E/T-scaling of the spin fluctuations in the Zn-Mg-Ho magnetic quasicrystal

We report inelastic neutron-scattering results on the icosahedral Zn-Mg-RE (RE: rare-earth) magnetic quasicrystals. In the Zn-Mg-RE quasicrystals, slowing down of spin dynamics starts at considerably high temperatures (about 50~K) with developing antiferromagnetic correlations, nevertheless, the spins stay paramagnetic until low-temperature freezing transitions ($T_{\rm f} = 1.95$~K for RE = Ho), indicative of strong frustration effect. Neutron inelastic scattering further reveals that for RE = Ho, the scattering function $S(Q, \hbar \omega)$ is almost temperature independent for $\hbar \omega > 0$ in a wide temperature range up to 200~K. Corresponding dynamic susceptibility for $\hbar \omega < 1.5$~meV is scaled as ${\rm Im}\chi(\hbar\omega, T)T^{1/3} \propto (\hbar\omega/T)^{-1/3}Z(\hbar\omega/T)$, where $Z(\hbar\omega, T) = \tanh(\alpha\hbar\omega/T)$ is the scaling function. This $\hbar\omega/T$ (or $E/T$) scaling is identical to those frequently observed in systems near a quantum critical point, such as UCu$_4$Pd. In view of the frustration-reduced low freezing temperature of the Zn-Mg-Ho quasicrystal, the $E/T$-scaling may also be indicative of the quantum criticality in this magnetic quasicrystal.