Theory of collective magnetic excitations in strong crystal fields. I. Dynamics of the angular momentum tensor operators

The collective motion of ionic spins in a crystal field of magnitude comparable with the exchange interaction is examined. A systematic scheme based upon angular momentum spherical tensor operators is developed to describe the dynamics of collective excitations in the system. The Green's-function equations of motion are linearized by suitably modified forms of conventional decoupling approximations, in particular the randomphase approximation. When the order parameters of the system are calculated, care is taken to eliminate correlation functions prohibited by kinematic restraints. Consequently, the order parameters are obtained uniquely by reducing a redundant set of Green's functions. Furthermore excitations out of different molecularfield levels are distinguished and the excitation out of the ground state is identified as the spin wave. The theory is applied to the spin-1 ($S=1\mathrm{}$) axial ferromagnet with some numerical results.