Dynamical spin structure factors of quantum spin nematic states

Abstract

Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-$\frac{1}{2}$ square-lattice ${J}_{1}$-${J}_{2}$ model with ferromagnetic ${J}_{1}$ and competing antiferromagnetic ${J}_{2}$ interactions. To this end, we use a fermion representation, generalizing it to $N$ flavors. We begin with a spin-triplet pairing state of fermion fields, called ${Z}_{2}$ planar state, which is a stable saddle-point solution in the large-$N$ limit in a finite parameter range where the couplings ${J}_{1}$ and ${J}_{2}$ compete strongly [R. Shindou and T. Momoi, Phys. Rev. B 80, 064410 (2009)]. Using a large-$N$ expansion, we take into account fluctuations around this saddle point up to corrections of order $1/N$. The dynamical spin structure factors thus obtained signify the existence of gapless $q$-linear director-wave (spin-wave) modes at $\mathbit{q}=(0,0)$ and gapped ``gauge-field''-like collective modes at $\mathbit{q}=(\ensuremath{\pi},\ensuremath{\pi})$, whose spectral weight vanishes as a linear and quadratic function of the momentum, respectively. The low-energy collective modes contain fluctuations of nematic-director, spin, and gauge degrees of freedom. Associated with the gapless $q$-linear modes, we evaluate the temperature dependence of the nuclear spin relaxation rate $1/{T}_{1}$ in the low-temperature regime as $1/{T}_{1}\ensuremath{\propto}{T}^{2d\ensuremath{-}1}$, where $d$ is the effective spatial dimension.