Theory of inelastic neutron scattering in a quantum spin nematic

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, despite being a viable form of magnetic order, None the less, experimental evidence for ``spin nematic'' states in magnetic insulators remains scarce. And 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 {\it not} exhibit magnetic Bragg peaks, a static splitting of lines in NMR spectra, or oscillations in $\mu$SR. However, as a consequence of breaking spin-rotation symmetry, spin-nematic states {\it do} posses a characteristic spectrum of dispersing excitations which could be observed in inelastic neutron scattering. With this in mind, we develop a symmetry-based description of long-wavelength excitations in a broad class of spin-nematic states, based on an SU(3) generalisation of the quantum non-linear sigma model. We use this field theory to make explicit predictions for inelastic neutron scattering, and argue that the wave-like excitations it predicts could be used to identify the symmetries broken by the unseen spin-nematic order.