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arXiv:1204.4983 · Physical Review B

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

A. V. Syromyatnikov

Published Jul 23, 2012• 22 citations
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Abstract

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 $H\ensuremath{\ge}{H}_{s}$ 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 $J\ensuremath{\gg}|{J}_{1}|$ 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 ${H}_{s}(0)\ensuremath{-}{H}_{s}(T)\ensuremath{\propto}{T}^{3/2}$. 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 $1/\mathrm{ln}(1+|{J}_{1}|/J)$. Dynamical spin susceptibilities are discussed and it is shown that the soft mode can be observed experimentally in the longitudinal channel.

DOI
10.1103/physrevb.86.014423

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