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The thermal conductivity of Sr2RuO4 along the least conducting directionperpendicular to the RuO2 plane has been studied down to 0.3 K. In thisconfiguration the phonons remain the dominant heat carriers down to the lowesttemperature, and their conductivity in the normal state is determined by thescattering on conduction electrons. We show that the phonon mean free path inthe superconducting state is sensitive to the density of the quasi-particles inthe bulk. An unusual magnetic field dependence of the phonon thermalconductivity is ascribed to the anisotropic superconducting gap structure inSr2RuO4.Comment: 14 pages, 6 eps figures, Latex. This article corresponds to the  reference 25 of Phys. Rev. Lett. vol.86 page2649-2652 (2001) and  cond-mat/010449

Quasi-particle density in Sr2RuO4 probed by means of the phonon thermal conductivity