Excitation spectra for spin-3/2 systems with high-degree pair interactions

We studied the excitation spectra of a spin-3/2 system with both dipolar and quadrupolar pair interactions. To study the thermal variations of the spectra we calculated the spectral-weight functions by using finite-temperature two-time Green's functions. These functions were evaluated by using the equation-of-motion method and by applying the random-phase decoupling approximation. At low temperatures when the system is ferromagnetically ordered we find for small wave vectors $k$ that the excitation spectra have a quadratic dependence on $k$. If the dipolar coupling is small compared to the quadrupolar, the system loses its magnetic ordering at a temperature $T_d$ but retains quadrupolar order up to a higher temperature $T_q$. As one increases the temperature from absolute zero, the excitation spectra for small wave vectors gradually change and become linearly dependent on $k$ when $T_d$ is reached. In the phase with only quadrupolar order, the excitation spectra remain linear in $k$. The amplitudes of the excitations are shown to satisfy sum rules and we discuss how these excitations may be observed by inelastic neutron scattering experiments.