Spin-waves in the $J_{1a}-J_{1b}-J_{2}$ orthorombic square-lattice Heisenberg models: Application to the iron pnictide materials

TL;DR

This study analyzes spin-wave spectra in anisotropic $J_{1a}-J_{1b}-J_{2}$ Heisenberg models on a square lattice, revealing how anisotropy affects spin-wave velocities and matching spectra observed in iron pnictide materials.

Contribution

It provides a systematic analysis of anisotropic exchange interactions in the $J_{1a}-J_{1b}-J_{2}$ model, applying it to iron pnictides and distinguishing different anisotropy regimes.

Findings

Anisotropic exchange constants lead to direction-dependent spin-wave velocities.

Extreme anisotropy with ferromagnetic $J_{1b}$ is distinguishable by spin-wave behavior near specific wavevectors.

Spectra for CaFe$_2$As$_2$ indicate extreme anisotropy in exchange interactions.

Abstract

Motivated by the observation of spatially anisotropic exchange constants in the iron pnictide materials, we study the spin-wave spectra of the $J_{1a}-J_{1b}-J_{2}$ Heisenberg models on a square-lattice with nearest neighbor exchange $J_{1a}$ along x and $J_{1b}$ along y axis and a second neighbor exchange $J_2$. We focus on the regime, where the spins order at ($\pi,0$), and compute the spectra by systematic expansions around the Ising limit. We study both spin-half and spin-one Heisenberg models as well as a range of parameters to cover various cases proposed for the iron pnictide materials. The low-energy spectra have anisotropic spin-wave velocities and are renormalized with respect to linear spin-wave theory by up to 20 percent, depending on parameters. Extreme anisotropy, consisting of a ferromagnetic $J_{1b}=- |J_F|$, is best distinguished from a weak anisotropy ($J_{1a}\approx J_{1b}=J_1$, $J_2>J_1/2$) by the nature of the spin-waves near the wavevectors ($0,\pi$) or ($\pi,\pi$). The reported spectra for the pnictide material CaFe$_2$As$_2$ clearly imply such an extreme anisotropy.