Spin Dynamics at Very Low Temperature in Spin Ice Dy${}_2$Ti${}_2$O${}_7$

We have performed AC susceptibility and DC magnetic relaxation measurements on the spin ice system Dy${}_2$Ti${}_2$O${}_7$ down to 0.08 K. The relaxation time of the magnetization has been estimated below 2 K down to 0.08 K. The spin dynamics of Dy${}_2$Ti${}_2$O${}_7$ is well described by using two relaxation times (${\tau }_{\mathrm{S}}$ (short time) and ${\tau }_{\mathrm{L}}$ (long time)). Both $\tau_{\rm S}$and$\tau_{\rm L}$ increase on cooling. Assuming the Arrhenius law in the temperature range 0.5-1 K, we obtained an energy barrier of 9 K. Below 0.5 K, both ${\tau }_{\mathrm{S}}$ and ${\tau }_{\mathrm{L}}$ show a clear deviation from the thermal activated dynamics toward temperature independent relaxation, suggesting a quantum dynamics.