Theory of collective magnetic excitations in strong crystal fields. II. Application toS=1singlet ground-state ferromagnet

The theory of collective magnetic excitations based upon the set of Green's functions of angular momentum spherical tensor operators is applied to the exchange-coupled ($S=1\mathrm{}$) magnet with a singlet crystal-field ground state. The spin Hamiltonian is brought to an approximately diagonal form via a unitary transformation by a spin operator functional, the best single-site approximation being located variationally. This enables the set of equations of motion for the Green's tensor to be linearized by conventional techniques. The essential features of induced-moment systems are clarified and displayed in the theory and numerical calculations, respectively. In particular, soft-mode behaviors at the second-order phase transition to ferromagnetism, mode-mode interactions, and a lack of temperature dependence for the excitation energies except at small wave vectors are evident. The nature of the phase transition is examined in detail and a relationship between the divergence of the static susceptibility and the soft-mode behavior is derived from the unitary transformation to pseudospace.