The broken symmetry that develops below 17.5 K in the heavy fermion compound ${\mathrm{URu}}_2{\mathrm{Si}}_2$ has long eluded identification. Here we argue that the recent observation of Ising quasiparticles in ${\mathrm{URu}}_2{\mathrm{Si}}_2$ results from a spinor hybridization order parameter that breaks double time-reversal symmetry by mixing states of integer and half-integer spin. Such “hastatic order” (hasta: [Latin] spear) hybridizes Kramers conduction electrons with Ising, non-Kramers $5f^2$ states of the uranium atoms to produce Ising quasiparticles. The development of a spinorial hybridization at 17.5 K accounts for both the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. This paper develops the theory of hastatic order in detail, providing the mathematical development of its key concepts. Hastatic order predicts a tiny transverse moment in the conduction sea, a colossal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states.

• Received 11 January 2015
• Revised 30 March 2015

DOI:https://doi.org/10.1103/PhysRevB.91.205103