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High-Throughput Quantification of Altermagnetic Band Splitting

arXiv:2509.14729v3 [cond-mat.mtrl-sci] 13 Mar 2026

Ali Sufyan, 1, 2, 3 Brahim Marfoua, 4 J. Andreas Larsson, 3, 5 Erik van Loon, 1, 2 and Rickard Armiento 4

1 NanoLund and Division of Mathematical Physics, Department of Physics, Lund University, SE-221 00 Lund, Sweden

2 Wallenberg Initiative Materials Science for Sustainability, Department of Physics, Lund University, SE-221 00 Lund, Sweden 3 Applied Physics, Division of Materials Science, Department of Engineering Sciences and Mathematics,

Luleå University of Technology, SE-971 87 Luleå Sweden

4 Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden 5 Wallenberg Initiative Materials Science for Sustainability, Luleå University of Technology, SE-971 87 Luleå Sweden

Altermagnetism represents a recently established class of collinear magnetism that combines zero net magnetization with momentum-dependent spin polarization, enabled by symmetry constraints rather than spin-orbit coupling. This distinctive behavior gives rise to sizable spin splitting even in materials composed of light, earth-abundant elements, offering promising prospects for nextgeneration spintronics applications. Here, we present a comprehensive high-throughput screening of the 2287 entiries comprising the MAGNDATA database, integrating symmetry analysis with spinpolarized density functional theory (DFT) calculations to identify and characterize altermagnetic candidates. Our workflow investigates the collinear structures in the data set and collinear versions of the ones reported to be non-collinear, uncovering 180 materials exhibiting significant spin splitting, spanning both metallic and semiconducting systems. Detailed results are available for all 180 materials, but we also particularly discuss UCr 2 Si 2 C, NbMnP, and YRuO 3 as representative cases with large spin splitting. Furthermore, comparison with the Computational 2D Materials Database (C2DB) and the AiiDA 2D repository gives 9 bulk altermagnets with chemically equivalent 2D counterparts linked to the same ICSD parent entry. Crucially, our momentum-resolved analysis reveals that the spin splitting varies strongly across the Brillouin zone, and that the maximal splitting tends to occur away from the high-symmetry paths, a result that directly informs and guides future photoemission experiments. By expanding the catalog of known altermagnets, this work lays a robust foundation for future experimental and theoretical advances in spintronics and quantum materials discovery.

I. INTRODUCTION

Altermagnetism has recently emerged as a distinct magnetic phase that expands beyond the traditional classifications of ferromagnetism (FM) and antiferromagnetism (AFM) [1–3]. The concept was initially introduced through theoretical predictions in rutile AFM RuO 2 in 2019 [4], and subsequently gained significant attention through systematic investigations of its distinctive characteristics in 2022, at which point the term “altermagnetism” was formally established [1, 2]. Conventional FM materials exhibit a net magnetization due to parallel alignment of spins, breaking time-reversal symmetry (TRS) uniformly throughout the crystal. In contrast, traditional AFMs have globally compensated spin arrangements with adjacent spins oriented antiparallel, thereby generating no net magnetization and typically enforcing spin degeneracy in their electronic band structure due to symmetry operations combining inversion or translational symmetry with TRS.

Altermagnets, however, possess globally compensated magnetization similar to AFMs but uniquely exhibit momentum-dependent spin polarization reminiscent of FM materials [1–12]. The essential distinction arises from the symmetry relations between their spin sublattices: in altermagnets, opposite-spin sublattices are related by rotation symmetries combined with TRS, rather than translation or inversion symmetries. This crucial difference in symmetry leads to nonrelativistic spin splitting of electronic bands, breaking Kramers degeneracy without the necessity of spin-orbit coupling (SOC) [4, 6, 7, 10, 13, 14]. In conventional AFMs, symmetry-enforced degeneracies typically prevent such splitting, while altermagnetic symmetry permits momentum-dependent spin-split bands that retain overall global spin compensation. Critically, because this spin splitting does not require SOC, altermagnetic behavior can manifest significantly even in materials composed of lighter, more earth-abundant elements like Fe and Mn. This broadens the scope for material discovery and significantly reduces reliance on heavier, expensive, or rare elements typically needed for SOC-driven phenomena [15]. Experimentally confirmed altermagnets now encompass diverse systems, from insulating compounds like CuF 2 [1], MnF 2 [7], and MnTe [14] to metallic materials such as RuO 2 [16], Mn 5 Si 3 [17], and CrSb [18]. These materials have demonstrated compelling and technologically relevant phenomena, including anomalous Hall effects (AHE), spin-polarized conductivity, spin-transfer torque, tunneling magnetoresistance, and giant magnetoresistance, which are essential ingredients for future spintronic applications [2, 19–24]. Consequently, the identification and characterization of alter2 magnetic materials represent a transformative advancement in magnetism and spintronics, sparking intensive research efforts aimed at uncovering new materials, elucidating underlying physical principles, and developing practical applications for this emerging class of magnetic materials.

However, discovering new altermagnets with significant spin splitting through trial-and-error experimental approaches is inherently challenging and resource-intensive. To overcome this limitation, highthroughput computational screening, leveraging reliable first-principles density functional theory (DFT) calculations, has emerged as an efficient and powerful methodology. This approach enables the rapid and systematic exploration of large material databases for candidates exhibiting desirable characteristics. Some recent efforts have used the MAGNDATA database [25, 26] for this purpose (see Sec. V for a comparison) with a focus on specific subclasses, such as metallic altermagnets or magnonic excitations in collinear systems, or using other selection criteria [27–29]. In this present work, we undertake an exhaustive and systematic high-throughput screening of the entire MAGNDATA database, including collinear versions of the non-collinear entries, without constraints to specific classes or properties, aiming to identify and comprehensively characterize all potential altermagnetic candidates. Through this extensive computational investigation, we successfully discover numerous previously unreported altermagnetic materials, validate several known candidates, and provide robust theoretical frameworks for future experimental realizations. This comprehensive approach not only significantly enhances the current understanding of altermagnetic phenomena but also expands the available pool of materials for next-generation spintronic devices, highlighting the critical importance and novelty of this study.

II. SCREENING WORKFLOW

We present a rigorous two-stage high-throughput computational screening workflow for the systematic identification of candidate altermagnetic materials, summarized schematically in Fig. 1. In the first stage of screening (Fig. 1a), we retrieved the March 11, 2025 state of the MAGNDATA database hosted by the Bilbao Crystallographic Server [25, 26, 30]. This database contains 2287 published magnetic structures with crystal structures and magnetic configurations primarily obtained via experimental characterization.

These magnetic materials were subsequently analyzed using the recently developed computational tool amcheck [31]. Amcheck operationalizes the symmetry-based theoretical framework underpinning altermagnetism by assessing symmetry operations relating spin-up and spin-down magnetic sublattices. Specifically, the algorithm evaluates whether the magnetic sublattices can be mapped onto each other through a spatial inversion or lattice translation combined with a spin-flip operation. If such mappings are universally applicable to all magnetic atoms, the material is pure AFM since these symmetry operations guarantee spin degeneracy across the electronic band structure. Conversely, the absence of such inversion or translation symmetries, coupled with the presence of alternative symmetry operations (e.g., rotational or mirror symmetries), indicates altermagnetism. This condition implies the presence of symmetry-protected spin splitting in the band structure despite zero net magnetization. The advantage of amcheck lies in its reliance solely on crystallographic and magnetic structural information, circumventing the need for computationally intensive electronic structure calculations. Consequently, it serves as a rapid, efficient, and theoretically robust tool ideally suited to large-scale, high-throughput screenings. The symmetry analysis, both internally in amcheck and for the details we report in the supplementary materials uses Spglib [32, 33].

We used Pymatgen [34] to read the mcif files from MAGNDATA. We applied amcheck to all the collinear structures, which resulted in 157 candidate altermagnetic materials. We then applied amcheck to collinear versions of all noncollinear materials, where we aligned the spins by the algorithm used by Pymatgen when converting a magnetic moment to a scalar: the magnitude of the magnetic moment is retained and the sign assigned by projecting the moment onto a standard axis. The standard axis is arbitrarily chosen to always have the direction defined by the Cartesian vec-

collinear variants are introduced solely to enable a uniform high-throughput screening; we do not assess their energetic stability relative to the noncollinear ground state. This resulted in 131 additional candidates. Overall, we obtained a total of 288 potential AM materials from the MAGNDATA database (157 collinear and 131 noncollinear). Eliminating duplicated structures based on chemical composition and space group, the final set was 188 candidates suitable for further computational examination.

In the second screening phase (Fig. 1b), input files for spin-polarized self-consistent field (SCF) and nonself-consistent field (non-SCF) DFT calculations were systematically generated using Pymatgen and the Highthroughput toolkit (httk ) [35]. The workflow manager in httk provides a powerful, flexible automation framework specifically tailored for large-scale computational workflows, significantly enhancing computational efficiency. Importantly, magnetic orders and initial magnetic moments of atoms were directly extracted from MAGNDATA’s mcif files, ensuring consistency with experimentally established configurations. In cases where the reported local magnetic moments were particularly small (e.g., below 1 µ B /atom), we initialized the corresponding magnetic moments to a slightly higher value (typically 1 µ B ) to avoid artificial quenching during SCF relaxation.

The resulting spin-polarized SCF calculations, per3

(a) (b)

MAGNDATA

.mcifs 2287 Magnetic

Materials

Fail amcheck

288 materials

Filter duplication Fail 198 candidate altermagnets 198 candidate altermagnets DFT input files Pymatgen Httk

Spin-polarized

DFT SCF VASP

NSCF DFT kmesh x2 VASP Δ>26 meV |E-E F |<3 eV Metals 22 Semiconductors 158 Altermagnetic

database Band structure

on hs-path 180 confirmed altermagnets VASP FIG. 1. Two-stage high-throughput computational workflow to identify candidate altermagnetic materials (AMs). (a) Initial screening selects experimentally characterized magnetic materials from the MAGNDATA database. Symmetry analysis via amcheck followed by deduplication filtering step, yielding a final set of 198 unique AM candidates. (b) In-depth computational verification using spin-polarized DFT calculations (VASP, pymatgen, and httk ). Materials exhibiting spin splitting (≥ 26 meV within ±3 eV of E F ) are confirmed as AM and included in the final database.

formed using the Vienna Ab-initio Simulation Package (VASP) [36–38], were analyzed to identify meaningful spin-splitting. To select only robust altermagnets, a minimum spin-splitting magnitude of 26 meV was used as a selection criterion and this splitting has to occur within an energy window of ±3 eV around the Fermi level. Figure S1 shows the distribution of ∆ max across the screened set and supports adopting 26 meV as a physically motivated lower bound, comparable to the room-temperature thermal energy scale (k B T ≈ 26 meV).

Based on these criteria, 180 materials were validated as exhibiting significant spin-splitting and advanced to the final characterization step, while the remaining candidates were discarded. Detailed electronic band structure calculations were subsequently conducted for these selected 180 altermagnets, enabling direct visualization and confirmation of spin-up and spin-down band splittings. Because magnetic symmetry can enforce nodal manifolds where the nonrelativistic splitting vanishes on many high-symmetry lines/planes, we evaluate ∆(k) on dense Brillouin-zone meshes (and fixed-k z slices when needed), rather than relying solely on conventional highsymmetry paths, to reliably capture ∆ max . In these computations, the magnetic moments were assumed to be in a collinear configuration, a commonly adopted simplification in high-throughput studies, which is sufficient for identifying the essential altermagnetic characteristics.

To further quantify the spin splitting, we computed both the average and volumetric spin-splitting metrics. The average spin splitting ⟨∆⟩ is defined as the mean of the maximum spin splitting across all k-points with eigenstates lying within a ±3 eV window around the Fermi level,

where W k is the set of bands at k within the energy window, and N is the number of contributing k-points.

The volumetric spin-splitting fraction F ∆ captures the fraction of bands and the portion of the Brillouin zone exhibiting appreciable spin splitting:

where w k is the k-point weight, M k is the number of bands within the energy window at k, and Θ is the Heaviside function applied with a small cutoff (e.g., 10 meV) to suppress numerical noise.

Note that the calculations are performed using the usual scalar-relativistic projector augmented-wave (PAW) pseudopotentials distributed with VASP, but we do not otherwise include spin–orbit coupling (SOC) or other relativistic corrections. This defines the nonrelativistic baseline for spin splitting in altermagnets, where the essential effect arises from exchange and crystalline symmetry rather than relativistic interactions. For compounds containing heavy 5d or 5f elements, however, SOC can strongly influence electronic phases [39] and consequently affect the magnitude of the spin splitting. The explicit inclusion of SOC in high-throughput workflows is computationally demanding and, in heavyelement systems, may also lead to convergence difficulties. Hence, in particular our results for heavy-element 4 compounds, which are expected to be more sensitive to these effects, may need further investigation for the contribution from SOC.

III. RESULTS AND DISCUSSION

Summarized in Table II are the key properties of the top candidate materials identified through our highthroughput screening, including their maximum, average, and volumetric spin-splitting magnitudes (∆F ), electronic band gaps, Hubbard U parameters, and minimum elemental abundances. Among these, six altermagnets, CrSb, MnTe, CrSe, RuO 2 , Ca(Al 2 Fe) 4 , and UCr 2 Si 2 C, exhibit particularly pronounced spin-band splitting. Notably, experimental evidence for altermagnetism in CrSb [18], MnTe [40], and RuO 2 [16] has recently been presented, providing strong validation for the predictive capability of our computational framework. In the following sections, we focus on three representative cases: the metallic altermagnets UCr 2 Si 2 C and MnNbP, and the semiconducting altermagnet YRuO 3 , each exhibiting spin-splitting features and serving as compelling examples of the diverse electronic characteristics accessible within the altermagnetic landscape.

UCr 2 Si 2 C crystallizes in a tetragonal structure belonging to the paramagnetic space group P 4/mmm (No. 123), characterized by lattice parameters a = b = 3.98 and c = 5.16 [41]. The structure is composed of alternating uranium and Cr 2 Si 2 C layers stacked along the crystallographic c-axis. Within each Cr 2 Si 2 C layer, chromium atoms form planar Cr 2 C networks arranged in a checkerboard motif. Magnetic moments are localized exclusively on the Cr atoms, which occupy two

to align antiparallel, with an estimated magnitude of ap-

Under this collinear AFM configuration, UCr 2 Si 2 C is associated with the magnetic space group P m ′ m ′ m (No. 47.252, BNS notation), which determine its magnetic symmetry properties. This group comprises eight symmetry elements: four unitary operations that preserve spin namely, the identity {1 | 0}, spatial inversion

and a mirror reflection across the plane perpendicular to the x-axis {m 100 | 0} as well as four anti-unitary operations combining spatial transformations with timereversal symmetry. These include the twofold rotations about the z-axis combined with time reversal {2 ′ 001 | 0} and a twofold rotation about the y-axis combined with time reversal {2 ′ 010 | 0}, and the time-reversed mirror reflections {m ′ 001 | 0} and {m ′ 010 | 0}. These operations collectively preserve the overall tetragonal crystal symmetry while accommodating a collinear antiferromagnetic configuration with Cr.

Crucially, although both inversion P {−1 | 0} and antiunitary time revesal T = {−1 ′ | 0} symmetries appear in the group, the combined operation PT = {−1 ′ | 0} does not constitute a symmetry of the system. The absence of PT symmetry lifts the constraint that would otherwise enforce spin degeneracy, thereby permitting spin splitting even in the absence of spin–orbit coupling. Furthermore, the system lacks the combined spin-rotation and non-primitive lattice translation symmetry U τ , which maps antiparallel magnetic sublattices onto one another via a 180 ◦ spin rotation coupled with a fractional lattice translation. Such symmetries are characteristic of conventional collinear antiferromagnets and protect spin degeneracy throughout the Brillouin zone. In contrast, the symmetry-inequivalent positioning of the Cr atoms in UCr 2 Si 2 C precludes the existence of any U τ operation. The simultaneous breaking of both PT and U τ symmetries thus defines the altermagnetic nature of UCr 2 Si 2 C.

Figure 2(c) presents the spin-polarized electronic band structure of UCr 2 Si 2 C along high-symmetry paths in the Brillouin zone, as defined in Fig.2(b). Spin-up and spin-down states are shown in red and blue, respectively. A prominent feature of the band structure is the coexistence of spin-degenerate and spin-split regions across momentum space, hallmarks of altermagnetic behavior. The maximum energy separation occurs near the ∆ max point, where the spin splitting reaches approximately 0.72 eV. The average spin splitting across the Brillouin zone is calculated to be 0.31eV, with a volumetric splitting ratio of roughly 47%. To explicitly identify symmetry-driven spin reversals, we analyzed symmetryequivalent paths in the reciprocal space, as shown in panel (d). Specifically, along paths such as ∆ max –Γ– ∆ ′ max and R–A–R ′ , exchanging the reciprocal-space coordinates k x ↔ k y directly leads to inversion of the spin polarization (spin-up states become spin-down and vice versa). This momentum-dependent spin reversal arises naturally from the magnetic symmetry operations of the P m ′ m ′ m space group and it distinguishes altermagnetic systems from conventional ferromagnets or Rashba-type spin–orbit coupled systems.

To further visualize the momentum-resolved spin splitting, we plot the two-dimensional (2D) contour map of the spin splitting magnitude (∆E) on the k z = 0.5 plane in Fig. 2(e). This plane includes the maximum splitting

splitting occurs. In this map, red and blue regions respectively indicate positive and negative spin splitting between spin-up and spin-down states. The most intense features appear in the vicinity of ∆ max , with symmetric but sign-reversed spin splitting observed on opposite sides of the Brillouin zone. This antisymmetric pattern

signature of altermagnetic order in this material.

Figure 2(f) shows the spin-resolved Fermi surface crosssections in the (001) plane. Spin-up and spin-down Fermi

contours are shown in red and blue, respectively. The contours are anisotropic and exhibit a clear 90 ◦ rotation between the spin channels, another hallmark of altermagnetism. To fully capture the spin-dependent topology of the Fermi surface, we plot the three-dimensional spin-resolved Fermi surfaces in Figs. 2(g) and 2(h) for the spin-up and spin-down channels, respectively. Each plot reveals four distinct Fermi surfaces corresponding to four partially occupied bands crossing the Fermi level. Notably, while the innermost Fermi surface centered at the corners of the Brillouin zone appears nearly identical for both spin channels, the remaining three Fermi sheets (colored yellow, blue, and pink) exhibit clear rotational asymmetry. The spin-down Fermi surfaces are clearly rotated by 90 ◦ relative to their spin-up counterparts, consistent with the antisymmetric spin texture expected from the symmetry constraints of the magnetic space group. Together, these observations, momentumantisymmetric spin splitting, 90 ◦ -rotated spin-resolved Fermi surfaces, and symmetry-induced spin channel inversion, provide compelling evidence for the robust altermagnetic character of UCr 2 Si 2 C.

B. NbMnP

NbMnP crystallizes in the TiNiSi−type orthorhombic structure belonging to the paramagnetic space group Pnma (No. 62), characterized by lattice parameters

structure comprises zigzag chains of Mn atoms aligned along the b-axis, embedded within a network formed by Nb and P atoms. In this study, we consider a collinear AFM configuration as depicted in Fig. 3(a).

The magnetic symmetry properties of this AFM state are governed by magnetic space group P n ′ m ′ a ′ (No. 62.449, BNS notation), a type-III magnetic subgroup of the paramagnetic parent group Pnma (No. 62). This magnetic group incorporates eight symmetry elements: four unitary operations preserving spin specifically, the identity {1 | 0}, spatial inversion {−1 | 0}, mirror reflec-

cluding time-reversed inversion {−1 ′ | 12 , 0, 12 }, a time-

6

Critically, both PT and U τ symmetries are absent which implies that no symmetry exists to map the antiparallel Mn sublattices onto one another, thereby lifting the constraints that would typically enforce spin degeneracy in conventional antiferromagnets.

firm the altermagnetic character of NbMnP.

The spin-polarized electronic band structure along standard high-symmetry paths is presented in Fig. 3(c), with spin-up and spin-down channels shown in red and blue, respectively. Pronounced spin splitting regions coexist with segments of near degeneracy. The maximum spin splitting, approximately 0.46 eV, occurs near the ∆ max point, whereas the BZ-averaged splitting is about 0.28 eV with a volumetric splitting ratio of 35%. To illustrate symmetry-enforced spin reversal explicitly, Fig. 3(d) displays the spin-resolved bands along the path ∆ max –Γ–∆ ′ max , demonstrating symmetric spin-band exchange under the transformation k x → −k x across Γ.

YRuO 3 crystallizes in the orthorhombic magnetic space group P n ′ ma ′ (No. 62.448, BNS notation), derived from the paramagnetic parent group Pnma (No. 62) [43]. The unit cell adopts lattice parameters a = 5.839 Å,

described as a tilted perovskite framework composed of corner-sharing RuO 6 octahedra, with Y atoms occupying the interstitial positions. The magnetic ground state is G-type antiferromagnetic, with antiparallel spin alignment between neighboring Ru 3+ sites along all three crystallographic directions. The spin moments are localized on the Ru sublattices, whereas Y and O atoms remain magnetically inactive. Addtionally, it includes standard unitary operations, such as inversion, mirror planes, and twofold rotations, along with anti-unitary operations that combine time reversal with rotations and mirrors (e.g., 2 ′ 001 , m ′ 100 , m ′ 001 ). The resulting AFM structure consists of two symmetry-inequivalent Ru sublattices with antiparallel spin orientations. This arrangement prevents any symmetry operation from mapping one sublattice onto the other via inversion–time-reversal (PT ) or spinrotation–translation (Uτ ). This dual symmetry breaking allows for spin splitting even without spin–orbit couFigure 3(e) shows the spin-splitting magnitude ∆E within the k z = 0.25 plane, revealing clearly signreversed splitting distributions across opposite sides of the BZ. Additionally, Fig. 3(f) presents the spin-resolved Fermi surface cross-section at k z = 0.05, exhibiting distinctly anisotropic contours and a clear 180 ◦ rotation between the spin channels, consistent with k x ↔ −k x symmetry. The 3D spin-resolved Fermi surfaces shown in Figs. 3(g) and 3(h) for spin-up and spin-down channels, respectively, further highlight this 180 ◦ spin-channel rotation. Taken together, these observations robustly con-

7

pling, which is what defines the altermagnetic nature of YRuO 3 .

Figure 4(b) shows the bulk Brillouin zone BZ YRuO 3 with the high-symmetry points labeled according to the Pnma convention. The spin-polarized electronic band structure, computed along these high-symmetry paths, is presented in Fig. 4(c). A key feature is the coexistence of spin-degenerate and spin-split bands. The magnitude of spin splitting varies across momentum space, reaching its maximum near the ∆ max point, where the energy separation between spin-up and spin-down bands is approximately 0.12 eV.

To visualize the symmetry-driven spin inversion, Fig. 4(d) compares the band dispersions along two momentum paths that are equivalent under the transformation k x → −k x . Along these symmetry-related paths, the spin polarization reverses: spin-up states on the ∆ max /Y side correspond to spin-down states on the −∆ max /−Y side, reflecting the momentum-antisymmetric spin splitting enforced by the P n ′ ma ′ magnetic group. Figure 4(e) further highlights this feature through a 2D contour map of ∆E in the k z = 0.1 plane, where the splitting is maximal around ∆ max . Figure 4(f) illustrates the spin texture in the (001) plane from a SOC (noncollinear) calculation, showing the in-plane orientation of the spin expectation value for states near the Fermi level. The spin-up and spin-down components exhibit opposite orientations across symmetry-related k-points, indicating a momentum-dependent spin reversal that extends across the Brillouin zone rather than being localized to a specific path or point.

IV. IDENTIFICATION IN 2D DATABASES

To identify bulk altermagnetic compounds with chemically equivalent 2D counterparts, we compared the reduced formulas and ICSD IDs of all 188 bulk AM candidates with entries in two major 2D materials databases: the Computational 2D Materials Database (C2DB) [44] and the AiiDA 2D repository [45]. We only retain entries for which the ICSD ID of the bulk parent coincides with that of the corresponding 2D record. In Table I, we collect all bulk AM materials whose reduced formula 8 TABLE I. Bulk altermagnetic materials with an existing 2D compound of the same reduced chemical formula in the C2DB or AiiDA databases. Multiple MCIF entries with identical formulas correspond to distinct MAGNDATA models. IDs 0.15 0.178, 0.334 0.335, 0.581, 1.0.33 0.36 0.607 0.800 1.0.47, 1.0.48 2.35 0.65, 0.66 Chemical formula

MnTe MnSe 2 CrSe Fe 2 O 3 C2DB Yes Yes Yes Yes Yes Yes Yes Yes – AiiDA

– – – – – – Yes – Yes appears in at least one of the 2D databases and indicate whether a match was found in C2DB, in AiiDA, or in both. These databases contain both experimentally synthesized and theoretically predicted monolayer compounds.

The list of bulk altermagnets with a corresponding two-dimensional compound is rather short. Indeed, the majority of compounds appearing in Table I contain transition–metal elements with partially filled d shells together with halogens (F, Cl) or chalcogens (S, Se, Te). The later help stabilizing layered or quasi-layered chemistries, while the former provide the local moments that form the basis of the magnetism.

Note that the first column of the table shows that some chemical formulas correspond to multiple MAGNDATA entries. The reason is that different experimental studies report distinct magnetic configurations, magnetic subgroup assignments, or slightly different crystallographic refinements. These duplicated entries correspond to separate magnetic models of the same material, not different compounds, and therefore belong match with a single two-dimensional material.

Table I identifies candidate bulk altermagnets which exist in 2D, but does not say that these materials are also altermagnetic as a monolayer. This question has been addressed by Sødequist and Olsen [46], who identified 7 altermagnetic monolayer candidates starting from C2DB. Crucially, they take into account the magnetic anisotropy coming from spin-orbit that is necessary to get a magnetically ordered phase in 2d, in accordance with the Mermin-Wagner theorem. Starting from C2DB, they identified which monolayers can be altermagnets, also taking into account spin-orbit coupling. The spin-orbit coupling introduces magnetic anisotropy that makes it possible to stabilize magnetism in 2d while satisfying the Mermin-Wagner theorem. Their 7 altermagnetic monolayer candidates similarly contain mostly transition metals terminated by halogens or chalcogens, although they also find two more complex compounds. Interestingly, there is zero overlap between Table I and the list in Sødequist and Olsen.

V. COMPARISON WITH OTHER STUDIES

The results reported here can be discussed in relation to two prior screenings of MAGNDATA. The highthroughput classification by Wan et al. relied on the absence of the antiunitary symmetries PT (inversion plus time reversal) and tT (translation plus time reversal) [27]. Moreover, they extended their candidate pool to include ferrimagnetic systems by considering their SOC-off configuration, resulting in 336 potential altermagnets. Guo et al. also focused on systems with PT symmetry [29]. They screened stoichiometric compounds with fully compensated collinear magnetic order without ferromagnetic component while avoiding some complications, including systems with magnetic order from rare-earth atoms, large unit cells, and DFT calculations difficult to converge, which resulted in 62 materials.

Our study employs the amcheck algorithm, which tests the same symmetry condition (absence of PT and tT ) to identify potential altermagnetic materials. However, amcheck strictly excludes ferrimagnetic states since their sublattices are completely not symmetry-related and are instead classified as “Luttinger ferrimagnets” that exhibit spin splitting but lack the required momentumodd, nodal spin texture over the Brillouin zone. For example, Cr 2 S 3 , listed as “interesting” in Ref. [27], shows spin splitting in the spin–polarized DFT consistent with ferrimagnetic behavior, yet lacks the nodal spin texture and is therefore not classified as altermagnetic here. On the other hand, we find a collinear AFM with Kramers–degenerate bands for SrMnSb 2 , and the small splittings of a few meV that appear at high energy are most likely numerical artifacts and not indicative of altermagnetism. These distinctions likely account for the smaller number of altermagnets identified in our study compared to Ref. [27], while remaining fully consistent with the symmetry–based definition of altermagnetism [1, 2]. The 59 non-metallic and 3 metallic compounds identified in Ref. [29] all appear in our list of 157 collinear entries with the right symmetries for altermagnetism (see table S2 in the supplementary materials), however, the criterion of a spin splitting threshold of 26 meV for our final list removes 10 of them.

Furthermore, we have considered a set of collinear versions of materials reported as noncollinear. This extended set of materials along with their computed spin splittings describe alternative spin configurations on otherwise stable crystal structures. They can be a valuable resource to aid the general understanding of altermagnetism. Some of them are arguably relevant due to them being very nearly collinear, shown in our analysis by the angle between the spin axes. We also speculate that for some of the ones with larger such angles, there could exist ways in practice to invoke a more aligned moments to give the altermagnetic configuration, via, e.g., external fields, stress/strain, or similar mechanisms.

9 TABLE II. Top altermagnet candidate materials with respect to their spin-splitting. Space group, max angle between spins for materials that were originally noncollinear (arccos(|S i · S j |/|S i ||S j |)), spin-splitting metrics, band gap, wave classification, Hubbard U , and minimum elemental abundance. For more information on symmetry data, refer to the supplementary materials. |S ·S | Material Space Group

i

j

VI. CONCLUSION

In this work, we have established a comprehensive and symmetry-aware high-throughput framework for the discovery and characterization of altermagnetic materials. We systematically screened more than 2,000 experimentally verified magnetic structures from the MAGNDATA database using a two-stage workflow. This approach, built on the magnetic symmetry diagnostic tool amcheck and the High-Throughput Toolkit, identified 180 candidate materials exhibiting significant momentumdependent spin splitting. These include both metallic and semiconducting systems, many of which had not been previously reported as altermagnets. Notably, our approach recovers experimentally confirmed compounds such as CrSb, MnTe, and RuO 2 , and highlights previously overlooked materials like UCr 2 Si 2 C, MnNbP, and YRuO 3 that display robust symmetry-protected spin splitting even in the absence of spin–orbit coupling. Furthermore, by cross-referencing our bulk AM candidates with the C2DB and AiiDA 2D repository, we identify nine materials with chemically equivalent 2D counterparts.

Crucially, our momentum-resolved analysis reveals that spin splitting varies strongly across the Brillouin zone, often away from high-symmetry paths, providing actionable insights for future spin and angle-resolved photoemission spectroscopy (ARPES) measurements. The open-access database generated through this effort offers a valuable resource for guiding experimental exploration and materials design in spintronics. More broadly, this study establishes a scalable and transferable blueprint for accelerating the discovery of unconventional magnetic phases and paves the way for targeted development of altermagnetic materials with desirable symmetry and transport properties.

VII. ACKNOWLEDGEMENTS

This work was partially supported by the Wallenberg Initiative Materials Science for Sustainability (WISE) funded by the Knut and Alice Wallenberg Foundation. R.A. acknowledges financial support from the Swedish e-Science Research Centre (SeRC). EvL acknowledges support from the Swedish Research Council (Vetenskapsrådet, VR) under grant 2022-03090, from the Royal Physiographic Society in Lund and by eSSENCE, a strategic research area for e-Science, grant number eSSENCE@LU 9:1. J.A.L thank the Kempe-stiftelserna, Sweden and Swedish Research Council under grant no. 2023-03894 for financial support. B.M. acknowledge the financial support of Olle Engkvists stiftelse, project 207- 10 0582. The computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS), partially funded by the Swedish Research Council through grant agreement no. 2022-06725.

Appendix A: Computational Details Density functional theory (DFT) calculations were carried out using the Vienna Ab initio Simulation Package (VASP) [37, 38], employing the projector augmentedwave (PAW) method and the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) functional to describe exchange-correlation effects [36, 47]. Electron correlation was treated using the rotationally invariant DFT+U approach [48], with the effective Hubbard U eff parameters taken from Pymatgen (Materials Project) [49] and supplemented by Wang et al. [50] where needed. The magnitude of the spin splitting depends on the value of U via the magnitude of the magnetic moments [51], whereas the structure of the splitting in the Brillouin Zone is expected to be weakly dependent on the value of U . Consistent with this, recalculations with U scaled by ±10% for all metallic candidates show that the altermagnetic classification is unchanged and sizable splittings persist; the variations are mainly quan[1] L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conven-

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Supplemental Material for High-Throughput Quantification of Altermagnetic Band Splitting

Ali Sufyan, 1,2,3 Brahim Marfoua, 4 J. Andreas Larsson, 3,5 Erik van Loon, 1,2 and Rickard Armiento 4 2 1 NanoLund and Division of Mathematical Physics, Department of Physics, Lund University, SE-221 00 Lund, Sweden Wallenberg Initiative Materials Science for Sustainability, Department of Physics, Lund University, SE-221 00 Lund, Sweden 3 Applied Physics, Division of Materials Science, Department of Engineering Sciences and Mathematics, Luleå University of

Technology, SE-971 87 Luleå, Sweden 4 Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden 5 Wallenberg Initiative Materials Science for Sustainability, Luleå University of Technology, SE-971 87 Luleå, Sweden Table S1: High-throughput screening results for candidate altermagnets. The table lists the MAGNDATA ID(s), material, space group, spin-splitting metrics (F ∆ , Max SS, Avg SS), band gap, and minimum elemental crustal abundance, and is ordered by decreasing Max SS. When multiple MAGNDATA IDs are listed for the same material/space group, the first ID corresponds to the record with the largest Max SS and the values reported in the remaining columns, while the other listed IDs are also identified as altermagnets with Max SS > 26 meV.

La 2 CoIrO 6 TbFeO 3 Fe 2 WO 6 P2 1 /c Pnma Pbcn 24.107 26.786 29.688 0.272 0.271 0.270 0.121 0.133 0.173 0.000 2.826 1.465

1.200 1.250

Er 2 Ru 2 O 7 FeBO 3 DyFeO 3 Fd-3m R-3c Pnma 20.313 29.688 26.786 0.268 0.262 0.261 0.266 0.177 0.134 0.412 2.660 2.863

5.200 TlCrO 3 CoH 6 (CO 3 ) 2 MnSiN 2 FeHSO 5 Mn 2 GeO 4 Pnma P2 1 /c Pna2 1 C2/c Pnma 24.107 14.773 18.750 26.563 23.125 0.246 0.245 0.245 0.242 0.239 0.146 0.132 0.114 0.156 0.127 0.625 1.908 2.733 2.625 0.594

Fe 2 O 3 ErCrO 3 CrInO 3 CeFeO 3 R-3c Pnma Pnma Pnma 28.977 21.875 20.536 27.679 0.237 0.234 0.232 0.227 0.152 0.108 0.132 0.121 2.566 3.143 1.886 2.818

3.500

ScCrO 3 Sr 2 TbIrO 6 SmCrO 3 YCrO 3 SmFeO 3 FeNiPO 5 Pnma P2 1 /c Pnma Pnma Pnma Pnma 20.536 27.083 20.536 21.429 27.679 24.375 0.227 0.226 0.222 0.221 0.215 0.207 0.127 0.114 0.095 0.115 0.124 0.121 2.987 0.139 3.115 3.121 2.843 2.694

7.050

7.050

continued on next page 1 Table S1 (continued). MAGNDATA ID Material Space group F ∆ (%) Max SS Avg SS Bandgap Min abund. (ppm) 0.609, 0.288, 0.37 0.592, 2.64, 2.63 0.587 0.983, 0.982 0.392 0.1085 0.26 0.25 0.336, 0.337 0.1071 0.642, 0.1 0.354, 2.62 0.114 0.1021, 0.1022 0.295 0.896 0.315 0.323, 0.417 1.0.47 0.608 0.298 0.5 0.21 0.314 0.788 0.792, 0.794, 0.793 0.589 0.105, 0.104 0.262 0.115 0.712 1.0.33 0.714 0.1068 0.116 0.747 0.334 0.937, 0.301 0.1036 0.575 0.984 1.0.26 0.189 0.6 0.204 0.218, 0.219 0.148 0.755 0.581, 0.335 0.722 0.681 0.79 NdMnO 3 Pnma 19.643 0.206 0.143 1.420 4.150 × 10 1

DyCrO 3 Pnma 20.833 0.206 0.103 3.079 5.200

TmCrO 3 TmVO 3 Fe 3 P 2 (HO 5 ) 2 PrFeO 3 CuFePO 5 NaOsO 3 NdFeO 3 Fe 2 SiO 4 LaMnO 3 TbCrO 3 CoCO 3 TmFeO 3 Cu 2 H 3 ClO 3 CrNiO 4 ZrMn 2 (GeO 3 ) 4 LaCrO 3 MnSe 2 PrMnO 3 BaNa 2 V 2 FeO 8 TiMnO 3 NiPbO 3 ZrCo 2 (GeO 3 ) 4 YVO 3 Sr 2 HoRuO 6 Pnma P2 1 /c P2 1 /c Pnma Pnma Pnma Pnma Pnma Pnma Pnma R-3c Pnma P2 1 /c Cmcm P4/nbm Pnma Pa-3 Pnma C2/c R3c R3c P4/nbm P2 1 /c P2 1 /c 25.000 18.750 23.611 28.571 27.500 22.917 27.679 17.361 20.536 23.958 25.000 22.321 23.125 31.250 14.423 20.536 45.833 21.429 20.956 25.000 26.136 17.788 20.833 22.321 0.202 0.200 0.197 0.197 0.194 0.193 0.192 0.192 0.188 0.188 0.188 0.188 0.186 0.186 0.184 0.182 0.178 0.176 0.174 0.173 0.170 0.170 0.168 0.166 0.117 0.100 0.126 0.120 0.119 0.082 0.122 0.132 0.106 0.098 0.125 0.124 0.055 0.109 0.105 0.097 0.133 0.107 0.102 0.101 0.111 0.110 0.067 0.084 3.141 1.739 2.051 2.822 1.955 0.119 2.833 2.940 1.283 3.114 2.766 0.762 1.749 2.000 2.309 3.105 0.983 0.896 2.710 2.470 0.561 2.628 2.043 1.031

NdCrO 3 ErVO 3 CoFePO 5 MnCO 3 Nb 3 VS 6 FeF 3 Li 2 Ni(SO 4 ) 2 LuCrO 3 FeCO 3 Ba 3 CoIr 2 O 9 CoF 3 Sr 2 CoTeO 6 CoTa 4 Se 8 ZnFeH 4 O 2 F 5 LuVO 3 RbCoBr 3 CeMn 2 Ge 4 O 12 YMnO 3 Ca 2 MnReO 6 Co 2 SiO 4 LiLa 2 RuO 6 Mn 2 SeO 3 F 2 FeF 3 Mn 4 Nb 2 O 9 Ce 4 Sb 3 Sr 2 DyRuO 6 Pnma Pnma Pnma R-3c P6 322 P6 3 /m P2 1 /c Pnma R-3c C2/c R-3c P2 1 /c P6 3 /mmc Imm2 Pnma P6 3 /mmc P4/nbm P6 3 cm P2 1 /c Pnma P2 1 /c Pnma R-3c Cc I-43d P2 1 /c 19.643 18.750 26.875 19.531 31.250 31.250 20.536 19.792 17.361 29.167 31.250 29.167 36.719 23.438 18.750 24.432 18.269 21.875 11.458 22.222 26.042 21.250 32.813 21.250 47.500 23.214 0.165 0.165 0.164 0.161 0.161 0.159 0.158 0.158 0.157 0.156 0.155 0.155 0.154 0.154 0.153 0.150 0.149 0.145 0.145 0.144 0.142 0.141 0.141 0.140 0.139 0.138 0.107 0.082 0.103 0.112 0.057 0.080 0.077 0.125 0.110 0.124 0.095 0.088 0.126 0.074 0.073 0.100 0.117 0.092 0.076 0.101 0.093 0.095 0.094 0.078 0.058 0.081 3.079 1.971 2.399 4.015 0.000 3.764 4.565 3.192 3.688

1.825 2.154 0.000 3.124 1.991 0.000 0.000 1.305 0.000 2.506 1.221 3.889 4.342 1.270 0.000 1.114

continued on next page 2

Table S1 (continued). MAGNDATA ID Material Space group F ∆ (%) Max SS Avg SS Bandgap Min abund. (ppm) 0.513 0.121 0.83 0.1008 0.795 0.263 0.31, 0.32, 0.33 0.98, 0.981, 0.979 0.999, 0.1 0.1059 0.117 0.67, 0.669 0.671 0.24 3.4 0.241 0.416 0.791 0.168 0.45 0.787 0.948 0.934 0.42 0.122 0.108 0.708 0.165 0.7, 0.8 0.582, 2.61 0.802 0.1082 0.748 0.192 1.0.39 0.936 0.368 0.41, 0.40 0.294 0.229 0.79 0.1018, 0.1019 0.967 0.292 0.917 0.785, 0.786 0.1013 0.726, 0.727 0.715, 0.716 0.404 0.316 0.361 0.434, 0.553 YRuO 3 Li 2 Co(SO 4 ) 2 LiFeP 2 O 7 Sr 2 ErRuO 6 Sr 2 YRuO 6 Fe 2 PO 5 HoMnO 3 Pnma P2 1 /c P2 1 P2 1 /c P2 1 /c Pnma P6 3 cm 18.750 20.536 22.917 22.321 22.321 22.500 25.000 0.138 0.136 0.136 0.134 0.134 0.134 0.134 0.067 0.088 0.085 0.075 0.075 0.102 0.084 0.569 3.224 2.958 1.009 1.012 2.086 1.310

continued on next page 3 Table S1 (continued). MAGNDATA ID Material 0.552 0.191 0.431 0.724 0.329 0.62 0.239 0.955 0.21 1.0.35 0.331 1.0.9, 1.0.38 0.3 0.56 0.398 0.13 0.134 0.13 0.1014 0.405 0.106 1.0.46 2.88 0.332 0.254, 0.255 0.303 1.0.44 0.1063 1.0.31, 1.0.32 0.425 0.849 0.658 1.0.4 0.109 0.53 Space group F ∆ (%) Max SS Avg SS Bandgap Min abund. (ppm) Mn(PbO 2 ) 2 P-42 1 c BaCuF 4 Cmc2 1 CuB 2 O 4 I-42d BaCoSiO 4 P6 3 RbMnF 4 P2 1 /c SrMn 2 V 2 O 8 I4 1 cd LiCa 3 RuO 6 R-3c Na 2 MnH 8 (C 3 O 5 ) 2 Pbca Sr 2 CoOsO 6 C2/c CsMnBr 3 P6 3 /mmc Fe 2 Mo 3 O 8 P6 3 mc CsCoCl 3 P6 3 /mmc LiCa 3 OsO 6 R-3c Ba 2 CoGe 2 O 7 P-42 1 m Ca 2 RuO 4 Pbca Cu 3 Mo 2 O 9 Pnma Mn 3 B 7 IO 13 Pca2 1 Ca 3 MnCoO 6 R-3c CsNiC 3 (SN) 3 P2 1 /c CsCoF 4 I-4c2 MnH 6 (CO 2 ) 3 Pca2 1 Ba 3 MnSb 2 O 9 C2/c UGaNi P-62m Co 2 Mo 3 O 8 P6 3 mc CuH 9 C 4 (NO 2 ) 3 Pna2 1 BaCrF 5 P2 12121 Ba 3 CoSb 2 O 9 P6 3 /mmc Fe 2 H 6 (SeO 4 ) 3 R3c Eu(InAs) 2 P6 3 /mmc Na 2 CoP 2 O 7 Pna2 1 Er 5 (In 2 Pd) 2 Pbam BaCu(TeO 3 ) 2 P4 132 CsNiCl 3 P6 3 /mmc CrH 4 NF 3 P4 2 /mbc SrCu(TeO 3 ) 2 P4 132 24.063 22.222 21.023 25.000 17.188 24.219 26.042 15.461 23.558 26.875 17.361 18.750 17.014 17.969 18.056 18.438 18.750 18.750 14.205 28.205 19.318 9.821 2.371 20.139 17.500 23.611 24.750 14.732 2.083 15.750 2.500 13.603 16.369 1.442 5.147 4 0.083 0.083 0.081 0.079 0.076 0.076 0.074 0.074 0.073 0.071 0.069 0.069 0.068 0.068 0.067 0.064 0.063 0.063 0.060 0.059 0.059 0.057 0.057 0.057 0.056 0.049 0.044 0.043 0.041 0.040 0.036 0.032 0.032 0.032 0.026 0.064 0.039 0.052 0.054 0.040 0.054 0.062 0.053 0.043 0.057 0.042 0.054 0.060 0.047 0.041 0.045 0.043 0.051 0.037 0.045 0.043 0.045 0.028 0.035 0.034 0.030 0.038 0.040 0.026 0.032 0.021 0.023 0.025 0.017 0.019 1.458 2.208 2.137 3.079 1.926 2.760 1.495 3.726 0.000 3.828 0.000 0.000 0.813 2.592 0.664 1.236 4.319 2.003 2.844 0.053 3.660 2.075 0.000 0.000 2.201 4.241 2.439 3.327 0.000 1.921 3.837 2.835 1.974

3.000

1.200

3.000 3.000

Table S2: Symmetry data for 157 collinear entries in MAGNDATA identified as potential altermagnets. Rows are identified by their MAGNDATA ID. For materials where the detected symmetries depend on the precision used for symmetry identification, values of the spglib symprec setting ranging from 10 −5 to 10 −1 were tested, and when the results differ, multiple rows are included in the table. The column SP shows the lowest value (i.e., the most precise symmetry matching) in this range that gives the respective result. The wave classification is made by matching the Laue classes of the parent spacegroup G and an identified halving subgroup H with Fig. 2 in [PRX 12, 031042 (2022)]. The identified phases are: AM = Altermagnet, FiM = Ferrimagnet. Materials are included as long as one choice of symmetry precision resulted in altermagnetism (i.e., gave a positive result from the amcheck is_altermagnet function). The BNS symbols and numbers are the ones in the MAGNDATA mcif files, whereas the (nonmagnetic) parent spacegroup (Parent SG) is shown as detected by spglib. ID ICSD Chemical formula 0.1 0.3 0.13 0.13 0.15 0.21 0.23 0.25 0.45 0.50 0.56 0.56 0.62 0.65 0.66 0.79 0.83 0.105 0.112 0.113 0.114 0.115 0.116 0.118 0.128 0.131 0.137 0.148 0.154 0.178 0.189 0.229 0.239 0.241 0.254 0.255 0.260 0.261 0.263 0.301 0.303 0.307 0.308 0.309 0.315 0.323 . LaMnO 3 . Ca 3 LiOsO 6 93775 Ca 3 Co 2 xMnxO 6 93775 Ca 3 Co 2 xMnxO 6 68735 MnF 2 . PbNiO 3 55666 Ca 3 Mn 2 O 7 . NaOsO 3 69753 La 2 NiO 4 . MnTiO 3 . Ba 2 CoGe 2 O 7 . Ba 2 CoGe 2 O 7 182224 SrMn 2 V 2 O 8 . Fe 2 O 3 alpha . Fe 2 O 3 alpha 160816 CaIrO 3 95751 LiFeP 2 O 7 185838 ErVO 3 34474 FeBO 3 173985 NiCO 3 61066 CoCO 3 . MnCO 3 100678 FeCO 3 99371 Ba 5 Co 5 ClO 13 182945 FeSO 4 F . Mn(N(CN 2 )) 2 . Cu 2 V 2 O 7 97488 La 2 LiRuO 6 97533 Er 2 Ru 2 O 7 98786 CoF 2 . CeMn 2 Ge 4 O 12 . Ba 2 MnSi 2 O 7 96219 Ca 3 LiRuO 6 79429 Y 2 Cu 2 O 5 248006 [C(ND 2 ) 3 ]Cu(DCOO) 3 248006 [C(ND 2 ) 3 ]Cu(DCOO) 3 93582 CuFePO 5 93581 NiFePO 5 32641 Fe 2 PO 5 195658 Sr 2 CoTeO 6 31705 BaCrF 5 . ScCrO 3 . InCrO 3 . TlCrO 3 257623 ZrMn 2 Ge 4 O 12 180183 LaCrO 3 SP BNS (mcif)

10 −4 R3c (161.69)

Parent SG Phase Pnma (62) R3c (167) R3c (161) R3c (167)

R3c (161) Cmc2 1 (36) Pnma (62)

R3c (161) P2 (3) P42 1 m (113) I4 1 cd (110) R3c (167) R3c (167) Cmcm (63) P2 1 (4) Pnma (62) R3c (167) R3c (167) R3c (167) R3c (167) R3c (167)

C2/c (15) Pnnm (58) Fdd2 (43) P2 1 /c (14) Fd3m (227)

Parent SG Phase P2 1 /c (14) P6 3 mc (186) P6 3 mc (186) R3c (167) R3c (167) Pnma (62) I43d (220) Pnma (62) Pnma (62)

R3c (167) Pnma (62) Pnma (62) P2 1 /c (14) Cmmm (65) C2/c (15) R3c (167) I4c2 (120) R3c (167) Pnma (62) P2 1 /c (14) Pnma (62) I4/mcm (140) P2 1 /c (14) I43d (220) P2 1 /c (14) P4/mmm (123)

Pnma (62)

Imm2 (44) R3c (167) C2/m (12) Pnma (62) Pnma (62) Pnma (62) Pnma (62)

Pnma (62) Pnma (62) Pnma (62) P2 1 /c (14) I43d (220) Cmcm (63) C2/c (15)

C222 1 (20) P6 3 22 (182) P2 1 /c (14) Cc (9) C2/c (15)

Pnma (62) Pnma (62)

AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM G H 2/m -1 6/mmm -3m 6/mmm -3m

-3m -3 -3m -3 mmm 2/m mmm 2/m mmm 2/m mmm 2/m 2/m -1 -3m -3 mmm 2/m mmm 2/m 2/m -1 mmm 2/m 2/m -1 -3m -3 4/mmm mmm

-3m -3 mmm 2/m 2/m -1 mmm 2/m 4/mmm 4/m

2/m -1 4/mmm 4/m

2/m -1 4/mmm mmm 4/mmm mmm mmm 2/m 6/mmm -3m

2/m -1 mmm 2/m -3m -3 2/m -1 mmm 2/m mmm 2/m mmm 2/m mmm 2/m 4/mmm mmm mmm 2/m mmm 2/m mmm 2/m 2/m -1 4/mmm mmm mmm 2/m 2/m -1 6/mmm -3m mmm 2/m 6/mmm -3m

2/m -1 2/m -1 2/m -1 6/mmm -3m mmm 2/m mmm 2/m Wave

dg g g g d d d d d g d d d d d g d g d d d g d g d d d d g d d g d d d d d d d d d d d d d g d g d d d g d d continued on next page 2 Table S2 (continued). ID ICSD Chemical formula SP BNS (mcif)

0.800 43541 MnTe 10 −4 Cmcm (63.457)

0.841 . DyFeO 3 10 −5 Pnma (62.441)

Parent SG Phase Pnma (62) C2/c (15)

I42d (122) Pbcn (60) Pbcn (60) Ima2 (46) Pnma (62) Pnma (62) Pnma (62) Pnma (62) Pnma (62) Pnma (62) Pnma (62) Cmcm (63)

P2 1 /c (14) Pnma (62) P2 1 /c (14) Pnma (62) Pnma (62) Pnma (62) Cmcm (63)

C222 1 (20) C222 1 (20) Pnma (62) Pnma (62)

Pmc2 1 (26) Pna2 1 (33) Pna2 1 (33) Pnma (62) Pnma (62) Pna2 1 (33) Pnma (62)

4 Parent SG Phase

Cmcm (63) P62m (189)

AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM AM G H 4/mmm mmm 6/mmm -3m 6/mmm -3m 6/mmm -3m 6/mmm -3m 6/mmm -3m 6/mmm -3m 6/mmm -3m 6/mmm -3m mmm 2/m mmm 2/m mmm 2/m mmm 2/m mmm 2/m mmm 2/m 6/mmm -3m Wave

dg g g g g g g g d d d d d d g Table S3: Symmetry data for 131 noncollinear entries in MAGNDATA converted into collinear systems and then identified as potential altermagnets. A measure of how much the spins were changed is provided by the highest value of arccos(|S i · S j |/|S i ||S j |) (i.e., 0 ◦ means all spins are aligned, 90 ◦ means that the original structure contains orthogonal spin directions). Rows are identified by their MAGNDATA ID. For materials where the detected symmetries depend on the precision used for symmetry identification, values of the spglib symprec setting ranging from 10 −5 to 10 −1 were tested, and when the results differ, multiple rows are included in the table. The column SP shows the lowest value (i.e., the most precise symmetry matching) in this range that gives the respective result. The wave classification is made via the Laue classes of the parent spacegroup G and an identified halving subgroup H that are matched with Fig. 2 in [PRX 12, 031042 (2022)]. The identified phases are: AM = Altermagnet, FiM = Ferrimagnet. Materials are included as long as one choice of symmetry precision resulted in altermagnetism (i.e., gave a positive result from the amcheck is_altermagnet function). The BNS symbols and numbers are the ones in the MAGNDATA mcif files, whereas the (nonmagnetic) parent spacegroup (Parent SG) is shown as detected by spglib. ID ICSD 0.6 0.7 0.8 0.10 0.11 0.29 0.31 0.32 0.33 0.36

0.40 0.41 0.47 0.69 0.90 0.101 0.102 0.103 0.104 0.107 0.117 0.121 0.122 0.129 0.130 0.132 0.134 0.165 0.165 0.168 0.175 0.191 0.192 0.204 0.207 0.210 0.218 0.219 0.236 Chemical formula BNS (mcif) Parent SG . YMnO 3 50694 ScMnO 3 50694 ScMnO 3 280091 DyFeO 3 280091 DyFeO 3 24152 Er 2 Ti 2 O 7 92838 HoMnO 3 92838 HoMnO 3 92838 HoMnO 3 . NiF 2

. Mn 2 O 3 alpha . Mn 2 O 3 alpha 84753 Gd 2 Sn 2 O 7 . Co 4 (OH) 2 (C 10 H 16 O 4 ) 3 . Rb 2 Fe 2 O(AsO 4 ) 2 . Mn 2 GeO 4 . Mn 2 GeO 4 . Mn 2 GeO 4 185838 ErVO 3 161912 Ho 2 Ge 2 O 7 183152 LuFeO 3 . Li 2 Co(SO 4 ) 2 290292 Li 2 Mn(SO 4 ) 2 173779 Cu 3 Mo 2 O 9 . Cu 3 Mo 2 O 9 . Fe(N(CN 2 )) 2 84319 Mn 3 B 7 O 13 I . SrMn(VO 4 )(OH) . SrMn(VO 4 )(OH) . NH 4 Fe 2 F 6 . Ca 2 CoSi 2 O 7 9930 BaCuF 4 186748 RbFe 2 F 6 . Ca 2 MnReO 6 . TlFe 1 · 6 Se 2 . Sr 2 CoOsO 6 260092 Co 2 SiO 4 260092 Co 2 SiO 4 . CaFe 4 Al 8 10 −5 Pbca (61.433) 10 −5 Pbca (61.433)

10 −5 C2/c (15.85) 10 −5 Pnma (62.441) 10 −5 Pnma (62.441)

P6 3 cm (185) P6 3 cm (185) P6 3 cm (185) Pnma (62) Pnma (62) Fd3m (227) P6 3 cm (185) P6 3 cm (185) P6 3 cm (185) P4 2 /mnm (136) Pbca (61) Pbca (61) Fd3m (227) P2 1 /c (14) Pnma (62) Pnma (62) Pnma (62) Pnma (62) Pnma (62) P4 1 2 1 2 (92)

Pnma (62) Pnma (62) Pnnm (58) Pca2 1 (29) P2 1 (4) P2 1 2 1 2 1 (19) Pnma (62) P2 1 2 1 2 (18) Cmc2 1 (36) Pnma (62) P2 1 /c (14) I4/m (87) C2/c (15) Pnma (62) Pnma (62) I4/mmm (139) Fd3m (227) Fd3m (227) Pna2 1 (33)

0.237 84749 Er 2 Sn 2 O 7 0.238 . Er 2 Pt 2 O 7 0.240 79430 Er 2 Cu 2 O 5 SP

AM mmm 2/m AM 4/mmm mmm AM 2/m -1 AM mmm 2/m AM mmm 2/m AM mmm 2/m AM mmm 2/m AM mmm 2/m AM mmm 2/m AM mmm 2/m AM 2/m -1 AM 2/m -1 AM mmm 2/m AM mmm 2/m AM mmm 2/m AM 2/m -1 AM 2/m -1 AM mmm 2/m AM 2/m -1 AM mmm 2/m AM mmm 2/m AM 2/m -1 AM 2/m -1 AM 2/m -1 AM 2/m -1 AM mmm 2/m AM mmm 2/m AM 4/mmm mmm d d d d d d d d d d d d d d d d d d d d d d d d d d d d d

AM 4/mmm mmm AM 4/mmm mmm AM mmm 2/m d d d continued on next page 1

continued on next page 2

continued on next page 3 Table S3 (continued). ID ICSD Chemical formula BNS (mcif) Parent SG

1.0.45 151442 Ba 3 CoSb 2 O 9 1.0.45 151442 Ba 3 CoSb 2 O 9 1.0.45 151442 Ba 3 CoSb 2 O 9

1.0.46 1.0.46 1.0.49 2.35 2.35 151441 Ba 3 MnSb 2 O 9 151441 Ba 3 MnSb 2 O 9 . BaCoSiO 4 626717 CrSe 626717 CrSe

Fe 3 F 8 (H 2 O) 2 TbCrO 3 DyCrO 3 DyCrO 3 MgCr 2 O 4 SP 4

AM 2/m -1 AM 2/m -1 AM 2/m -1 AM 2/m -1 AM 6/mmm -3m d d d d g

AM 2/m -1 AM mmm 2/m AM 2/m -1 AM 2/m -1 AM 4/mmm mmm d d d d d

S14 Table S1. Sensitivity of the band gap E g , maximum splitting ∆ max , and average splitting ∆ avg to ±10% variations of the Hubbard U values (relative to the reference values used in the main text). Band gaps are reported with two decimal places.