Theory of the evolution of magnetic order in Fe$_{1+y}$Te compounds with increasing interstitial iron

TL;DR

This paper models how increasing interstitial iron in Fe$_{1+y}$Te compounds alters magnetic order, showing a transition from a double-stripe to an incommensurate spiral state due to changes in electronic structure and exchange interactions.

Contribution

It introduces a multi-orbital model combining localized and itinerant electrons to explain the evolution of magnetic order with excess Fe in Fe$_{1+y}$Te.

Findings

Excess Fe suppresses Fermi surface nesting at key momenta.

The magnetic ground state transitions from double-stripe to incommensurate spiral.

Results align with experimental observations of magnetic order changes.

Abstract

We examine the influence of the excess of interstitial Fe on the magnetic properties of Fe$_{1+y}$Te compounds. Because in iron chalcogenides the correlations are stronger than in the iron arsenides, we assume in our model that some of the Fe orbitals give rise to localized magnetic moments. These moments interact with each other via exchange interactions as well as phonon-mediated biquadratic interactions that favor a collinear double-stripe state, corresponding to the ordering vectors $\left(\pm\pi/2,\pm\pi/2\right)$. The remaining Fe orbitals are assumed to be itinerant, giving rise to the first-principle derived Fermi surface displaying nesting features at momenta $\left(\pi,0\right)/\left(0,\pi\right)$. Increasing the amount of itinerant electrons due to excess Fe, $y$, leads to changes in the Fermi surface and to the suppression of its nesting properties. As a result, due to the Hund's coupling between the itinerant and localized moments, increasing $y$ leads to modifications in the local moments' exchange interactions via the multi-orbital generalization of the long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. By numerically computing the RKKY corrections and minimizing the resulting effective exchange Hamiltonian, we find, in general, that the excess electrons introduced in the system change the classical magnetic ground state from a double-stripe state to an incommensurate spiral, consistent with the experimental observations. We show that these results can be understood as a result of the suppression of magnetic spectral weight of the itinerant electrons at momenta $\left(\pi,0\right)/\left(0,\pi\right)$, combined with the transfer of broad magnetic spectral weight from large to small momenta, promoted by the introduction of excess Fe.