Hidden octupole order in URu₂Si₂

Abstract

We propose that the hidden order in URu₂Si₂ is an incommensurate octupole order, which is derived from a spin-1 XXZ model with XX octupole and Z dipole interactions based on the singlet-doublet crystal-field level scheme. The octupole moments break time-reversal invariance and give rise to finite hyperfine fields on the nuclei of the ligand Si and Ru ions. In order for the hyperfine fields to be observed as a nuclear magnetic resonance (NMR) linewidth, the order must be incommensurate, with the ordering vector determined so as to account for the ²⁹Si NMR linewidth data quantitatively.