Magnetic and transport properties of single-grain $R-\mathrm{M}\mathrm{g}-\mathrm{Z}\mathrm{n}$ icosahedral quasicrystals [$R=\mathrm{Y},$ $\left({\mathrm{Y}}_{1-x}{\mathrm{Gd}}_x\right),$ $\left({\mathrm{Y}}_{1-x}{\mathrm{Tb}}_x\right),$ Tb, Dy, Ho, and Er]

We report measurements of the dc magnetization, the low-field ac magnetic susceptibility, and the electrical resistivity of large (up to 0.5 ${\mathrm{cm}}^3$) single-grain samples of icosahedral $R-\mathrm{M}\mathrm{g}-\mathrm{Z}\mathrm{n}$ $(R=\mathrm{Y},$ Tb, Dy, Ho, and Er). The dc magnetization and ac magnetic susceptibility data both indicate that icosahedral Tb-Mg-Zn and Dy-Mg-Zn undergo a transition to a spin-glass state at $T_f=5.8\mathrm{}$ and 3.6 K, respectively, while low-temperature ac susceptibility measurements show that $T_f=1.95\mathrm{}$ and 1.3 K for Ho-Mg-Zn and Er-Mg-Zn, respectively. For the series of solid solutions $\left({\mathrm{Y}}_{1-x}{\mathrm{Tb}}_x\right)-\mathrm{M}\mathrm{g}-\mathrm{Z}\mathrm{n},$ the freezing temperature $T_f$ varies approximately as $x^{2/3}.$ The $\left({\mathrm{Y}}_{1-x}{\mathrm{Gd}}_x\right)-\mathrm{M}\mathrm{g}-\mathrm{Z}\mathrm{n}$ solid solutions have lower $T_f$ values than $\left({\mathrm{Y}}_{1-x}{\mathrm{Tb}}_x\right)-\mathrm{M}\mathrm{g}-\mathrm{Z}\mathrm{n}$ for the same magnetic rare-earth concentrations (x), indicating that local moment anisotropy caused by crystalline electric-field effects plays a significant role in increasing $T_f.$ On the other hand, angular-dependent studies show that the dc magnetization for $T>\mathrm{}{T}_f$ is isotropic within the experimental uncertainty. The electrical resistivity $\rho \mathrm{}\left(T\right)\mathrm{}$ of the single-grain samples is only weakly temperature dependent, with a small, negative $d\rho /dT.\mathrm{}$ Absolute values of the resistivity fall in the range between 150 and 200 μΩ cm, which is distinctly lower than the values previously reported for other thermodynamically stable icosahedral quasicrystals.