The dielectric and ac/dc transport properties of single crystals of yttrium iron garnet (Y3Fe5O12andY3Fe5O12:Si), and barium hexaferrite(BaFe12O19andBaFe12O1 9:Co,Ti) were investigated after irradiations with Xe and Pb ions in the GeV range. In the virginn-type samples (Y3Fe5O12:SiandBaFe12O19:Co,Ti), the strong dielectric relaxation below 100 kHz is found to correspond to a space-charge polarization at the blocking metal/insulator contacts yielding a nonohmic dc conductivity. The relaxation frequency decreases with increasing amorphization yield in relation to the decrease of the insulators bulk dc conductivity which becomes ohmic in the amorphous phases. The ac conductivity data of both crystalline and amorphousY3Fe5O12:Siabove 100 kHz and for100 K<T<300 Kexhibit two contributions: (i) that of carrier transport in a disordered or inhomogeneous medium varying as&ngr;s,withs≃0.8,(ii) and that of a two-site polaron hopping process of charge transfer betweenFe2+andFe3+with an activation energy of 0.29 eV forT>180 K.The dc conductivity data of crystallineY3Fe5O12:Sifor80 K<T<300 Kare discussed on the basis of a small polaron hopping conduction mechanism betweenFe2+andFe3+with an activation energy around 0.28 eV forT>125 K,in agreement with the activation energy around 0.28 eV of the space-charge dielectric relaxation frequency forT>180 K.All amorphous phases data are consistent with the picture of hopping conduction between gap states in a disordered medium with (i) an&ngr;sdependence for the ac conductivity above a critical frequency proportional to the dc conductivity, (ii) and anexp(−T−1/4)law for the dc conductivity. ©1997 American Institute of Physics.