Phenomenological Description of Aggregates of Exchange‐Bonded Paramagnetic Ions in Crystalline Environment. II. Microscopical Model for a Rectangular Aggregate of Four Paramagnetic Ions with Spin One Half

Abstract

AbstractThe general theory of Part I is applied to an aggregate consisting of four exchange‐bonded paramagnetic ions with spin one half forming a planar rectangle. As a zero‐order approximation, eigenvalues and eigenstates of the isotropic Heisenberg Hamiltonian inside the sixteen dimensional suhspace of the low‐energetical states of the system are found. The isotropic interactions form one energetical quintet, three triplets, and two singlets; the further splitting of which are caused by anisotropic interactions and can he described in terms of spin Hamiltonian with effective spins S = 2, 1, and 0, respectively. The magnetic dipole–dipole interactions and also simple anisotropic exchange interactions are considered as & perturbation, and the microscopical model for the phenomenological parameters of the spin Hamiltonians is given in second order. Finally, the effective g‐tensors are discussed.