Anion correlation induced nonrelativistic spin splitting in rutile antiferromagnets

TL;DR

This work investigates how short-range anion ordering in rutile FeOF influences non-relativistic spin splitting (NRSS) in antiferromagnets. By combining density functional theory (DFT), cluster expansion modeling, and magneto-optical Kerr effect (MOKE) simulations, it identifies four near-degenerate FeOF SRO structures that reproduce experimentally observed anion correlations and reveals robust NRSS along the $Γ$-$M$ direction even without long-range order. The NRSS magnitude and the occurrence of $Γ$-point splitting depend sensitively on the specific anion correlations, a feature absent in long-range ordered FeF$_2$ or in the virtual crystal approximation (VCA) for FeOF. The study further predicts distinguishable MOKE signatures for these configurations and argues that heteroanionic oxides like FeOF offer a high-$T_N$ platform for NRSS antiferromagnets, with FeOF’s Néel temperature exceeding that of FeF$_2$ and approaching room temperature, underscoring their potential for antiferromagnetic spintronics applications.

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 $Γ$-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 $Γ$-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 Néel temperature (315\,K) than FeF$_2$ (79\,K).

Figures (9)

• Figure 1: Schematic illustration of (a) fully ordered FeF$_2$ and (c) fully disordered FeOF structure in the rutile framework. (b) Anionic short-range order (SRO) in FeOF), illustrating the ordering within the (110) plane with an $\cdots$O-F/O-F$\cdots$ pattern along [001] but with variable plane-to-plane correlations. Magnetic ordering of spin-up and spin-down sublattices are color coded as purple and green in their spin structure motif pairs (SSMPs), respectively.
• Figure 2: Crystal and electronic structures of (a) FeF$_2$, (b) VCA FeOF, and (c-f) four chosen FeOF configurations. The crystal structures shown are viewed along the rutile $c$ [001] axis (top-down view), showcasing the variations in O/F correlations. Their band structures are unfolded onto the primitive rutile unit cell for easy comparison, and the line widths represent the spectral weights at each $k$ point. The spin-up (magenta) and spin-down (cyan) motifs are connected by a 90° four-fold rotation in the (a) FeF$_2$ ($P4_2/mnm$) structure, (b) FeOF VCA ($P4_2/mnm$), (c) FeOF SRO1 ($Pmn2_1$), and (d) FeOF SRO2 ($P4_2/m$) cells, but not in the (e) FeOF SRO3 ($Pmc2_1$) and (f) FeOF SRO4 ($Pm$) cells, leading to spin-splitting of energy bands at $\Gamma$. All 4 structures show robust spin splitting along the $\Gamma-\mathrm{M}$ direction, which are contained in the (110) plane. Notice that the degeneracy of the energy bands at $\Gamma$ in panels (c,d) and the $\Gamma$ split bands in panels (e,f).
• Figure 3: Schematic representation of rutile FeF$_2$ and FeOF models (top-down view) illustrating the main symmetries connecting the two opposite spin sublattices and structural motifs (A–F). Preserved symmetries are shown in blue, while broken symmetries are shown in gray. The symmetry operations $4_2^\prime$, $Mx^\prime_1$, $My^\prime_1$, $2x^\prime_1$, and $2y^\prime_1$ corresponds to $\{\Theta C_4|1/2,1/2,1/2\}$, $\{\Theta M_x|1/2,1/2,1/2\}$, $\{\Theta M_y|1/2,1/2,1/2\}$, $\{\Theta C_{2x}|1/2,1/2,1/2\}$, and $\{\Theta C_{2y}|1/2,1/2,1/2\}$, respectively. The lower panel summarizes the symmetry group, relative energy, spin splitting, and key properties of the considered configurations. Magnetic space groups (MSGs) with and without SOC are listed as the combined space–time symmetry groups of the magnets. The difference between the two cases arises from whether spatial and spin symmetry operations are coupled (with SOC) or decoupled (without SOC). The value of the maximum spin splitting (SS) is given for the top two valences bands along $\Gamma-\mathrm{M}$, and the value is averaged over multiple fractional weighted unfolded bands for SRO models.
• Figure 4: Calculated Kerr rotation spectra for all structures including the null spectra (a) FeF$_2$, (b) VCA model of FeOF and two of our selected configurations; (c) $Pmn2_1$ and (d) $P4_2/m$. (e) and (f) show the nonzero MOKE responses of the $Pmc2_1$ and $Pm$ configurations, respectively.
• Figure 5: Néel temperatures of antiferromagnetic rutile oxides, fluorides, and oxyfluorides. Unlike oxides and fluorides, magnetic characterization data for many rutile oxyfluorides is incomplete. All values taken from Ref. chamberland1970preparation.