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 $\theta$ 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 $\kappa_{xx}$ and $\kappa_{xy}$ were respectively recorded in accordance with the d-wave pairing symmetry of the order parameter. The oscillation amplitude of the transverse thermal conductivity $\kappa^0_{xy}$ was found to be larger than the longitudinal one $\kappa^0_{xx}$ 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. 
Roberto Oca\~na and Pablo Esquinazi