Abstract
The current focus of material science researchers is on the magnetic behavior of transition metal clusters due to its great hope for future technological applications. It is common knowledge that the 4d transition elements are not magnetic at their bulk size. However, studies indicate that their magnetic properties are strongly dependent on their cluster sizes. This study attempts to identify magnetic properties of 4d transition metal clusters. Using a tight-binding Friedel model for the density of d-electron states, we investigated the critical size for the magnetic-nonmagnetic transition of 4d transition-metal clusters. Approaching to the critical point, the density of states of the cluster near the Fermi level is higher than and the discrete energy levels form a quasi-continuous band. Where is correlation integral. In order to determine the critical size, we considered a square shape band and fcc, bcc, icosahedral and cuboctahedral close-packed structures of the clusters. We also investigated this size dependent magnetic behavior using Heisenberg model. Taking some quantum mechanical approximations in to consideration, we determined magnetic behavior of the clusters. For practicality, we considered three clusters of transition metals (Ru, Rh and Pd) and the obtained results are in line with the results of previous studies.
Highlights
It can be reckoned that magnetic properties of clusters of transition metal atoms are dependent on different internal factors such as the bond length, number of nearest neighbor interactions with the d-band electrons, the number of atoms in the cluster (N) and the symmetry of the cluster
One of the fundamental problems of the Heisenberg theory of ferromagnetism is how to determine the characteristic values of the considered Hamiltonian and the energy states belonging to various resultant spins of the cluster
We studied the magnetic to non-magnetic transition of 4d transition metal by using tight binding
Summary
It can be reckoned that magnetic properties of clusters of transition metal atoms are dependent on different internal factors such as the bond length, number of nearest neighbor interactions with the d-band electrons, the number of atoms in the cluster (N) and the symmetry of the cluster. The astonishing magnetic and electronic properties of transition metal clusters have greatly attracted the attention of researchers in the area in the last decade [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. These mysterious properties are results of a transition from bonds to bands as the atoms form clusters and become the bulk solid. Using well known approximations and criterion we determined the critical size of the materials and investigated their magnetic behaviors
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