Interplay between spatial anisotropy and next-nearest-neighbor exchange interactions in the triangular Heisenberg model

We investigate the interplay between spatial anisotropy and further exchange interactions in the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic model on a triangular lattice. We use the Schwinger boson theory by including Gaussian fluctuations above the mean-field approach. The phase diagram exhibits a strong reduction of the long-range collinear and incommensurate spiral regions with respect to the mean-field ones. This reduction is accompanied by the emergence of its short-range order counterparts, leaving an ample room for zero-flux and nematic spin-liquid regions. Remarkably, within the neighborhood of the spatially isotropic line, there is a range where the spirals are so fragile that only the commensurate ${120}^{\ensuremath{\circ}}$ N\'eel ones survive. The good agreement with recent variational Monte Carlo predictions gives support to the rich phase diagram induced by spatial anisotropy.