Using large-scale density-matrix renormalzation group calculations and minimally augmented spin-wave theory, we demonstrate that the phase diagram of the quantum $S=\frac{1}{2}{J}_1$–$J_3$ ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-$z$ phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases replace the classical spiral state.

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• Frustrated magnetism
• Density matrix renormalization group
• Linear spin wave theory