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

Abstract

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 ${J}_{\ensuremath{\alpha}}{/J}_{\ensuremath{\beta}}=0.5,$ conventional spin-wave theory predicts that quantum fluctuations melt the classical structures, for $S=1/2.$ For the regime ${J}_{\ensuremath{\beta}}<{J}_{\ensuremath{\alpha}},$ it is shown that the incommensurate spiral phases survive until ${J}_{\ensuremath{\beta}}{/J}_{\ensuremath{\alpha}}=0.27,$ leaving a wide region where the ground state is disordered. The existence of such nonmagnetic states suggests the possibility of spin-liquid behavior for intermediate values of the anisotropy.