Bulk evidence for a time reversal symmetry broken superconducting state in URu2Si2

Abstract

URu$_2$Si$_2$ is claimed to be a chiral \emph{d}-wave superconductor with a $k_z (k_x \pm ik_y)$ time-reversal symmetry broken orbital component for the Cooper pair wave-function, which contains both nodal points and lines of nodes \cite{kasahara, kasahara2}. To study the magnetic response of such an unconventional state through a bulk, thermodynamic probe, we measured the magnetic torque $\tau$ in very high-quality, well-characterized URu$_2$Si$_2$ single-crystals \cite{altarawneh,altarawneh2} at high magnetic-fields $H$ and at very low temperatures $T$. The magnetization $M(H) \propto \tau(H) /H$ of URu$_2$Si$_2$, in its superconducting state and for angles within $15^{\circ}$ from the \emph{ab}-plane, reveals a change in its sign for $H$ approaching $H_{c2}$: from a clear diamagnetic response dominated by the pinning of vortices to a state with a smaller but "paramagnetic-like" hysteretic response which \emph{disappears} at $H_{c2}$, thus implying that it is intrinsically related to the superconducting state. We argue that this anomalous, angular-dependent behavior is evidence for a time-reversal symmetry broken superconducting state in URu$_2$Si$_2$, although not necessarily for the $k_z (k_x \pm ik_y)$ state.