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Thermal Conductivity Tensor in YBa$_2$Cu$_3$O$_{7-x}$: Effects of a Planar Magnetic Field

We have measured the thermal conductivity tensor of a twinned YBa$_2$Cu$_3$O$_{7-x}$ single crystal as a function of angle $θ$ between the magnetic field applied parallel to the CuO$_2$ planes and the heat current direction, at different magnetic fields and at T=13.8 K. Clear fourfold and twofold variations in the field-angle dependence of $κ_{xx}$ and $κ_{xy}$ were respectively recorded in accordance with the d-wave pairing symmetry of the order parameter. The oscillation amplitude of the transverse thermal conductivity $κ^0_{xy}$ was found to be larger than the longitudinal one $κ^0_{xx}$ in the range of magnetic field studied here ($0 T $$ \le B \le 9 $$T$). From our data we obtain quantities that are free from non-electronic contributions and they allow us a comparison of the experimental results with current models for the quasiparticle transport in the mixed state.