Excited-state spin waves, soft modes, and crystal field effects

There are several branches of the spin‐wave spectrum in materials where the exchange and crystalline field are comparable. Spin waves out of excited states can play an important role by mixing and interacting with the conventional spin waves out of the ground state. These effects are illustrated by neutron scattering results for TbSb, where several branches were observed, for TbAl2, where an excited‐state spin wave has been directly observed, and for Pr3Tl where the mode‐mode interaction has been found to be responsible in part for the surprising lack of temperature dependence through Tc of the spin‐wave peak. A theory of the dynamical susceptibility has been developed that includes, the RPA, all spin waves allowed within the ground multiplet, and is found to be in good agreement with experiment in contrast to the singlet‐singlet or singlet‐triplet models. For Pr3Tl as T→Tc the frequencies of the singlet‐triplet modes decrease but remain finite. The modes within the triplets do tend to zero frequency at T...