The magnetoresistance (MR) $\mathrm{\Delta }\rho /\rho$ of the cage-glass compound ${\mathrm{Ho}}_x{\mathrm{Lu}}_{1-x}{\mathrm{B}}_{12}$ with various concentrations of magnetic holmium ions $\left(x\le 0.5\right)$ has been studied in detail concurrently with magnetization $M\left(T\right)$ and Hall effect investigations on high-quality single crystals at temperatures 1.9–120 K and in magnetic field up to 80 kOe. The undertaken analysis of $\mathrm{\Delta }\rho /\rho$ allows us to conclude that the large negative magnetoresistance (nMR) observed in the vicinity of the Néel temperature is caused by scattering of charge carriers on magnetic clusters of ${\mathrm{Ho}}^{3+}$ ions, and that these nanosize regions with antiferromagnetic (AF) exchange inside may be considered as short-range-order AF domains. It was shown that the Yosida relation $-\mathrm{\Delta }\rho /\rho \sim M^2$ provides an adequate description of the nMR effect for the case of Langevin-type behavior of magnetization. Moreover, a reduction of Ho-ion effective magnetic moments in the range 3–9 ${\mu }_B$ was found to develop both with temperature lowering and under the increase of holmium content. A phenomenological description of the large positive quadratic contribution $\mathrm{\Delta }\rho /\rho \sim {\mu }_D^2{H}^2$ which dominates in ${\mathrm{Ho}}_x{\mathrm{Lu}}_{1-x}{\mathrm{B}}_{12}$ in the intermediate temperature range 20–120 K allows us to estimate the drift mobility exponential changes ${\mu }_D\sim T^{-\alpha }$ with $\alpha =1.3$–1.6 depending on Ho concentration. An even more comprehensive behavior of magnetoresistance has been found in the AF state of ${\mathrm{Ho}}_x{\mathrm{Lu}}_{1-x}{\mathrm{B}}_{12}$ where an additional linear positive component was observed and attributed to charge-carrier scattering on the spin density wave (SDW). High-precision measurements of $\mathrm{\Delta }\rho /\rho =f(H,T)$ have allowed us also to reconstruct the magnetic H-T phase diagram of ${\mathrm{Ho}}_{0.5}{\mathrm{Lu}}_{0.5}{\mathrm{B}}_{12}$ and to resolve its magnetic structure as a superposition of $4f$ (based on localized moments) and $5d$ (based on SDW) components.

• Received 12 December 2014
• Revised 27 April 2015

DOI:https://doi.org/10.1103/PhysRevB.91.235104