This thesis concerns the thermal-transport properties of the spin-ice compound Dy2Ti2O7 and the spin-1/2 Ising-like spin chain BaCo2V2O8. In zero field, the thermal conductivity of Dy2Ti2O7 shows an anomalous magnetic heat transport which appears as an additional shoulder on top of the phononic background kappa_ph. The zero-field magnetic contribution kappa_mag has a maximum close to the maximum of the magnetic specific heat c_mag and is strongly suppressed by the external magnetic field. The field dependence of kappa_mag depends on the field-induced ground-state degeneracy of the magnetic spin-ice system. In zero field, the ground-state degeneracy is maximum and, hence, kappa_mag is maximum. Different field directions result in different field-induced ground states of the spin ice. This leads to a strong anisotropy of kappa(B) with respect to the field direction. Moreover, the phononic background kappa_ph also is magnetic-field dependent. This results from lattice distortions due to torques affecting the Dy momenta in the external magnetic field. The field dependence of kappa_mag is studied by measurements of the thermal conductivity of the reference compound (Dy0.5Y0.5)2Ti2O7. Here, the spin-ice features are supposed to be suppressed compared to Dy2Ti2O7. In the Zr-doped compound Dy2(Ti0.9Zr0.1)2O7, the phononic contribution kappa_ph is suppressed and almost field independent due to additional defect scattering, essentially conserving the spin-ice properties and, hence, the magnetic contribution kappa_mag.
In the second part of this thesis, the thermal transport properties of the Ising-like effective spin-1/2 chain are studied by measurements of the thermal conductivity parallel and perpendicular to the spin chains. For both heat-current directions, the thermal conductivity exhibits a sharp dip around the ordering temperature TN. Below TN, the thermal conductivity of BaCo2V2O8 is strongly field dependent and anisotropic with respect to the field direction. To study the transport mechanisms in BaCo2V2O8, additional thermal-conductivity measurements of two doped compounds, (Ba0.9Sr0.1)Co2V2O8 and Ba(Co0.95Mg0.05)2V2O8, and of the iso-structural compound BaMn2V2O8 were performed. Sr doping increases defect scattering of phonons while the magnetic system is basically unaffected. In case of Ba(Co0.95Mg0.05)2V2O8, doping into the Co chains strongly influences the magnetic properties. The Heisenberg spin-5/2 chain BaMn2V2O8 is an iso-structural reference compound with isotropic magnetic properties. The experimental kappa data of BaCo2V2O8 and of the reference compounds show no indication of a magnetic heat transport in BaCo2V2O8 and give rise to the assumption that the thermal conductivity of BaCo2V2O8 is of purely phononic origin and that the anomaly around TN can be attributed to phonon scattering on magnetic excitations. This is supported by analyses of the thermal conductivity of BaCo2V2O8 by means of the phononic Debye model
