Hysteresis and Relaxation Effects in the Spin-Ice Compound Dy$_2$Ti$_2$O$_7$ studied by Heat Transport

The low-temperature thermal conductivity $\kappa$ of the spin-ice compound Dy$_2$Ti$_2$O$_7$ shows pronounced hysteresis as a function of magnetic field. Here, we investigate how these hysteresis effects depend on temperature, the magnetic-field direction, the rate of magnetic-field change, and on the direction of the heat current. In addition, the time-dependent relaxation of the heat conductivity is investigated. These measurements yield information about possible equilibrium states and reveal that in the low-field and low-temperature region extremely slow relaxation processes occur.