  A detailed microscopic and quantitative description of the electronic and
magnetic properties of Gd$^{3+}$-doped YCo$_{2}$Zn$_{20}$ single crystals
(Y$_{1-x}$Gd$_{x}$Co$_{2}$Zn$_{20}$: (0.002 $\lesssim x \leq $ 1.00) is
reported through a combination of temperature-dependent electron spin resonance
(ESR), heat capacity and $dc$ magnetic susceptibility experiments, plus
first-principles density functional theory (DFT) calculations. The ESR results
indicate that this system features an \emph{exchange bottleneck} scenario
wherein various channels for the spin-lattice relaxation mechanism of the
Gd$^{3+}$ ions can be identified via exchange interactions with different types
of conduction electrons at the Fermi level. Quantitative support from the other
techniques allow to extract the exchange interaction parameters between the
localized magnetic moments of the Gd$^{3+}$ ions and the different types of
conduction electrons present at the Fermi level ($J_{fs}$, $J_{fp}$ and
$J_{fd}$). Despite the complexity of the crystal structure, our combination of
experimental and electronic structure data establish GdCo$_{2}$Zn$_{20}$ as a
model RKKY system by predicting a Curie-Weiss temperature $\theta_{C} =
-1.2(2)$~K directly from microscopic parameters, in very good agreement with
the bulk value from magnetization data. The successful microscopic
understanding of the electronic structure and behavior for the two end
compounds YCo$_{2}$Zn$_{20}$ and GdCo$_{2}$Zn$_{20}$ means they can be used as
references to help describe the more complex electronic properties of related
materials.
