Spin wave analysis to the spatially-anisotropic Heisenberg antiferromagnet on triangular lattice

We study the phase diagram at T = 0 of the antiferromagnetic Heisenberg model on the triangular lattice with spatially-anisotropic interactions. For values of the anisotropy very close to Jα/Jβ = 0.5, conventional spin wave theory predicts that quantum fluctuations melt the classical structures, even for arbitrary values of S. From the limit of weakly coupled chains, Jβ << Jα, it is shown that a finite value of Jβ/Jα = 0.27 is required to switch on a magnetization. The existence of such nonmagnetic states suggests the possibility of spin liquid behavior for intermediate values of the anisotropy. For a long time frustrated quantum antiferromagnets have been intensively studied. In this context, the antiferromagnetic Heisenberg model on a triangular lattice is a prototype for such systems. From the proposition of Anderson and Fazekas that this model is a candidate to exhibit spin liquid behavior [1], a lot of work was done to understand the nature of its ground state. Although there is a general conviction that the ground state is ordered with a magnetic vector Q = (4π/3, 0) [2,3], some authors found a situation very close to a critical one or no magnetic order at all, leaving the answer still controversial [4,5]. A systematic way to study the role of frustration is to vary the strength of the exchange interaction along the bonds. Recently Bhaumik et al. [6] explored the existence of collinear phases on triangular and pentagonal lattices and proposed that the critical value of the anisotropy, below which the ground state has collinear order, can be taken as a measure of frustration. From the experimental point of view, the unconventional properties of the organic superconductors κ− (BEDT − TTF )2X and their similarities with the cuprates [8] renewed the interest in the triangular topology. In particular, it was argued [7,9] that the Hubbard model on a triangular lattice with anisotropic interactions at half filling could be a good candidate to explain such properties. In the limit of strong coupling this model can be mapped to the Heisenberg model with anisotropic interactions Jα = t 2 α/U , Jβ = t 2 β/U where tα and tβ are the anisotropic hoppings. Furthermore, experiments suggest that the relevant values of Jα/Jβ are about 0.3 − 1 (see for details Ref. [9]), so the combined effect of anisotropy and frustration will take an important role in these materials. In this paper we address the phase diagram of the Heisenberg model on the triangular lattice with spatially-anisotropic interactions by mean of conventional spin wave theory. Our approach provides the values of anisotropy where nonmagnetic states appear signaling the possible existence of spin liquid behavior.