The Stability And Magnetic Moments Of Bi_mCo_n Clusters: A Study Based On Density Function Theory

In recent years, the study of binary clusters formed by transition metals and either metals or nonmetals has been a very active research field. Taking into account the fact that transition metal clusters have stronger magnetic properties, people have investigated novel properties of clusters that transition metal atoms doped in other clusters. Bismuth (Bi) is a semi-metal, with a relatively small effective mass, a highly anisotropic Fermi surface, a small band overlap energy, and many other unusual electronic properties. Clusters containing Bi therefore provide an ideal model system for the study of many physical phenomenon. The structures and physical properties of these small clusters that Co, Mn, and Dy etc doped in Bi cluster have also attracted the attention of many theorists.In the present paper, we continue the study of transition metal cobalt clusters containing bismuth using density functional theory. Exchange and correlations are treated within the generalized gradient approximation (GGA) of Becke exchange plus Perdew correlation (BP). The double-numerical basis set with polarized functions (DNP) is used to study the evolution of the nature of BiCo binary clusters as the cluster size is changed. Taking into account that bismuth is a heavy metal, we have adopted the effective core potential (ECP) to calculate the properties of Bi_mCo (m = 1-12) and Bi_mCo₂ (m = 1-8) clusters. The most probable low-energy structures were found following an extensive search based on the low-energy structures of pure bismuth clusters. Through global optimization using spin-polarized wave functions with no symmetry restrictions, we have identified the ground state structures of Bi_mCo (m = 1-12) and Bi_mCo₂ (m = 1-8) clusters. Analysis of their electronic structures and magnetic properties, and comparison with the corresponding experimental results have shown that:1. As for the growth pattern of Bi_mCo (m = 1-12) and Bi_mCo₂ (m = 1-8) clusters, it is amorphous. Cobalt atoms doped in Bi cluster is partial to lie in the center or symmetry axis of cluster. Cobalt atoms are inclined to three-coordinate with Bi atoms. The binding energy of bismuth clusters is reduced significantly as a result of doping with a single cobalt atom. Clusters doped with two cobalt atoms have their structural stability further enhanced compared to pure Bi clusters with the same total number of atoms.2. By calculating the numerical second derivative of the binding energies of Bi_mCo (m = 1-12) clusters we show that: Bi₂Co, Bi₄Co, Bi₆Co, Bi₉Co, Bi₁₀Co are magic number clusters in stability. As for Bi_mCo₂ (m = 1-8) clusters, Bi₂Co₂, Bi₄Co₂ and Bi₇Co₂ are magic number clusters in structure stability. Noting that the magic numbers for pure Bi clusters are all even numbers, it may be seen that doping with cobalt induces changes in the magic numbers.3. The odd-even oscillations of the HOMO-LUMO Gaps of pure bismuth clusters are changed in cobalt-doped clusters. Overall the magnitude of the oscillations decreases with increasing cluster sizes. The magnitude of change with two cobalts doped in Bi_n cluster decreases more obviously with increasing cluster sizes, which indicates some smaller Bi_n cluster with less cobalts doped performs in the role of metal, some performs in the role of semiconductor. It changes to semi-metallic of block during the oscillations changes.4. The total spin magnetic moments of Bi_mCo (m =1-12) clusters with a single doped cobalt atom are no longer the same as those of pure bismuth clusters, showing changes in the odd-even oscillation. The change in the trends of the spin magnetic moments of the Bi_mCo (m = 1-12) clusters is parallel to the changes in the trends in the spin magnetic moments of the cobalt atoms. For Bi_mCo₂ (m = 1 -8) clusters, the total spin magnetic moment changes have the same trends as the spin magnetic moments of the cobalt atoms in the Bi_mCo₂ (m = 1 -8) clusters. This is in agreement with corresponding experimental results, and implies that the spin magnetic moments of bismuth-cobalt clusters arise mainly from the spin magnetic moments of the cobalt atoms.