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The idea that a quantum magnet could act like a liquid crystal, breakingspin-rotation symmetry without breaking time-reversal symmetry, holds anabiding fascination. However, the very fact that spin nematic states do notbreak time-reversal symmetry renders them "invisible" to the most common probesof magnetism - they do not exhibit magnetic Bragg peaks, a static splitting oflines in NMR spectra, or oscillations in muSR. Nonetheless, as a consequence ofbreaking spin-rotation symmetry, spin-nematic states do possess acharacteristic spectrum of dispersing excitations which could be observed inexperiment. With this in mind, we develop a symmetry-based description oflong-wavelength excitations in a spin-nematic state, based on an SU(3)generalisation of the quantum non-linear sigma model. We use this field theoryto make explicit predictions for inelastic neutron scattering, and argue thatthe wave-like excitations it predicts could be used to identify the symmetriesbroken by the otherwise unseen spin-nematic order.

Waves in the unseen : theory of spin excitations in a quantum spin nematic