Single crystals of yttrium iron garnet Y_3Fe_5O_12 have been irradiated with 270 MeV ~52Te, 760 MeV ~86Kr and 1040 MeV ~208Pb ions. The extent of the induced damage is determiend using Rutherford backscattering spectrometry (RBS) in channeling geometry with a 2 MeV ~4He beam. Taking into account these new results and the previous ones, the thermal spike model was applied to calculate track radii versus electronic stopping power for different beam energies using only one fitting parameter, lambda the mean diffusion length of the energy deposited on the electrons by the slowing down of a swift heavy ion in the garnet. As the latent heat of fusion is unknown for yttrium garnet, the calculation was first performed by neglefting it. A lambda value of (6.3+-0.3) nm is extracted by fitting all the different resutls taking into account a velocity effect. Such a lambda value is the high limit of the mean diffusion length since it decreases if the latent heat of fusion is not neglected. This value of lambda is in agreement with the previosu determinations made in the same conditions for resistant insulators, showing that lambda should decrease when the band-gap increases.
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