Features of the formation of magnetic moments of Tm$^{3+}$ and Yb$^{3+}$ rare-earth ions in LuB$_{12}$ cage glass

The features of the formation of the magnetic moments of Tm$^{3+}$ and Yb$^{3+}$ ions in a metallic matrix of LuB$_{12}$ cage glass have been studied in measurements of the magnetization and specific heat in the temperature range of $1.9$–$300$ K in magnetic fields up to $90$ kOe. It has been shown that a paramagnetic response from the localized moments of isolated ions Tm$^{3+}$ ($7.6\mu_{\text{B}}$) and Yb$^{3+}$ ($4.5\mu_{\text{B}}$) is observed at temperatures of $150$–$300$ K. A transition to the cage glass phase at low temperatures $(T\ll T^*\sim60\,$K) is accompanied by disordering in the system of rare-earth ions and by formation of many-body states near Tm$^{3+}$ and Yb$^{3+}$ ions. At low temperatures near $T_m$ in low magnetic fields, the appearance of an additional spin polarization, which is suppressed with an increase in the field, has been observed. The effective moments and $g$-factors of Tm and Yb obtained in high fields imply both the binding of a small fraction of magnetic ions to antiferromagnetic dimers and the $\Gamma_6$ ground state of the ${}^2F_{7/2}$ multiplet of the ytterbium ion. A scenario alternative to the Kondo-type behavior has been proposed to explain the nature of many-body states and the appearance of the spin polarization in rare-earth dodecaborides.