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We report a study of the thermal conductivity $\kappa$ of the spin-icematerial Dy$_2$Ti$_2$O$_7$. From the anisotropic magnetic-field dependence of\kappa$ and by additional measurements on the phononic reference compoundsY$_2$Ti$_2$O$_7$ and DyYTi$_2$O$_7$, we are able to separate the phononic andthe magnetic contributions to the total heat transport, i.e. $\kappa_{ph}$ and$\kappa_{mag}$, respectively, which both depend on the magnetic field. Thefield dependent $\kappa_{ph}$ arises from lattice distortions due tomagnetic-field induced torques on the non-collinear magnetic moments of the Dyions. For $\kappa_{mag}$, we observe a highly anisotropic magnetic-fielddependence, which correlates with the corresponding magnetization datareflecting the different magnetic-field induced spin-ice ground states. Themagnitude of $\kappa_{mag}$ increases with the degree of the ground-statedegeneracy. This anisotropic field dependence as well as various hysteresiseffects suggest that $\kappa_{mag}$ is essentially determined by the mobilityof the magnetic monopole excitations in spin ice.

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