Excitonic transverse and amplitude fluctuations in noncollinear and charge-ordered RbFe2+Fe3+F6

Conventional spin-wave theory of magnetic insulators deals with the investigation of transverse excitations of magnetic moments of fixed length. However, when single-ion energetics such as spin-orbit coupling are relevant, such symmetries are not necessarily present, allowing fluctuations of the magnitude of the magnetic moment. These excitations are termed amplitude modes. Here, the authors develop and investigate a theory for such excitations applied to neutron spectroscopy. They focus their attention on magnetic excitations in the low-temperature phase of RbFe${}²⁺$Fe${}³⁺$F${}₆$ which is based on a noncollinear arrangement of Fe${}³⁺$ (S=5/2, l$\ensuremath{\approx}0$) and orbitally active Fe${}²⁺$(S = 2, l =1) magnetic moments. Conditions for the existence and the observation of amplitude modes are discussed, establishing a convention for predicting and analyzing neutron spectra when spin-orbit coupling is a pertinent energy scale.