Critical Size for Magnetic–Non-magnetic Transition in Transition Metal Clusters

The magnetic–non-magnetic transition in non-magnetic 3 d and 4 d metal clusters is investigated by means of a tight-binding Friedel model of d -band and Stoner criterion. An analytic equation for the critical size has been introduced for the cluster with close-packed structure. Below the critical size, the density of states for the cluster at Fermi level D ( E F ) exceeds 1/ I ( I is the exchange-correlation integral) and the transition towards the (ferro)-magnetic behaviour takes place. Our estimation of the critical sizes for V, Cr, Rh, Ru, Pd clusters conforms to recent experiments and ab initio calculations. Furthermore, we found that the small Zr, Nb, Mo, Tc clusters are almost non-magnetic while the Y clusters up to about 90 atoms may be ferromagnetic like Rh. The prediction of the non-magnetism in Mo, Tc clusters is indirectly supported by the calculation of Mo, Tc monolayer on Ag(001) and Au(001).