Noncollinear magnetic order in antiferromagnetic and weak-ferromagnetic transition-metal clusters

The magnetic properties of transition-metal clusters having N≤19 atoms are determined using a d-band model Hamiltonian within the unrestricted Hartree–Fock approximation, which allows noncollinear magnetic arrangements of the local magnetic moments μ→l at different cluster atoms l. Results are given for μ→l and for the average magnetic moment per atom μN=(1/N)|∑lμ→l| as a function of d-band filling, nd, and J/W (J refers to the d-electron effective exchange integral and W to the d-band width). It is shown that compact clusters near half-band filling present antiferromagnetic-like noncollinear magnetic arrangements, which attempt to minimize antiferromagnetic frustration in nonbipartite structures. The resulting μN are very small, in agreement with experiments in CrN clusters (typically μN≤0.5μB for N≤19). For nd≃6.5–7 as a function of J/W, the clusters undergo a transition from antiferromagnetic- to ferromagnetic-like orders. Thereby a novel physical picture for the onset of ferromagnetism is discussed. Comparison is made with the available noncollinear ab initio results.