Microscopically derived Ginzburg-Landau theory for magnetic order in the iron pnictides

TL;DR

This paper derives a microscopic Ginzburg-Landau theory to analyze the competition among different magnetic stripe and SDW phases in iron pnictides, highlighting the role of Fermi surface nesting and doping.

Contribution

It provides a rigorous derivation of free energy expansion from a two-band model, revealing the conditions for various SDW states in pnictides.

Findings

Stripe phase is generally stable but varies with doping.

Number of hole Fermi pockets influences phase stability.

Electron-hole pocket competition affects magnetic order.

Abstract

We examine the competition of the observed stripe spin density wave (SDW) with other commensurate and incommensurate SDW phases in a two-band model of the pnictides. Starting from this microscopic model, we rigorously derive an expansion of the free energy in terms of the different order parameters at the mean-field level. We show that three distinct commensurate SDW states are possible and study their appearance as a function of the doping and the electronic structure. We show that the stripe phase is generally present, but its extent in the phase diagram depends strongly upon the number of hole Fermi pockets that are nested with the electron Fermi pockets. Electron pockets competing for the same portion of a hole pocket play a crucial role. We discuss the relevance of our results for the antiferromagnetism of the pnictides.