The identification of spin-nematic states is challenging due to the absence of Bragg peaks. However, the study of dynamical physical quantities provides a promising avenue 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 bimagnons. Our particular focus lies 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 valuable information about the form factor of bimagnon states and the underlying structure of spin-nematic order. Furthermore, we find a temperature dependence in the NMR relaxation rate proportional to $T^3$ at low temperatures, similar to canted antiferromagnets. A clear distinction arises as there is no critical divergence of the NMR relaxation rate at the spin-nematic transition temperature. Our theoretical framework provides a comprehensive understanding of the excitation spectrum and the dynamical properties of spin-nematic states, covering arbitrary spin values $S$ and encompassing site and bond nematic orders. Additionally, we apply the same methodology to analyze these dynamical quantities in a canted antiferromagnetic state and compare the results with those in the spin-nematic states.

• Received 25 August 2023
• Revised 28 December 2023
• Accepted 10 January 2024

DOI:https://doi.org/10.1103/PhysRevResearch.6.013169

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society