Theory of spin excitations in a quantum spin-nematic state

Abstract

The idea that a quantum magnet could act like a liquid crystal, breaking spin-rotation symmetry without breaking time-reversal symmetry, holds an abiding fascination. However, the very fact that spin nematic states do not break time-reversal symmetry renders them ``invisible'' to the most common probes of magnetism---they do not exhibit magnetic Bragg peaks, a static splitting of lines in NMR spectra, or oscillations in $\ensuremath{\mu}$SR. Nonetheless, as a consequence of breaking spin-rotation symmetry, spin-nematic states $\mathit{do}$ possess a characteristic spectrum of dispersing excitations which could be observed in experiment. With this in mind, we develop a symmetry-based description of long-wavelength excitations in a spin-nematic state, based on an SU(3) generalization of the quantum nonlinear $\ensuremath{\sigma}$ model. We use this field theory to make explicit predictions for inelastic neutron scattering, and argue that the wavelike excitations it predicts could be used to identify the symmetries broken by the otherwise unseen spin-nematic order.