Application of the Green's function diagrammatic technique to complex crystal field systems with bilinear and biquadratic exchange

A diagrammatic Green's function technique is used to obtain the elementary excitations in a rare earth system with cubic crystal field and both bilinear and biquadratic couplings. We find three distinct modes of excitations: longitudinal (L) and transverse (T1 and T2). L modes and T1 modes consist of mixed dipolar and quadrupolar excitations below T/sub c/, but above T/sub c/ they are either pure dipolar or pure quadrupolar in character. The T2 modes are pure quadrupolar. Dispersion and temperature dependence of the exciton energies are shown for a particular model system, DySb, but the computer program used is general enough to be used on other systems whose molecular field states are known