  We report a linear dependence of the phonon splitting \Delta\omega on the
non-dominant exchange coupling constant J_{nd} in the antiferromagnetic
transition-metal monoxides MnO, FeO, CoO, NiO, and in the frustrated
antiferromagnetic oxide spinels CdCr2O4, MgCr2O4, and ZnCr2O4. It directly
confirms the theoretical prediction of an exchange induced splitting of the
zone-centre optical phonon for the monoxides and explains the magnitude and the
change of sign of the phonon splitting on changing the sign of the non-dominant
exchange also in the frustrated oxide spinels. The experimentally found linear
relation \hbar\Delta\omega = \beta J_{nd} S^2 with slope \beta = 3.7 describes
the splitting for both systems and agrees with the observations in the
antiferromagnets KCoF3 and KNiF3 with perovskite structure and negligible
next-nearest neighbour coupling. The common behavior found for very different
classes of cubic antiferromagnets suggests a universal dependence of the
exchange-induced phonon splitting at the antiferromagnetic transition on the
non-dominant exchange coupling.
