Dynamics

Abstract

The dynamics of typical spin ice compound Dy$_2$Ti$_2$O$_7$ investigated by mainly AC susceptibility and DC magnetization are represented. In addition, considering the results of $\mu$SR and neutron scattering measurements, the common features in spin dynamics are discussed in comparison with the other spin in ice compounds. The spin dynamics of spin ice show a quite unique behavior. The temperature dependence of relaxation time $\tau (T)$ can be roughly described by three regimes. (I) Above 10 K, the temperature dependence of the relaxation time $\tau (T)$ is effectively explained on the basis of the Arrhenius law with an energy barrier $E_\mathrm{B}$ = 200–300 K. (II) In the temperature range of 2–10 K, $\tau (T)$ is almost constant. (III) Below 2 K, $\tau (T)$ increases again, and reaches $\sim$1 s at $\sim$0.7 K. Spin ice state is formed. The dynamics above 10 K is due to single ion process and mixing with excited states; $E_\mathrm{B}$ corresponds to the energy of the excited CEF levels which results in the Ising-like anisotropy. At low temperature below 10 K, the dynamics comes from the creation or annihilation of magnetic monopoles, and their diffusion. In the narrow temperature range $\sim$0.5–1 K, the thermal activated dynamics is observed; the energy barrier of $\sim$9 K is obtained for Dy$_2$Ti$_2$O$_7$. The results indicate that a description taking into account the long range Coulomb interaction between the monopoles is needed to explain the dynamics below 1 K. Below 0.5 K, $\tau (T)$ show a clear deviation from the thermal activated dynamics toward temperature independent relaxation. Furthermore, recent topics on the very slow spin dynamics at very low temperature are also represented.