Low-temperature spectrum and damping of elementary excitations in biquadratic exchange systems (S = 1)

The diagrammatic technique for the standard basis operators and the expansion in powers of 1/z (where z is the number of spins interacting with any given spin) are used to calculate the energies of magnons (in the ferromagnetic and quadrupolar phases) and quadrons (in the ferromagnetic phase) and the bipolar and quadrupolar order parameters (in both phases) in the (1/z)1 approximation and at low temperatures. it is shown that magnons are damped with the exception of the (ferromagnetic and quadrupolar) case of the Schrödinger exchange model and quadrupolar phase; the quadrons are undamped only in a special case of the ferromagnetic phase, i.e. in the ferrogmatic case of the Schrödinger exchange model. In the limit K → 0, i.e. the biquadratic exchange interaction tends to zero, the spectrum of magnons and their damping are identical with the results by Balakhonov et al. The spin waves and quadrupolar order parameter are discussed in more detail in the following cases of the quadrupolar phase: ferromagnetic-quadrupolar limit, isotropic purely quadrupolar interactions, and quadrupolar-antiferromagnetic limit.