We present a detailed characterization of the recently discovered i-$R$-Cd ($R$ = Y, Gd-Tm) binary quasicrystals by means of x-ray diffraction, temperature-dependent dc and ac magnetization, temperature-dependent resistance and temperature-dependent specific heat measurements. Structurally, the broadening of x-ray diffraction peaks found for i-$R$-Cd is dominated by frozen-in phason strain, which is essentially independent of $R$. i-Y-Cd is weakly diamagnetic and manifests a temperature-independent susceptibility. i-Gd-Cd can be characterized as a spin-glass below 4.6 K via dc magnetization cusp, a third order non-linear magnetic susceptibility peak, a frequency-dependent freezing temperature and a broad maximum in the specific heat. i-$R$-Cd ($R$ = Ho-Tm) is similar to i-Gd-Cd in terms of features observed in thermodynamic measurements. i-Tb-Cd and i-Dy-Cd do not show a clear cusp in their zero-field-cooled dc magnetization data, but instead show a more rounded, broad local maximum. The resistivity for i-$R$-Cd is of order 300 $mu Omega$ cm and weakly temperature-dependent. The characteristic freezing temperatures for i-$R$-Cd ($R$ = Gd-Tm) deviate from the de Gennes scaling, in a manner consistent with crystal electric field splitting induced local moment anisotropy.
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