Broken Rotational Symmetry in the Hidden Order Phase of URu$_2$Si$_2$

The nature of the so-called `hidden order' phase transition at $T_h = 17.5$ K in the heavy fermion compound URu$_2$Si$_2$ has posed a long-standing mystery, because despite 25 years of study it remains unidentified what symmetry is broken in this ordered phase. We report the emergence of an in-plane anisotropy of the magnetic susceptibility below $T_h$, which breaks four-fold rotational symmetry in tetragonal URu$_2$Si$_2$. Two-fold oscillations in the magnetic torque, which is measured in magnetic ?elds rotating precisely within the ab plane, are sensitively detected in small pure crystals for the first time. The amplitude of the two-fold oscillations onsets precisely at $T_h$, indicating its close link to an order parameter of the hidden order phase. Our findings uncover that the hidden order phase is an electronic `nematic' phase, a translationally invariant metallic phase with spontaneous breaking of rotational symmetry.