We discuss spin-

\frac{1}{2}

one-dimensional (1D) and quasi-1D magnets with competing ferromagnetic nearest-neighbor

J_{1}

and antiferromagnetic next-nearest-neighbor

J

exchange interactions in a strong magnetic field

H

. It is well known that, due to attraction between magnons, quantum phase transitions (QPTs) take place at

H = H_{s}

from the fully polarized phase to the nematic phase if

J > | J_{1} | / 4

. Such a transition at

J > 0.368 | J_{1} |

is characterized by a softening of the two-magnon bound-state spectrum. Using a bond-operator formalism we propose a bosonic representation of the spin Hamiltonian containing, aside from bosons describing one-magnon spin-1 excitations, a boson describing spin-2 excitations whose spectrum coincides at

H \geq H_{s}

with the two-magnon bound-state spectrum obtained before. The presence of the bosonic mode in the theory that softens at

H = H_{s}

makes the QPT consideration substantially standard. In the 1D case at

H < H_{s}

, we find an expression for the magnetization which well describes existing numerical data. Expressions for spin correlators are obtained which coincide with those derived before, either in the limiting case of

J ≫ | J_{1} |

or using a phenomenological theory. In quasi-1D magnets, we find that the boundary in the

H

T

plane between the fully polarized and the nematic phases is given by

H_{s} (0) - H_{s} (T) \propto T^{3 / 2}

. Simple expressions are obtained in the nematic phase for static spin correlators, spectra of magnons and the soft mode, magnetization, and the nematic order parameter. All static two-spin correlation functions are short ranged with the correlation length proportional to

1 / \ln (1 + | J_{1} | / J)

. Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel. DOI: http://dx.doi.org/10.1103/PhysRevB.86.014423 ©2012 American Physical Society

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