The First-principle Studies Of Geometrical Structure, Electronic Structure, And Magnetism Of Transition Metal Clusters

The field of transition metal (TM) nanostructures has become one of the most impor-tant issues in nanotechnology due to possible important applications in electronic devices,magnetic recording, effective catalysis, optical communication and so on. Due to the largesurface to volume ratio, small TM clusters show a different magnetic behavior from that ofthe corresponding bulk. Although the ferromagnetism bulk is only find in Fe, Co, Ni ele-mental material, previous studies indicate that most TM clusters do exhibit high magneticmoments, especially for 4d and 5d elemental clusters. The geometrical evolution, electronicstructure, and magnetism of small TM clusters are investigated in this thesis, and we mainlyconcern the following contents: 1. Theoretical study of geometrical evolution and magnetism of group-III clusters. More recently, Knickelbein has measured the magnetic moments of Sc_n, Y_n, and La_n(n = 5 - 20) clusters in the Stern- Gerlach molecular-beam deffection experiment, whereasfor scandium and yttrium clusters, until now, there are no systematical theoretical calcula-tions on their structures, stabilities, and magnetic properties. With this in mind, we performan extensive study on the evolution of the structural and electronic properties as well asmagnetism for Scn and Yn clusters up to n = 17 by using a fully self-consistent density-functional-theory (DFT) based method. The calculated results show that the structural evo-lution of yttrium and scandium clusters favors a compact and icosahedral structural growthpattern, and Sc₁₃ and Y₁₃ clusters adopt the Ih icosahedron structure. The group-III elemen-tal clusters with n = 7, 13 atoms have higher stability than their neighboring sizes and canbe regarded as magic number. The theoretical magnetic behavior follows the experimentaltrend qualitatively well as a function of the cluster size, including the experimentally ob-served minima and maxima (n = 6, 8, 13), and we find that Sc13 and Y13 clusters have agiant moment of 19?_B. Although our calculations overestimate these some values, the size-dependent trend is generally consistent with the experimental trend. Additionally, it is ob-served that the clusters undergo a change from ferromagnetic(FM) ordering for the smallestsizes n < 7 to antiferromagnetic(AF) ordering for the intermediate sizes n = 7-12, 15-16.The comparison between the Y_n clusters and Sc_n clusters indicates that the displayed samemagnetic features are the consequence of a similar structural motif for these two series. Ourcalculated ionization potentials (IPs) trend is qualitatively in agreement with the experimen-tal one, indicating that the structures would be close with reality and our obtained physical properties are appropriate. 2. Density-functional study of small neutral and cationic bismuth clusters Bin andBi_n⁺ (n = 2 - 24). DFT with scalar-relativistic pseudopotential(RECP) and a generalized gradient correc-tion(GGA) is used to calculate the neutral and cationic Bin clusters (n = 2-24), with the aimto elucidate their structural evolution, relative stability, and magnetic property. The structuresof neutral Bi clusters are found to be similar to that of other group-V elemental clusters, withthe extensively studied sizes of n = 4 and 8 having a tetrahedron and wedgelike structure,respectively. Generally, larger Bi clusters consist of a combination of several stable units ofBi4, Bi6, and Bi8, and they have a tendency to form an amorphous structure with the increaseof cluster sizes. The curves of second order energy difference exhibit strong odd-even alter-nations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizesare relatively stable in neutral clusters (cationic clusters). The calculated magnetic momentsare 1?_B for odd-atom clusters and zero for even-atom clusters. We propose that the differ-ence in magnetism between experiment and theory can be greatly improved by consideringthe orbital contribution. The calculated fragmentation behavior agrees well with the experi-ment, and for each cationic cluster the dissociation into Bi4 or Bi₇⁺ subclusters confirms thespecial stability of Bi₄ and Bi₇⁺ . Moreover, the bond orders and the gaps between the high-est occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMOgap) show that small Bi clusters would prefer semiconductor characters to metallicity. 3. First-principle investigation of the electronic structure and magnetism in V₁₂TMclusters. The DFT with the GGA method is adopted to study the electronic structures and mag-netic properties of V₁₃ cluster and doped V₁₂TM clusters (TM: Sc, Ti, Cr, Mn, Fe, Co, Ni,Y, Zr, Nb, Mo, Tc, Ru, Rh). The binding energy, electronic structure and magnetism of theclusters have been obtained. Further more, the information of cluster magnetism and therelationship between magnetic moments and electronic structures of clusters were analyzed.The results show that V₁₂Fe and V₁₂Ru clusters are the most stable structures which havethe closed-shell system with larger binding energies and larger HOMO-LUMO gaps. V₁₂Ycluster has a giant moment of 11?_B. The ground states of most clusters are shown to bemagnetic, but their magnetic moments are not striking. 4. Geometrical evolution, electronic structures, and magnetic properties of Bi-Mn bi- nary clusters. The geometrical evolution, electronic structures, and magnetic properties of small bi-nary clusters Bi_nMn_m (n?13, m?6) are investigated using DFT with the view ofexplaining the experimentally observed magnetic moments in these systems. The resultsdemonstrate that the magnetic moments of the dopant Mn atoms exhibit a weak dependenceon the structure, composition, and environment, holding a general constant of 4?B/atomapproximately, whereas the magnetic couplings among these Mn atoms are strongly depen-dent. We propose that the preferred ferromagnetic couplings in the dopant Mn_m componentsresult in pronounced magnetic moments represented by certain combinations in which theBi to Mn ratio is close to 2. Moreover, a faint antiferromagnetic perturbation is providedby the Bin units. The hybridization among Mn 3d, 4s, and Bi 6p induces -0.1?B on Biatoms and reduces the Mn atomic moments by 1?_B. On the whole, the calculated magnetictrends of the different composition series qualitatively fit well with experimental measure-ments. The lowest-energy structures of the clusters are segregated cases in which the dopantMn_m components assemble together, forming a pentagonal bipyramid shape and surroundedby irregular Bin components. Generally, an amorphous configuration is observed for low-Mn-concentration clusters, but the evolution of a defective polyicosahedron pattern with aMn core shell is favored for high-Mn-concentration clusters and this tendency will keep themost stable geometrical structure for larger sizes. By analyzing the binding energies andthe second-order energy differences, we find that the monatomic doping BinMn series con-taining n = 4, 6, 10, and 12 is more stable than its neighboring sizes. Furthermore, theHOMO-LUMO gaps decrease as a function of Mn concentration in the clusters, indicatingan enhancement of metallicity.