We develop a microscopic theory of finite-temperature spin-nematic orderings in three-dimensional spatially anisotropic magnets consisting of weakly coupled frustrated spin-$\frac{1}{2}$ chains with nearest-neighbor and next-nearest-neighbor couplings in a magnetic field. Combining a field theoretical technique with density-matrix renormalization group results, we complete finite-temperature phase diagrams in a wide magnetic-field range that possess spin-bond-nematic and incommensurate spin-density-wave ordered phases. The effects of a four-spin interaction are also studied. The relevance of our results to quasi-one-dimensional edge-shared cuprate magnets such as ${\mathrm{LiCuVO}}_4$ is discussed.

• Received 10 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.077206