In-plane torque measurements on CeCoIn$_5$ single crystals

In-plane torque measurements were performed on single crystals of CeCoIn$_5$ in the mixed state in order to determine the symmetry of the superconducting gap. The reversible part of the mixed state torque shows a four fold symmetry. The sign of the four fold symmetry is positive. The amplitude of the in-plane torque first increases with increasing magnetic field H, and then decreases with further increasing field until it vanishes towards H$_{c2}$. Sharp irreversible peaks are present in the irreversible torque at 45, 135, 225, and 315$^{0}$. These experimental results imply d$_{xy}$ symmetry of the superconducting order parameter. We also performed in-plane torque measurements in the normal state. Another four fold symmetry is found which has a different origin than the one in the mixed state. The amplitude of the normal state torque has an $H^{4}$ dependence and it shows no saturation up to 14 T. This later four fold symmetry could be related with the symmetry of the Fermi surface.