Electron paramagnetic resonance in Ho$_x$Lu$_{1-x}$B$_{12}$ dodecaborides

The high-frequency ($60$ GHz) electron paramagnetic resonance is studied in Ho$_x$Lu$_{1-x}$B$_{12}$ single crystals at low temperatures ($2$–$80$ K) in an applied magnetic field up to $7$ T within a wide doping range, $0.01 \leqslant x\leqslant 1$. These compounds are characterized by the presence of a low-temperature cage glass phase with random displacements of magnetic holmium ions from the centrosymmetric position in B$_{12}$ boron cuboctahedra. For the samples with $x\geqslant 0.1$, it is demonstrated that the electron paramagnetic resonance in the form of a single broad line with a $g$-factor of about $5$ appears in the cage glass phase at $T < T^*= 60$ K because of the decrease in the relaxation rate for magnetic moments of Ho$^{3+}$ ions. For the compounds with $x > 0.3$, the pronounced broadening of the resonance line and a steep decrease in the $g$-factor related to antiferromagnetic correlations is observed on cooling at $T < 30$ K. The performed simulation of the electron paramagnetic resonance spectra suggests the dominant role of the exchange interaction effects and positional disorder in determining the characteristic features of spin dynamics in Ho$_x$Lu$_{1-x}$B$_{12}$.