Spin and quadrupolar orders in the spin-1 bilinear-biquadratic model for iron-based superconductors

TL;DR

This paper analyzes the spin-1 bilinear-biquadratic model on a square lattice, revealing various magnetic phases and excitations, and fits experimental data to refine exchange couplings relevant to iron-based superconductors.

Contribution

It provides a comprehensive mean-field analysis of magnetic phases, including quadrupolar orders, and introduces flavor-wave theory for excitations in the spin-1 BBQ model.

Findings

Identified multiple magnetic phases, including quadrupolar and mixed orders.

Fitted experimental spin-wave data to determine exchange couplings.

Described elementary excitations using flavor-wave theory within SU(3).

Abstract

Motivated by recent experimental and theoretical progresses of the magnetic properties of iron-based superconductors, we provide a comprehensive analysis of the spin-1 bilinear-biquadratic (BBQ) model on the square lattice. Using variational approach in the mean-field level, we identify the existence of various magnetic phases, including conventional spin dipolar orderings (ferro- or antiferromagnet), novel quadrupolar (spin nematic) orderings and mixed dipolar-quadrupolar orderings. In contrast to the usual Heisenberg model, the elementary excitations of the spin-1 BBQ model are described by the flavor-wave theory within the SU(3) representation. By fitting the experimental spin-wave dispersion, we determine the refined exchange couplings corresponding to the collinear antiferromagnetic iron pnictides. We also present the dynamic structure factors of both spin dipolar and quadrupolar components with connections to the future experiments.