The solid solution between the ferromagnetic metal SrRuO$_3$ and the enhanced paramagnetic metal SrRhO$_3$ was recently reported [K. Yamaura et al., Phys. Rev. B 69 (2004) 024410], and an unexpected feature was found in the specific heat data at $x$=0.9 of SrRu$_{1-x}$Rh$_x$O$_3$. The feature was reinvestigated further by characterizing additional samples with various Ru concentrations in the vicinity of $x$=0.9. Specific heat and magnetic susceptibility data indicate that the feature reflects a peculiar magnetism of the doped perovskite, which appears only in the very narrow composition range 0.85$<$$x$$le$0.95.
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