In-plane Torque Measurement on CeCoIn$_5$ Single Crystals*

We report in-plane torque measurements on single crystals of the heavy fermion superconductor CeCoIn$_5$ performed in the normal state at 1.9, 3, 6, and 10 K, as a function of angle and applied magnetic field. The measurements at constant angle were done in sweeping the magnetic field up to 14 T. The measured torque has a reversible and an irreversible component, with the former larger than the latter. The reversible component can be expressed as $\tau_{rev} (\theta) = \tau_{2}sin2\theta + \tau_{4}sin4\theta$ ($\theta$ is the angle between the applied field and the a-axis of the crystal), which is typical of systems with long range magnetic order. However, it has been reported that the heavy fermion superconductor CeCoIn$_{5}$ has no long range magnetic order, but only short range antiferromagntic fluctuations. The temperature and magnetic field dependence of the coefficients $\tau_{2}$ and $\tau_{4}$ will be discussed. The torque vs field curves at fixed angles show De-Hass Van-Alphen effect at temperatures as high as 10 K. The possible reasons behind this will also be discussed.