Dynamical spin structure factors of quantum spin nematic states

TL;DR

This paper calculates the dynamical spin structure factors of quantum spin nematic states in a frustrated J1-J2 model, revealing gapless and gapped collective modes and their temperature-dependent effects on nuclear spin relaxation.

Contribution

It introduces a large-N fermionic approach to analyze spin nematic states, identifying collective modes and their spectral properties in a frustrated quantum magnet.

Findings

Existence of gapless spin-wave modes at q=(0,0).

Presence of gapped gauge-like collective modes at q=(pi,pi).

Temperature dependence of 1/T1 proportional to T^{2d-1}.

Abstract

Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-1/2 square-lattice J1-J2 model with ferromagnetic J1 and competing antiferromagnetic J2 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 Z2 planar state, which is a stable saddle-point solution in the large-N limit in a finite parameter range where the couplings J1 and J2 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 q=(0,0) and gapped `gauge-field' like collective modes at q=(pi,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/T1 in the low-temperature regime as 1/T1 \propto T^{2d-1}, where d is the effective spatial dimension.