Single-ion anisotropy in a four-spin system: mixing of S-states

A four-spin system with s=1 and the single-ion anisotropy, D∑ _j [s _jz ] ² , is considered. When D≠0 the Hamiltonian of the system does not commute with S ² and, therefore, S cannot be used as an additional label of energy levels. In this work we concentrate on the problem of mixing states with different total spins S. The Hamiltonian matrix is transformed to the symmetry-adapted basis (with subspaces labeled by the irreducible representations of the symmetry group) and next, after solving the eigenproblem for S ², to the basis with vectors labeled by S. Each eigenproblem is solved exactly (at least numerically) and the eigenstates are expressed as ∑ _S a _S |S〉. The coefficients a_S are analyzed, especially for their D-dependence. Even in such a small system different schemes of level mixing can be observed.