Ab initio study of free and deposited transition metal clusters

TLDR: In this article, the authors studied the properties of transition metal (TM) clusters and cluster related phenomena using the density functional theory total energy formalism through the Kohn-Sham approach and found that TM clusters have the advantage of developing magnetic moments.

Abstract: Transition metal (TM) clusters occupy an important role in the class of materials projected for nano applications. In addition to the unusual properties due to their cluster form, TM clusters have the advantage of developing magnetic moments. The goal of this thesis is to study the properties of clusters and cluster related phenomena. Physical properties of clusters are suitable platform to study quantum effects, which becomes prominent at such low dimensions. Thus, it is essential to study the properties of clusters using first-principles methods because they cannot be easily handeled by empirical approaches. The present thesis deals with the density functional theory total energy formalism through the Kohn-Sham approach. The many-body correlation effects are accounted for the generalized gradient approximation (GGA) which has been successful in describing the properties of materials, especially metals. The ground state structure of various sizes of elemental and binary TM clusters is studied. One of the main observation is that the icosahedron is one of the most stable geometries for 13-atom elemental (Fe, Co, Ni) clusters. For large Fe clusters with regular icosahedron geometry, the core of the cluster relaxes towards the cuboctahedral geometry. For all sizes, after geometrical optimization, we find slight structural distortions. This is associated with the physics of Jahn-Teller effect. We observe that the Jahn-Teller effect is more prominent in Fe clusters as compared to Ni and Co clusters. Also, the evolution of magnetic moment with cluster size is studied. The clusters show enhanced magnetic moment which is inversely related to the cluster size. The magnetic moment versus cluster size obtained from calculations match very well with the experimental results. One of the main goals of studying binary cluster is to understand the site-specific occupation of atomic species in a multi-component (here binary) cluster. This is achieved this by studying the competition between chemical ordering and segregation for binary Fe-(Co, Ni, Pt) and Co-(Pt, Mn) icosahedral clusters. The energetically favorable distribution of constituent elements in binary cluster is examined for different compositions. Using the lowest energy structure so obtained, the composition-dependent mixing energy is studied. It is observed that the qualitative behavior of mixing energy with respect to composition for 13-atom Fe-Ni clusters is very similar to that of the bulk alloy. It is found that Ni atoms tend to occupy the surface sites on a cluster (segregation tendency) for Fe-rich and Ni-rich compositions. This appears to be a common trend which has been verified for both 13- and 55-atom clusters. Owing to heavy computational demand, we have verified the trend at some specific compositions for 55-atom clusters. Magnetic properties like the orbital magnetic moment and the magnetic anisotropy are studied for free and deposited clusters. 13- and 55-atom icosahedral clusters of Fe, Ni and Co are deposited on the substrates like Pt(111) and Pt(001) for these studies. Both the free clusters and the deposited clusters are observed to exhibit large magnetic anisotropy as compared to that of the respective bulk metals. The angle (angle between magnetization and the spin-quantization axis) dependent anisotropy energy is calculated from DFT and then fitted to the classical Heisenberg model containing an anisotropy term. Large values of magnetic anisotropy energy are found for relaxed clusters as compared to perfect clusters because of the structural symmetry-breaking. In addition to its structural and magnetic properties, transition metal clusters are attractive candidates for catalysis. In principle, the catalysis can be studied by estimating the activation energy barrier of various paths of a reaction by nudged elastic band method. There are studies in literature of the catalytic properties of TM clusters (for example Fe and Pt) for the oxidation of carbon monoxide to carbon-dioxide on graphene surface. We have attempted to study the oxidation of carbon monoxide on graphene surface. The goal is to understand the role of TM clusters in reducing the activation barrier of the chemical reaction and to derive the possible reaction paths. Presently, the proper site for adsorption of CO molecule on free and graphene-supported TM clusters are identified within the accuracy of GGA. From another aspect, we tried to extrapolate the magnetic properties of clusters to finite temperature using the exact diagonalization technique. We have only studied the magnetic properties of 4- and 13-atom clusters. The exact diagonalization method is applied to the quantum Heisenberg Hamiltonian with nearest-neighbor spin-interactions. The role of dipolar interaction and local uniaxial anisotropy terms in the Heisenberg Hamiltonian are taken into account which has non-negligible contribution for clusters. We observe discontinuities in the magnetization with change in external magnetic field for clusters with antiferromagnetic interactions, which is unlike for clusters with ferromagnetic interaction. The ground state and the temperature-dependent spin-spin correlation functions are also studied. The findings of these studies for elemental and binary clusters like the size-dependent structural and magnetic properties, the composition-dependent atomic distributions of multi-component clusters (segregation), magnetic anisotropy of free and supported TM clusters are expected to shed light on the understanding of physics of clusters in general and may be helpful for experimentalists.