Anion correlation induced nonrelativistic spin splitting in rutile antiferromagnets

TL;DR

This study reveals how local anion correlations in partially ordered antiferromagnetic FeOF induce nonrelativistic spin splitting in energy bands, with implications for designing new antiferromagnetic materials exhibiting altermagnetism.

Contribution

It demonstrates that short-range anion ordering can cause robust nonrelativistic spin splitting in antiferromagnets, even without long-range order, and predicts experimental signatures for detection.

Findings

NRSS observed along the Γ-M direction in all structures

Anion correlation direction affects spin splitting magnitude and character

Distinct MOKE signatures predicted for different local structures

Abstract

Many studies of non-relativistic spin-splitting (NRSS), or altermagnetism, have focused on idealized, perfectly ordered crystals, relying on symmetry-based approaches to identify candidate materials. Here, we theoretically investigate how local short-range ordering (SRO) influences NRSS of energy bands in partially ordered collinear antiferromagnetic iron oxyfluoride (FeOF). Using the cluster expansion method, we identify four nearly degenerate structures (energy difference $\leq 8$ meV per formula unit) that represent distinct snapshots of local plane-to-plane O/F correlations. Our density functional theory (DFT) results show robust NRSS along the $\Gamma$-M direction in all four structures, despite the absence of long-range order. The magnitude and character of the splitting depend sensitively on the specific direction of anion correlations, effects that are not fully captured in high-symmetry average structures. Notably, two configurations ($Pmc2_1$ and $Pm$) exhibit $\Gamma$-point spin splitting absent in ordered FeF$_2$ and a virtual crystal approximation model of FeOF. We further predict distinct magneto-optical Kerr effect (MOKE) signatures, enabling experimental detection of SRO-driven electronic structure changes. These results highlight heteroanionic compounds as a promising design space for NRSS antiferromagnets, with experimentally synthesized FeOF already exhibiting a substantially higher N\'eel temperature (315\,K) than FeF$_2$ (79\,K).