# Vacancy Ordering in Fe-Deficient Iron Sulfide with the NiAs-Type Structure

## TL;DR

This study explores the structure and properties of an iron sulfide material with missing iron atoms, revealing it is antiferromagnetic and semimetallic.

## Contribution

The paper presents new insights into Fe-vacancy ordering and electronic properties of nonstoichiometric iron sulfide using DFT + U – D3(BJ) calculations.

## Key findings

- Fe deficiencies are evenly distributed along the c-axis in the most stable configuration.
- The material is predicted to be antiferromagnetic and semimetallic.
- Thermodynamic analysis shows full ordering at equilibrium.

## Abstract

An Fe-deficient iron
sulfide thin film with a nickeline (NiAs)
type structure has been reported with a stoichiometry close to greigite
(Fe3S4) [DavisE. M.; Phys. Chem. Chem. Phys.2019, 21, 20204–2021031486466
10.1039/c9cp04157e]. We have investigated the Fe-vacancy ordering
in the nonstoichiometric iron sulfide with the NiAs-like structure
using density functional theory calculations with a Hubbard Hamiltonian
and long-range dispersion corrections [DFT + U –
D3(BJ)]. We applied canonical statistical mechanics to study the thermodynamics
of ordering and in the most stable configuration we found the same
concentration of Fe deficiencies in each layer along the c axis. We discuss the probabilities of the configurations and the
averages of observables, such as lattice parameters and magnetic moments,
as a function of temperature. At equilibrium, the Fe-deficient iron
sulfide is expected to be fully ordered. The predicted electronic
properties of the most stable configuration suggest that this material
is antiferromagnetic. The simulated electronic structure shows that
the most stable configuration of the Fe-deficient iron sulfide has
semimetallic properties.