Dynamics of quantum spin-nematics: comparisons with canted antiferromagnets
Detecting spin-nematic states is challenging due to the absence of Bragg peaks, but dynamical physical quantities offer promising means for characterizing these states. In this study, we investigate the dynamical properties of spin-nematic states in three-dimensional quantum spin systems in a magnetic field. Using a two-component boson theory that incorporates magnons and bi-magnons, we explore the dynamical quantities in the spin-nematic and paramagnetic phases, with a particular focus on the dynamical spin structure factor at zero temperature and the nuclear magnetic resonance (NMR) relaxation rate at finite temperatures. Our findings reveal that the dynamical structure factor does not exhibit any diverging singularity across momentum and frequency while providing a valuable information about the form factor of bi-magnon states and the underlying structure of spin-nematic order. Additionally, we find a temperature dependence in the NMR relaxation rate proportional to $T^3$ at low temperatures, similar to canted antiferromagnets. A clear distinction is found as there is no critical divergence of the NMR relaxation rate at the spin-nematic transition temperature. Our theory provides a comprehensive understanding of the dynamical properties of spin-nematic states, covering arbitrary spin values $S$ and encompassing site and bond nematic orders. We also analyze these dynamical quantities using the same methodology in a canted antiferromagnetic state. These are compared with the results in the spin-nematic states.