Elementary excitations in the spin-ice compound Dy 2 Ti2O7 can be described as magnetic monopoles propagating independently within the pyrochlore lattice formed by magnetic Dy ions. We studied the magnetic-field dependence of the thermal conductivity κ(B) for B || [001] and observe clear evidence for magnetic heat transport originating from the monopole excitations. The magnetic contribution κmag is strongly field-dependent and correlates with the magnetization M (B). The diffusion coefficient obtained from the ratio of κmag and the magnetic specific heat is strongly enhanced below 1 K indicating a high mobility of the monopole excitations in the spin-ice state.PACS numbers: 75.40.Gb, The recent prediction of magnetic monopoles in the spin-ice compounds has attracted a lot of interest [1][2][3][4][5][6][7][8][9][10]. Spin ice is a geometrically frustrated spin system, which is realized in Dy 2 Ti 2 O 7 by a sublattice of corner-sharing Dy 3+ tetrahedra. Due to a strong Ising anisotropy, the magnetic moments of Dy 3+ point either in or out of a tetrahedron. The magnetic dipole energy is minimized, when two spins point in and two out of a tetrahedron (2in-2out), what is realized by 6 out of 2 4 = 16 possible configurations for a single tetrahedron. In this respect, the spin orientation of Dy 3+ corresponds to the hydrogen displacement in water ice [11] and the ground state is highly degenerate with a residual entropy S 0 = N k B /2 ln(3/2) for T → 0 K [12-15]. Excited states can be created by flipping one spin, resulting in two adjacent tetrahedra with configurations 3in-1out and 1in-3out, respectively. In zero magnetic field, such a dipole excitation can fractionalize into two individual excitations, a monopole (3in-1out) and an anti-monopole (1in-3out), which can propagate independently. This can be visualized by flipping, e.g., another in-pointing spin of the 3in-1out tetrahedron such that it relaxes back to (another) 2in-2out ground state configuration, while the 3in-1out state has moved to a neighboring tetrahedron.The model of magnetic monopoles has been widely used to describe many experimental observations of Dy 2 Ti 2 O 7 [1-10]. Nevertheless, there are basic properties of the spin-ice materials, which are far from being understood. For example, the specific heat c p of Dy 2 Ti 2 O 7 has a pronounced maximum around 1.2 K resulting from the magnetic excitations and the corresponding entropy is close to the expected S 0 = 1.68 J K −1 mol −1 Dy [2,14,16,17]. Below ∼ 600 mK, however, c p (T ) data published by several groups differ by almost an order of magnitude, see figure 1 [2, 16-18]. Very recently it became clear that in this low-temperature regime the magnetic subsystem of Dy 2 Ti 2 O 7 enters a region of very slow dynamics with relaxation processes that may extend over extremely long time scales [10,17]. Another open issue is the dynamics of the magnetic monopoles.The possible observation of a monopole current in an external magnetic field is currently under strong debate [8, 9, 19]. In this context, i...

We report a study of the thermal conductivity κ of the spin-ice material Dy2Ti2O7. From the anisotropic magnetic-field dependence of κ and by additional measurements on the phononic reference compounds Y2Ti2O7 and (Dy0.5Y0.5)2Ti2O7, we are able to separate the phononic and the magnetic contributions to the total heat transport, i.e. κ ph and κmag, respectively, which both depend on the magnetic field. The field dependent κ ph (B) arises from lattice distortions due to magnetic-field induced torques on the non-collinear magnetic moments of the Dy ions. For κmag, 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 κmag increases with the degree of the ground-state degeneracy. This anisotropic field dependence as well as various hysteresis effects suggest that κmag is essentially determined by the mobility of the magnetic monopole excitations in spin ice.

The low-temperature thermal conductivity κ 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 lowfield and low-temperature region extremely slow relaxation processes occur.