Physics of Nickel Clusters. 2. Electronic Structure and Magnetic Properties

Abstract

Using a combination of classical molecular dynamics simulation and first principles molecular orbital theory, we provide the first comprehensive study of the equilibrium geometries, energetics, electronic structure, vertical ionization potential, and magnetic properties of Ni clusters containing up to 21 atoms. The molecular dynamics simulation makes use of a tight binding many-body potential, while the calculations based on molecular orbital theory are carried out self-consistently using the numerical atomic bases and the density functional theory. The adequacy of the molecular dynamics results on the energetics and equilibrium geometries is tested by comparing the results with those obtained from the self-consistent molecular orbital theory for clusters of up to six atoms. For larger clusters, equilibrium geometries were obtained from molecular dynamics simulation, and their electronic structure and properties were calculated using molecular orbital theory without further geometry reoptimization. Frozen core and local spin density approximations were used in the molecular orbital calculations. In small clusters (n ≤ 6), the calculations were repeated by including all electrons and the gradient correction to the exchange−correlation potential. The calculated vertical ionization potential and magnetic moments of Ni clusters are compared with recent experimental data.

A Magnetic Study of Low Moment Nickel Clusters Formed from the Solid-State Decomposition Reaction of Nickel bis-1,5-Cyclooctadiene

“…Khanna et al modelled the magnetic moment of clusters using a Langevin function where they predicted that the moment rose as n → 2 however there were variations in the moment due to different geometries causing different surface areas for each value of n. Khanna et al also comment on other predictions of the calculations of magnetic moment carried out by other groups stating that discrepancies may arise if the atomic spacing is considered to be similar to the bulk metal as the clusters moment will be sensitive to the local geometry and exchange distances. Khanna and Reuse used the local density approximation to calculate that for, Ni 3 , the moment per atom will equal 0.6 µ B and for Ni 5 , 1.6 µ B which is close to an experimental result of 1.8 µ B obtained by Reddy et al [20] and Reuse and Khanna [22] . Khanna et al have also reported that the electronic structure shows band-like behaviour at n = 14 suggesting a similarity to bulk behaviour which is radically different to prior experimental data.…”

“…For the case of the 2 K results, the best fit to the data was achieved with a combination of two Langevin functions, which suggests that superparamagnetic nanoparticles are primarily responsible for the paramagnetic response. However, the Langevin function has also been used to describe the low temperature magnetic response of clusters of sub-nanometer scale [20,17,26,27]. The fitting function is given in equation 1, where N is the number of particles per kilogram, µ is the relative magnetic moment, µ B is the Bohr magneton and k B is the Boltzmann constant.…”

“…It is important to note that it was necessary to record the image in a few seconds because further irradiation with the electron beam resulted in the formation of an assembly of nanoparticles; bright Field and Dark Field TEM images of these e-beam induced particles show that their sizes vary from 2 -10 nm (see Supplementary Information). Their growth may be due to the electron beam providing thermal energy into the matrix allowing the the Ni clusters to combine and form a larger bulk FCC Ni particle [20]. Electron diffraction patterns (see supplementary information) taken after exposure to the beam indicate crystalline FCC Ni particles do form [37], where the lattice parameters are slightly larger than bulk values, suggesting that there may be a large amount of surface strain on the Ni nanoparticles.…”

“…Theoretical studies have also been carried out on Ni clusters to provide insight into the geometry and moment of individual clusters [20,21]. Khanna et al modelled the magnetic moment of clusters using a Langevin function where they predicted that the moment rose as n → 2 however there were variations in the moment due to different geometries causing different surface areas for each value of n. Khanna et al also comment on other predictions of the calculations of magnetic moment carried out by other groups stating that discrepancies may arise if the atomic spacing is considered to be similar to the bulk metal as the clusters moment will be sensitive to the local geometry and exchange distances.…”

Orbital polarization, surface enhancement and quantum confinement in nanocluster magnetism

“…Comparison with first-principles results serves as a critical justification of our TB parametrization scheme. Figure 3 compares our results with those given by Reddy et al, 10 who, using first-principles molecular-orbital theory, studied the magnetic properties of Ni clusters in most detail. For Ni n with nϭ9 -14, and nϭ19, our spin 's are in perfect agreement with their results.…”