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Anisotropic Monopole Heat Transport in the Spin-Ice Compound Dy$_2$Ti$_2$O$_7$

We report a study of the thermal conductivity $κ$ of the spin-ice material Dy$_2$Ti$_2$O$_7$. From the anisotropic magnetic-field dependence of κ$ and by additional measurements on the phononic reference compounds Y$_2$Ti$_2$O$_7$ and DyYTi$_2$O$_7$, we are able to separate the phononic and the magnetic contributions to the total heat transport, i.e. $κ_{ph}$ and $κ_{mag}$, respectively, which both depend on the magnetic field. The field dependent $κ_{ph}$ arises from lattice distortions due to magnetic-field induced torques on the non-collinear magnetic moments of the Dy ions. For $κ_{mag}$, we observe a highly anisotropic magnetic-field dependence, which correlates with the corresponding magnetization data reflecting the different magnetic-field induced spin-ice ground states. The magnitude of $κ_{mag}$ increases with the degree of the ground-state degeneracy. This anisotropic field dependence as well as various hysteresis effects suggest that $κ_{mag}$ is essentially determined by the mobility of the magnetic monopole excitations in spin ice.