Spin nematic phase in (quasi-)one-dimensional frustrated magnet in strong magnetic field

TL;DR

This paper investigates the spin nematic phase in one-dimensional frustrated magnets under strong magnetic fields, proposing a bosonic model that captures quantum phase transitions and provides analytical expressions for various physical quantities.

Contribution

The authors introduce a bosonic representation including spin-2 excitations to analyze quantum phase transitions in frustrated 1D magnets, extending previous models and matching numerical data.

Findings

Identification of the boundary between polarized and nematic phases as a function of temperature.

Analytical expressions for static spin correlators and spectra in the nematic phase.

Prediction that the soft mode can be experimentally observed in the longitudinal channel.

Abstract

We discuss spin-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 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 nematic ones if $J>|J_1|/4$. Such a transition at $J>0.368|J_1|$ is characterized by 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 which 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 substantially standard the QPT consideration. In 1D case at $H<H_s$, we find an expression for the magnetization which describes well 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 $H_s(0)-H_s(T)\propto T^{3/2}$. 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.