Magnetotransversaler Phononentransport

In analogy with Ohm s law for the electrical conductivity, diffusive transport of heat can be described by a linear relation between the resulting heat current and the original gradient. In 1931 Onsager showed, that the thermal conductivity tensor may contain an antisymmetric contribution, induced by a magnetic field. This leads to a heat current perpendicular to both, the original gradient and the applied magnetic field. In a confined sample geometry, this transverse current is balanced by a transverse temperature difference. in metals the corresponding effect has been known for a long time: The Righi-Leduc-effect is caused by the electronic contribution to the thermal conductivity. Later, a magneto-transverse thermal conductivity of paramagnetic molecular gases, the so called Senftleben-Beenakker-effect was observed. The effect is due to an anisotropic scattering cross-section of the diffusing gas molecules responsible for the conduction of heat.As there is no net charge associated with phonons no such effect has been expected for the phonon thermal conductivity. But phonons describe the collective motion of particles carrying charge and spin and are thus influenced by a magnetic field. The observation of the magneto-transverse diffusion of light gives a clue on how such an effect might be realized in the diffusion of classical waves.To our knowledge there is no investigation of the magneto-transverse thermal conductivity reported in the scientific literature. In the diploma-thesis of the author, weinvestigated this new effect in diamagnetic samples, however without an unambiguousobservation of the effect.In this thesis we investigated the effect in paramagnetic materials in which largeeffects are expected due to the resonant scattering of phonons.In the theoretical introduction we argue, that an antisymmetric contribution to the thermal conductivity tensor is thermodynamically allowed, using Onsagers relations for diffusive transport. We show that this contribution will lead to a transverse temperature difference in confined sample geometries. Today there is no theory on a microscopic realization of the effect. We therefore recur on a comparison of phonon sand photons. After a review of the results of Rikken and Tiggelen for the optical case, we therefore worked out the analogies between photons and phonons and presented useful relations for the choice of samples and the understanding of the experiments.In the experimental part we presented the techniques for the measurement of the thermal conductivity as a function of temperature and magnetic field. We specially focused on the setup for the measurement of the magneto-transverse thermal conductivity with ultra high resolution. we analyzed the setup and the protocols to identify possible artifacts.All measurements presented in this thesis have been performed on samples of Terbium-Gallium-Garnet. The sample has been specified by measuring the longitudinal thermal conductivity as function of temperature and magnetic field. The analysis of the low temperature part of the thermal conductivity shows that scattering mean free path is dominated by scattering at point defects and by resonant scattering. From the magnetic field dependence of the thermal conductivity on can conclude on a strong spin phonon coupling which makes the material suitable for an investigation of the magneto-transverse thermal conductivity.We present a complete data set fulfilling all criteria for a phenomenological observationof the effect. A detailed analysis of possible artifacts supports the significanceof the data