Pairing Symmetry of CeCoIn\(_5\) Detected by In-plane Torque Measurements

Abstract

In-plane torque measurements were performed on heavy fermion CeCoIn\(_5\) single crystals in the temperature \(T\) range 1.8 K \(\leq T \leq 10\) K and applied magnetic field \(H\) up to 14 T. The normal-state torque is given by \(\tau_n \propto H^4(1+T/T_K)^{-1}\sin 4\phi\). The reversible part of the mixed-state torque, obtained after subtracting the corresponding normal state torque, shows also a four-fold symmetry. In addition, sharp peaks are present in the irreversible torque at angles of \(\pi/\)4, 3\(\pi\)/4, 5\(\pi\)/4, 7\(\pi\)/4, etc. Both the four-fold symmetry in the reversible torque and the sharp peaks in the irreversible torque of the mixed state imply \(d_{xy}\) symmetry of the superconducting order parameter. The field and temperature dependences of the reversible mixed-state torque provide further evidence for \(d_{xy}\) wave symmetry. The four-fold symmetry in the normal state has a different origin since it has different field and temperature dependences than the one in the mixed state. The possible reasons of the normal state four-fold symmetry are discussed.