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We examine the stability of classical states with a generic incommensuratespiral order against quantum fluctuations. Specifically, we focus on thefrustrated spin-1/2 $XY$ and Heisenberg models on the honeycomb lattice withnearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagneticcouplings. Our variational approach is based on the Jastrow wave functions,which include quantum correlations on top of classical spin waves. We perform asystematic optimization of wave vectors and Jastrow pseudo-potentials withinthis class of variational states and find that quantum fluctuations favorcollinear states over generic coplanar spirals. The N\'eel state with ${\bfQ}=(0,0)$ extends its stability well beyond the classical value $J_2/J_1=1/6$.Most importantly, the collinear states with ${\bf Q}=(0,2\pi/\sqrt{3})$ (andthe two symmetry-related states) are found to be stable in a large regime withintermediate frustration, while at the classical level they are limited to thepoint $J_2/J_1=0.5$. For large frustration, the $120^\circ$ state is stabilizedfor finite values of $J_2/J_1$ in both models.

Spiral antiferromagnets beyond the spin-wave approximation: frustrated $XY$ and Heisenberg models in the honeycomb lattice