals. However, the small clusters of all the early transition metals are magnetic and those of late transition metals possess magnetic moments enhanced from their bulk values due to their spatial confinement. Local spin density based calculation 1 showed that the face centered cubic (fcc) phase is the lowest energy state for bulk Co in the paramagnetic phase, whereas the magnetic order stabilizes the hexagonal close packed (hcp) phase as the ground state. This indicates a strong correlation between the stable structure and magnetism. Although, a metastable antiferromagnetic state exists for bulk Co, the ferromagnetic state is found to be the most stable for all crystal structures. This is unlike other 3d transition metals Cr, Mn, and Fe which have a stable antiferromagnetic structure in their fcc phase. This means that not only the crystal structure, but also the electronic configuration controls magnetism. In the present communication, we focus on Co n clusters to understand this interplay.
The magnetic properties of bare Co n clusters were first investigated via Stern-Gerlach (SG) molecular beam deflection experiment by Bloomfield and co-workers for Co 20 -Co 215 clusters 2,3 and by de Heer and co-workers for Co 30 -Co 300 clusters. 4,5,6 These studies showed that in the temperature range of 77-300 K, the Co n clusters display high-field deflections, which are characteristic of superparamagnetic behavior. The superparamagnetic model for free clusters was recently revisited by Xu et al. 7 and they proposed that adiabatic magnetiza-tion together with avoided Zeeman levels crossing in isolated clusters can lead to the same high-field beam deflection behavior as observed in the superparamagnetic spin relaxation. However, both the models predict the same high temperature limiting form for magnetization as given by the Curie law, 7,8 M = µ 2 B/3kT , where µ is the cluster magnetic moment, B is the magnetic field and T is the cluster temperature. The intrinsic per-atom magnetic moment for small Co n clusters was found to be substantially larger than the bulk value 2,3,4,5,6,7,8 and generally decreases with increasing cluster size, eventually reaching the bulk value at ∼ 500 atoms. 4 The enhancement in the magnetic moment in small clusters has been attributed to the lower coordination of the surface atoms resulting in a narrowing of the d-bands and hence greater spin polarization.
Information on the ground state geometry of the transition metal clusters is usually obtained from the experiments involving chemical probe methods and photoelectron spectroscopy, though, such studies for the Co n clusters are very limited and not definitive. Reactions of Co n clusters with ammonia and water 9 indicate icosahedral structures for the bare and ammoniated clusters in the size range n = 50-120 and nonicosahedral packing for small (around 19 atoms) Co n clusters. Although the structures of ammoniated Fe n , Co n and Ni n clusters in the size range of n = 19-34 atoms have been found to be polyicosahedral, 10 it has been mentioned that the bare clusters probably adopt a variety of structures. The photoionization experiment, 11 indicated icosahedral atomic shell structures for large Ni n and Co n clusters of 50-800 atoms. However, structures were not well identified for small Co n clusters (n 50) because atomic sub-shell closings in different symmetry based clusters occur in close sequences. These experimental results put together indicate that the icosahedral growth pattern for small sized Co n clusters is less evident.
Theoretical works on cobalt clusters are limited and the available results are contradictory. Li and Gu 12 performed first-principles calculation of small Co n clusters (4 n 19) using spin-polarized discrete variational method within local density functional theory (DFT). However, they had not optimized the structures and considered only some special structures with lattice parameters same as the bulk Co. Guevara et al. 13 used an unrestricted Hartree-Fock (HF) tight-binding formalism, starting from spd-bulk parameterization, but they only considered fixed body-centered cubic (bcc) and fcc geometries for a maximum of 177 atoms without structural relaxation. Andriotis and Menon 14 have used a tightbinding molecular dynamics scheme to study cobalt clusters for some selected cluster sizes. Castro et al. 15 performed all-electron density functional calculations using both local density and generalized gradient approximations. However, the size of the clusters were limited only up to 5 atoms
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