Dynamics of quantum spin-nematics: Comparisons with canted antiferromagnets

TL;DR

This paper investigates the dynamical properties of quantum spin-nematic states using a boson theory, revealing key differences from canted antiferromagnets and providing insights into their excitation spectra and experimental signatures.

Contribution

It introduces a comprehensive theoretical framework for analyzing dynamical quantities in spin-nematic states and compares these with canted antiferromagnets, highlighting distinctive features.

Findings

Dynamical structure factor shows no diverging singularity across momentum and frequency.

NMR relaxation rate scales as T^3 at low temperatures without critical divergence.

Theoretical results apply to arbitrary spin values and distinguish spin-nematic from canted antiferromagnetic states.

Abstract

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 bi-magnons. 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 bi-magnon 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.