Spin correlations in the ground state of hexanuclear magnetic ring Fe6

Abstract A finite spin system invariant under a symmetry group G is a very illustrative example of the finite group action on a set of mappings f : X → Y . In the case of spin systems X is a set of spin carriers and Y contains 2 s +1 z -components − s ⩽ m ⩽ s for a given spin number s . Orbits and stabilisers are used as additional indices of the symmetry adapted basis. Their mathematical nature does not lead to smaller eigenproblems, but they label states in a systematic way. This enables us to determine eigenstates of a spin operator with high (numerical) precision. Having eigenvectors expressed as linear combinations of the so-called Ising configurations (mappings μ :{1,2,…, N }→{− s ,…, s −1, s }) their properties can be investigated. In this paper such approach is applied to the small “ferric wheel” Fe 6 : a macromolecular antiferromagnet containing six iron (III) ions with the spin number s= 5 2 . The ground state and some excited states (with the total spin S =0) are determined and spin correlations are calculated. The results obtained are compared with spin correlations in the Neel state | s ,− s , s ,− s , s ,− s 〉, the ground state of a classical antiferromagnetic system.