Low-energy properties of two-dimensional quantum triangular antiferromagnets: Nonperturbative renormalization group approach

Abstract

We explore low temperature properties of quantum triangular Heisenberg antiferromagnets in two dimension in the vicinity of the quantum phase transition at zero temperature. Using the effective field theory described by the O(3) × O(2) matrix Ginzburg-Landau-Wilson model and the non-perturbative renormalization group method, we clarify how quantum and thermal fluctuations affect long-wavelength behaviors in the parameter region where the systems exhibit a fluctuationdriven first order transition to a long-range ordered state. We show that at finite temperatures the crossover from a quantum φ 6 theory to a renormalized two-dimensional classical nonlinear sigma model region appears, and in this crossover region, massless fluctuation modes with linear dispersion a la spin waves govern low-energy physics. Our results are partly in good agreement with the recent experimental observations for the two-dimensional triangular Heisenberg spin system, NiGa2S4.

Short-range magnetic ordering process for the triangular-lattice compoundNiGa2S4: A positive muon spin rotation and relaxation study

“…29 However, because of spin-wave interactions, the correlation length is finite. [31][32][33][34] It is therefore tempting to attribute the transition at T c to the dissociation of the Z 2 vortices and T cross to the crossover temperature where the spin dynamics starts to be driven by the usual Heisenberg spin fluctuations. Remarkably, the Z 2 vortices manifest themselves in the temperature vicinity where C m has a rounded peak.…”

“…29,30 Gapless excitation modes and a nearly constant susceptibility are predicted. 31 Based on the Monte Carlo simulations, a phase transition was suggested. 29 However, because of spin-wave interactions, the correlation length is finite.…”

Spin Dependent Impurity Effects on the 2D Frustrated Magnetism ofNiGa2S4

“…It is likely that Ising type impurity spins destabilize such crossover as in our experiment because vector spin chirality can be only defined for Heisenberg spins. A recent theory [16] based on quantum calculations predicts the ðT=j W jÞ 2 -dependent C M and the constant susceptibility as T ! 0 K, which is consistent with our observations.…”

Ba8CoNb6O24: A spin-12triangular-lattice Heisenberg antiferromagnet in the two-dimensional limit

“…In real materials, however, weak interlayer interactions and spin or spatial anisotropies are likely present. Even extremely small perturbations are sufficient to induce long-range magnetic order at a sizable Néel temperature T N , because T N increases logarithmically in the interlayer-coupling or in the exchange anisotropy [14][15][16][17][18]. This is the case for well-studied compounds comprising transition-metal ions, such as Cs 2 CuCl 4 (T N = 0.62 K [19]) and Ba 3 CoSb 2 O 9 (T N = 3.8 K [20]).…”