Effective Gyromagnetic Ratio for Triangular Ferrimagnetic States

It is shown from the semiclassical equations of motion and the molecular-field approximation that the triangular ferrimagnetic state can also be described by an effective gyromagnetic ratio. This effective ratio depends explicitly on the ratio of the inter- to intra-sublattice molecular field constants rather than on the static sublattice magnetizations as in the antiparallel state. It is estimated that the shift in $g$ values for Fe${\mathrm{Cr}}_2$ ${\mathrm{O}}_4$ should be observable if there is a transition from a triangular to an antiparallel state.