M\"ossbauer spectroscopy of damage induced by energetic Ar, Kr, and Xe ions in the giga-electron-volt range in two ferrimagnetic oxides, ${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ and ${\mathrm{BaFe}}_{12}$${\mathrm{O}}_{19}$, is presented. The enhancement of the paramagnetic phase observed after an irradiation with high-energy deposition (Xe and Kr ions) compared to low-energy deposition (Ar ions) supports a damage mechanism based on the electronic stopping power. Threshold energy-deposition values close to 17 and 25 MeV ${\mathrm{cm}}^{2}$ ${\mathrm{mg}}^{\mathrm{\ensuremath{-}}1}$ have thus been determined for ${\mathrm{Y}}_{3}$${\mathrm{Fe}}_{5}$${\mathrm{O}}_{12}$ and ${\mathrm{BaFe}}_{12}$${\mathrm{O}}_{19}$, respectively. Furthermore, drastic changes in the bulk orientation of the hyperfine magnetic field ${H}_{f}$ have been observed in yttrium iron garnet: The ${H}_{f}$ distribution is isotropic for Ar irradiations and anisotropic for Xe irradiations, while two types of ${H}_{f}$ distributions are observed for Kr irradiations, depending on the values of the deposited energy compared to that of the threshold energy. Comparison with latent-track models is performed.