Magnetization, resistivity and specific heat measurements were performed on the solution-grown, single crystals of six GdT$_2$Zn$_{20}$ (T = Fe, Ru, Os, Co, Rh and Ir) compounds, as well as their Y analogues. For the Gd compounds, the Fe column members manifest a ferromagnetic (FM) ground state (with an enhanced Curie temperature, $T_{mathrm{C}}$, for T = Fe and Ru), whereas the Co column members manifest an antiferromagnetic (AFM) ground state. Thermodynamic measurements on the YT$_2$Zn$_{20}$ revealed that the enhanced $T_{mathrm{C}}$ for GdFe$_2$Zn$_{20}$ and GdRu$_2$Zn$_{20}$ can be understood within the framework of Heisenberg moments embedded in a nearly ferromagnetic Fermi liquid. Furthermore, electronic structure calculations indicate that this significant enhancement is due to large, close to the Stoner FM criterion, transition metal partial density of states at Fermi level, whereas the change of FM to AFM ordering is associated with filling of electronic states with two additional electrons per formula unit. The degree of this sensitivity is addressed by the studies of the pseudo-ternary compounds Gd(Fe$_x$Co$_{1-x}$)$_2$Zn$_{20}$ and Y(Fe$_x$Co$_{1-x}$)$_2$Zn$_{20}$ which clearly reveal the effect of 3d band filling on their magnetic properties.
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