Magnetism in parent Fe-chalcogenides: quantum fluctuations select a plaquette order

TL;DR

This paper demonstrates that quantum fluctuations favor a plaquette magnetic order in Fe$_{1+y}$Te, preserving rotational symmetry and aligning with experimental observations, contrasting previous single-$Q$ state models.

Contribution

It reveals that quantum fluctuations select a double $Q$ plaquette order in Fe$_{1+y}$Te, challenging earlier single-$Q$ models and explaining experimental data.

Findings

Quantum fluctuations favor a double $Q$ plaquette state.

The plaquette state preserves $C_4$ symmetry.

Results align with recent neutron scattering experiments.

Abstract

We analyze magnetic order in iron-chalcogenide Fe$_{1+y}$Te -- the parent compound of high-temperature superconductor Fe$_{1+y}$Te$_{1-x}$Se$_x$. Neutron scattering experiments show that magnetic order in this material contains components with momentum $Q_1=(\pi/2, \pi/2)$ and $Q_2 =(\pi/2, -\pi/2)$ in Fe-only Brillouin zone. The actual spin order depends on the interplay between these two components. Previous works argued that spin order is a single-$Q$ state (either $Q_1$ or $Q_2$). Such an order breaks rotational $C_4$ symmetry and order spins into a double diagonal stripe. We show that quantum fluctuations actually select another order -- a double $Q$ plaquette state with equal weight of $Q_1$ and $Q_2$ components, which preserves $C_4$ symmetry but breaks $Z_4$ translational symmetry. We argue that the plaquette state is consistent with recent neutron scattering experiments on Fe$_{1+y}$Te.