Magnetic excitations in rare-earth antiferromagnets with bilinear and biquadratic pair couplings: Application to DySb

A Green's-function formalism is constructed for the purpose of computing the elementary excitation energies in a type-II antiferromagnet with Heisenberg exchange and quadrupolar couplings in a cubic crystal field. Three types of excitation modes are found: a longitudinal mode (L mode) associated with O₀¹ and O₀² operators (Δm=0), a transverse mode ($T1$ mode) associated with O_±1¹ and O_±1² operators (Δm=±1), and a second transverse mode ($T2$ mode) associated with O_±2² operators (Δm=±2). In the ordered phase the L-mode and $T1$-mode excitations are mixed magnetic dipolar and quadrupolar excitations. In the disordered phase, as a consequence of cubic symmetry, the magnetic dipolar modes decouple from the quadrupolar modes, giving rise to the possibility of observing a pure quadrupolar excitation. Cubic symmetry also demands that in the disordered phase certain of the excitation energies in the L, $T1$, and $T2$ modes have identical dispersion curves. In general, the dispersion in both the ordered and disordered phase is complicated owing to the inclusion of next-nearest-neighbor coupling. The theory is applied to DySb, a type-II antiferromagnet with strong evidences of quadrupolar coupling.