Theory of singlet-doublet excitations in praseodymium

The magnetic excitation spectrum in a paramagnetic singlet-doublet system is calculated using a diagrammatic high density expansion technique. The lowest order diagrams, which correspond to the random phase approximation (RPA), give a detailed description of the wave vector and temperature dependence of the four exciton modes in praseodymium in terms of a Hamiltonian including isotropic Heisenberg exchange interactions and anisotropic, dipolar-like interactions. The leading contributions to the linewidths of the excitations are obtained by extending the 1/Z expansion of the generalized susceptibility propagators one order beyond the random phase approximation. This damping corresponds to spin wave scattering on single-site fluctuations. The theoretical spectral functions are in detailed agreement with experiment