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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 ($τ_{\rm S}$ (short time) and $τ_{\rm L}$ (long time)). Both $τ_{\rm S}$ and $τ_{\rm L}$ 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 $τ_{\rm S}$ and $τ_{\rm L}$ show a clear deviation from the thermal activated dynamics toward temperature independent relaxation, suggesting a quantum dynamics.