Dynamical properties of a crystalline rare-earth boron cluster spin-glass system

Dynamical properties of the magnetic ${\mathrm{B}}_{12}$ cluster compound ${\mathrm{HoB}}_{22}{\mathrm{C}}_2\mathrm{N}$ were investigated. ${\mathrm{HoB}}_{22}{\mathrm{C}}_2\mathrm{N}$ is taken to be representative of the class of trigonal and rhombohedral ${\mathrm{B}}_{12}$ cluster compounds which were found to exhibit spin-glass behavior as measured by dc superconducting quantum interference device magnetometer and specific-heat measurements. These are examples of magnetic glassiness being observed in rare earth boron-rich crystalline cluster compounds. Well defined maxima in the in-phase linear ac susceptibility ${\chi }^{\prime }$ curves were observed, indicative of the spin-glass transition. Strong frequency dependence of the cusp temperature $T_f$ was found. The dependence of $T_f$ could not be analyzed satisfactorily by the dynamical scaling theory of a three-dimensional spin glass. A more detailed investigation of the behavior of relaxation times by Cole-Cole analysis showed that the behavior in ${\mathrm{HoB}}_{22}{\mathrm{C}}_2\mathrm{N}$ is different from the simple blocking of a superparamagnetic system, because of the temperature dependence of the parameter $\alpha$ representing the width of the relaxation-time distribution function $g\left(\tau \right).\mathrm{}$ The median relaxation time was also determined and the data were found to be described well in terms of a generalized Arrhenius law $\ln \tau \propto {\mathrm{T}}^{-2.5}.$ These results indicate that ${\mathrm{HoB}}_{22}{\mathrm{C}}_2\mathrm{N}$ is a two-dimensional spin-glass system, which supports what has been speculated previously.