Spin nematic phase in one-dimensional and quasi-one-dimensional frustrated magnets in a strong magnetic field

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 $H\ge H_s$ 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 $J\gg |J_1|$ 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 $H_s\left(0\right)-H_s\left(T\right)\propto T^{3/2}$. 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