DxMag Heusler Database

• DxMag Heusler Database is a specialized repository for Heusler compounds, delivering curated structural, magnetic, and thermodynamic properties.
• It integrates high-throughput DFT calculations with ML techniques to predict formation energies, phonon stability, Curie temperatures, and magnetocrystalline anisotropy.
• The database underpins discovery with extensive screening over 130,000 compositions, enabling practical insights for materials design and magnetism research.

Searching arXiv for DxMag Heusler-related papers and validating the cited records. The DxMag Heusler Database is a comprehensive database of Heusler compounds designed to support data-driven magnetism research. Its original purpose was to assemble a broad and systematic set of conventional ternary Heusler compounds, including the conventional, inverse, and half-Heusler structural variants, so that predictive models could be trained on a consistent Heusler-specific dataset rather than on mixed materials databases. In the benchmark workflow that most explicitly describes DxMag, the database provides ground-state structures of conventional ternary Heuslers, formation energies and convex-hull distances, local magnetic moments, Curie temperatures, phonon stability information for stable ground states, and newly computed magnetocrystalline anisotropy energies for magnetic tetragonal ground states (Xiao et al., 28 Aug 2025).

1. Scope, purpose, and database identity

DxMag is positioned as a Heusler-specific data foundation rather than a generic materials repository. The central design choice is chemical and structural specialization: the database focuses on Heusler compounds because the family admits systematic variation over conventional, inverse, and half-Heusler prototypes, while also hosting magnetism, martensitic distortion, half-metallicity, magnetocaloric behavior, and magnetocrystalline anisotropy within a comparatively uniform crystallographic vocabulary (Xiao et al., 28 Aug 2025).

In the workflow centered on DxMag, the database had previously covered “nearly all conventional ternary Heusler compounds,” and the same study extends screening to conventional quaternary Heuslers and all-$d$ Heuslers. The enumerated spaces are explicit: 131,544 unique compositions for conventional quaternary Heuslers and 104,139 unique compositions for all-$d$ Heuslers. This makes DxMag both a repository of known ternary ground states and a training backbone for extrapolation into larger chemical spaces (Xiao et al., 28 Aug 2025).

A broader Heusler high-throughput screening study provides the surrounding scale of modern Heusler informatics: it screened 27,864 Heusler compositions in the main space and reported 106,235 optimized structures, spanning regular, inverse, half-Heusler, and $X_3Z$ cases in both cubic and tetragonal phases. That study is not presented as DxMag itself, but it is directly aligned with the database’s discovery-oriented role because it supplies composition, structural type, formation energy, hull distance, phonon stability, magnetic moments, calibrated $T_C$, and transport properties such as anomalous Hall and anomalous Nernst conductivity (Xiao et al., 25 Feb 2025).

This specialization distinguishes DxMag from earlier Heusler datasets used for narrower tasks. A machine-learning study on Fe-based Heuslers, for example, relied on an in-house Heusler database containing ground-state site occupations, relaxed structures, lattice volumes, magnetic moments, and formation enthalpies; that workflow demonstrated how a Heusler-focused data resource can support both physical inference and rapid screening (Žic et al., 2017). This suggests that DxMag should be understood as part of a lineage of Heusler-specific infrastructures in which curated structural, magnetic, and thermodynamic labels are treated as first-class research objects.

2. Core data content and property schema

The database supports both structural records and derived property labels. In the machine-learning benchmark, the supervised targets trained from DxMag-derived data are local magnetic moments $\{\mathbf{m}_i\}$, minimum phonon frequency $\omega_{\min}$ (denoted $\mathrm{mpf}$), Curie temperature $T_c$, and magnetocrystalline anisotropy energy $E_{\mathrm{aniso}}$ or MAE. The same workflow also uses formation energy $\Delta E$ and distance to convex hull $d$0 as thermodynamic labels in screening (Xiao et al., 28 Aug 2025).

Property or label	Dataset size	Stated scope
Local magnetic moments ($d$1)	27,864	ground-state entries
Phonon minimum frequency ($d$2)	8,198	thermodynamically stable ground states
Curie temperature ($d$3)	2,106	includes 750 newly computed values
MAE	6,123	magnetic tetragonal ground-state systems

The database therefore encodes both state variables and decision variables. Structural and energetic descriptors determine whether a Heusler candidate is plausible; magnetic, phononic, and anisotropy labels determine whether it is useful for a given application domain. The MAE label is defined by

$d$4

where $d$5 and $d$6 are energies for magnetization perpendicular and parallel to the reference axis, respectively (Xiao et al., 28 Aug 2025).

Related Heusler-wide screening work shows how such labels are typically interpreted in practice. In that larger dataset, stability is expressed through negative formation energy, distance to the convex hull, and a phonon criterion based on the minimum phonon frequency $d$7, while magnetic ordering temperature is estimated from exchange constants through

$d$8

The same study further identifies 47 low-moment ferrimagnets using

$d$9

and supplements structural and magnetic labels with spin polarization, anomalous Hall conductivity, and anomalous Nernst conductivity (Xiao et al., 25 Feb 2025). This suggests a natural ontology for a DxMag-type database: phase stability, magnetic ordering, lattice distortion, and transport response are not separate modules but coupled descriptors of the same Heusler state space.

3. Data generation workflow and screening logic

The database is built from DFT-computed Heusler structures and properties, mostly using VASP with PAW-PBE. In the machine-learning-accelerated workflow, structure optimization is performed with the eSEN interatomic potential in ASE/FIRE; thermodynamic quantities $X_3Z$0 and $X_3Z$1 are computed from eSEN-predicted energies of the target compound, elemental references, and competing phases; phonons are computed with ALAMODE; Curie temperatures are computed with SPRKKR; and MAE is computed using the force theorem (Xiao et al., 28 Aug 2025).

The screening protocol is explicitly multistage. Candidate compositions are first enumerated, then an initial cubic conventional cell is generated, and 14 starting structures are produced via isotropic and anisotropic strain. The scaling operations are also explicit: $X_3Z$2 are scaled by $X_3Z$3 and $X_3Z$4, while the $X_3Z$5-axis alone is scaled by $X_3Z$6. Structures are then relaxed with the eSEN MLIP under ASE + FIRE + symmetry constraints, and the lowest-energy relaxed structure is selected as the ground state (Xiao et al., 28 Aug 2025).

The operational thermodynamic and functional thresholds are likewise stated explicitly. In the DxMag-centered workflow, the principal thresholds are

$X_3Z$7

magnetic classification by

$X_3Z$8

dynamical stability by

$X_3Z$9

magnetic stability by

$T_C$0

and anisotropy selection by

$T_C$1

These definitions make the database directly queryable for room-temperature magnetic materials with robust anisotropy and acceptable dynamical stability (Xiao et al., 28 Aug 2025).

A related Heusler-wide phonon-aware screening study uses a similar but not identical logic. It treats $T_C$2, $T_C$3, and $T_C$4 as a practical combined criterion, while also discussing alternative thresholds such as $T_C$5 eV/atom and $T_C$6 eV/atom for improved recall, or $T_C$7, $T_C$8 eV/atom, and $T_C$9 for improved precision (Xiao et al., 25 Feb 2025). One common misconception is that formation energy alone is an adequate stability filter. The combined use of $\{\mathbf{m}_i\}$0, $\{\mathbf{m}_i\}$1, and phonons in these workflows directly contradicts that simplification.

4. Machine-learning architecture, transfer learning, and benchmarked performance

DxMag is not only a data store but the training substrate for task-specific machine-learning regressors. The property models are called eSEM models, built on the eSEN architecture and trained using frozen transfer learning. The pretrained base model is eSEN-30M-OAM, trained on OMat, MPtrj, and sAlexandria. For the Heusler property tasks, the embedding layer and the first seven message-passing layers are frozen, while the final three layers plus the output layer are fine-tuned on DxMag-derived target data. The notation is TL-MLIP-$\{\mathbf{m}_i\}$2, and performance improves as the number of frozen layers increases up to $\{\mathbf{m}_i\}$3, after which performance degrades; TL-MLIP-7 is therefore selected as the final model for local magnetic moment, minimum phonon frequency, Curie temperature, and MAE (Xiao et al., 28 Aug 2025).

The training protocol uses an 8:1:1 train/validation/test split. Reported test performance is strong for magnetic quantities and more modest for the more delicate targets. The benchmark table reports $\{\mathbf{m}_i\}$4 for local magnetic moments, $\{\mathbf{m}_i\}$5 for total magnetization $\{\mathbf{m}_i\}$6, $\{\mathbf{m}_i\}$7 for $\{\mathbf{m}_i\}$8, $\{\mathbf{m}_i\}$9 for minimum phonon frequency, $\omega_{\min}$0 and classification accuracy $\omega_{\min}$1 for $\omega_{\min}$2, and $\omega_{\min}$3 for MAE. For structure optimization and thermodynamic quantities, eSEN achieves $\omega_{\min}$4 for $\omega_{\min}$5, $\omega_{\min}$6 for formation energy, and $\omega_{\min}$7 for hull distance (Xiao et al., 28 Aug 2025).

The screening results provide an application-level benchmark. The final workflow produced 366 conventional quaternary candidates and 924 all-$\omega_{\min}$8 candidates; another summary in the same work reports 334 conventional quaternary Heusler compounds and 924 all-$\omega_{\min}$9 Heusler compounds. DFT validation indicates that 99.1% of quaternary candidates and 97.8% of all-$\mathrm{mpf}$0 candidates satisfy $\mathrm{mpf}$1, while 96.4% and 98.8% satisfy $\mathrm{mpf}$2 eV/atom. Magnetic classification by local moments achieves 100% precision; $\mathrm{mpf}$3 validation reaches 89.2% for quaternary and 93.1% for all-$\mathrm{mpf}$4; $\mathrm{mpf}$5 K validation reaches 81.7% and 80.4%; and $\mathrm{mpf}$6 MJ/m$\mathrm{mpf}$7 validation reaches 82.0% and 68.2% (Xiao et al., 28 Aug 2025).

Several caveats are intrinsic to the learning problem. The local-moment model reproduces both magnitude and sign of site-resolved moments well, but some sign errors remain. Because flipping all spins produces a physically equivalent state, the loss function is modified to compare both the predicted moment pattern and its sign-inverted counterpart and then take the smaller loss. MAE is the hardest target: the database benchmark states that MAE is highly sensitive to subtle spin-orbit-driven electronic details and to chemical domain shift, especially when the $\mathrm{mpf}$8 site in all-$\mathrm{mpf}$9 compounds samples environments absent from the training set (Xiao et al., 28 Aug 2025).

5. Heusler-specific scientific regimes represented by database descriptors

The scientific value of a DxMag-type database is clearest when the same descriptor stack is viewed across distinct Heusler application regimes. A phonon-aware high-throughput study over regular, inverse, half-Heusler, and $T_c$0 systems identifies 631 magnetic compounds with $T_c$1 K as promising room-temperature candidates, including 240 regular, 291 inverse, 24 $T_c$2, and 76 half-Heusler structures. It also reports that among 490 stable inverse compounds, 390 (80%) lie in a region characterized by $T_c$3 and $T_c$4, and that when $T_c$5 eV$T_c$6, the probability of tetragonal distortion exceeds 80% for $T_c$7 and 70% for half-Heuslers (Xiao et al., 25 Feb 2025). These are precisely the kinds of physically interpretable trends that make database queries scientifically meaningful rather than merely combinatorial.

For magnetocaloric Heuslers, thermodynamic phase stability is indispensable. A CALPHAD study on Ni–Mn–Ga develops a self-consistent thermodynamic database by optimizing the Mn–Ga and Ni–Ga binaries and combining them with the previously optimized Mn–Ni system. The liquid phase is described with the Modified Quasichemical Model, solid-solution phases with the Compound Energy Formalism, and differential thermal analysis is used to resolve binary phase-diagram discrepancies. The resulting ternary Ni–Mn–Ga isothermal section at 1073 K identifies the FCC $T_c$8 phase field and coexistence regions such as $T_c$9, $E_{\mathrm{aniso}}$0, and $E_{\mathrm{aniso}}$1, which is directly relevant to composition selection for magnetocaloric applications (Tiwari et al., 2023). This suggests that a Heusler database oriented toward magnetic function cannot be limited to zero-temperature crystal labels; it also requires a thermodynamic backbone for processing windows and phase constitution.

For martensitic and magnetic shape-memory behavior, the relevant descriptors shift toward structural energetics, distortion pathways, and magnetic response. First-principles calculations on the Heusler-type series Pt$E_{\mathrm{aniso}}$2Mn$E_{\mathrm{aniso}}$3Ga predict that a magnetic martensitic transformation is possible for all studied compositions $E_{\mathrm{aniso}}$4, with tetragonal minima near $E_{\mathrm{aniso}}$5 and stabilization energies between −48.44 meV/atom and −81.06 meV/atom relative to the cubic austenite. The tetragonal phase is stabilized by pseudogap formation at the Fermi level, and large magnetic-field-induced strain is identified as likely for Pt$E_{\mathrm{aniso}}$6MnGa, Pt$E_{\mathrm{aniso}}$7Mn$E_{\mathrm{aniso}}$8Ga, Pt$E_{\mathrm{aniso}}$9Mn$\Delta E$0Ga, and Mn$\Delta E$1PtGa (Feng et al., 2014). In database terms, this is a case where total energy versus $\Delta E$2, magnetic moment changes under distortion, and electronic-structure signatures near $\Delta E$3 are indispensable retrieval keys.

Spintronics and permanent-magnet design require yet another subset of the descriptor space. A systematic study of half-Heuslers computes 378 $\Delta E$4 compounds and identifies 26 18-electron semiconductors, 45 half-metals, and 34 near half-metals with negative formation energy, while emphasizing hull distance as a practical synthesizability metric and the Slater-Pauling relation $\Delta E$5 for half-metallic moments (Ma et al., 2016). A separate high-throughput study of all-3d tetragonal Heuslers for permanent magnets identifies Fe$\Delta E$6NiZn, Fe$\Delta E$7NiTi, and Ni$\Delta E$8CoFe as the best candidates, with out-of-plane MAE values of 1.23, 0.97, and 0.82 MJ/m$\Delta E$9 and Curie temperatures more than 200 K above room temperature (Marathe et al., 2022). Earlier machine-learning analysis of Fe-based Heuslers, using a DFT Heusler database as the training source, further distilled design rules that late transition metals are the best nearest neighbors for Fe and that $d$00 should be a main-group element for thermodynamic stability; within that framework, Co$d$01FeSi reaches magnetization values up to 1.2 T, while the Cu$d$02Fe$d$03 family offers approximately 0.65 T as a cost-effective class (Žic et al., 2017). Together these studies show why a mature DxMag-style database must expose not only equilibrium structures but also electron counting, hull distance, anisotropy, exchange-derived $d$04, and local magnetic environments.

6. Limitations, misconceptions, and likely development directions

The most important limitation is transferability across chemical domains. In the DxMag benchmark, the lower MAE precision for all-$d$05 systems is attributed to domain shift because the all-$d$06 chemical environments contain $d$07-site $d$08-block elements absent from the training set. The same work also notes that local-moment prediction is better at identifying whether a site is magnetic than at exact quantitative moment prediction, and that performance should improve with larger datasets (Xiao et al., 28 Aug 2025). A plausible implication is that future DxMag expansions will need chemically broader supervision, not merely more data from the same subspace.

A second misconception is that tetragonal database entries can be interpreted directly as functional martensites or hard magnets. A permanent-magnet search based on AFLOW explicitly notes as a limitation that cubic Heusler symmetries were deliberately excluded from the initial database search, even though metastable tetragonal entries may appear when the cubic phase is more stable (Marathe et al., 2022). The corresponding lesson for DxMag is that symmetry labels must be coupled to relative phase energetics, phonons, and, where relevant, magnetic order.

A third limitation concerns the meaning of stability itself. The phonon-aware Heusler screening study validated predictions against 189 experimentally synthesized Heusler compounds from ICSD and showed that $d$09 and $d$10 eV/atom recover 159 of 169 $d$11 ICSD compounds, or 94% recall, while adding phonon stability reduces recovery to 124 compounds, or 78%, but improves precision. For half-Heuslers, 19 of 21 ICSD examples satisfy the thermodynamic thresholds, and 18 of 21 satisfy the full thermodynamic-plus-phonon criteria (Xiao et al., 25 Feb 2025). This indicates that database thresholds are operational filters rather than absolute synthesizeability laws.

The present architecture nevertheless points toward a coherent development path. DxMag already functions as a Heusler-specific data foundation for replacing expensive DFT steps with accurate machine-learning predictions for structure optimization, thermodynamic stability, local magnetic moments, phonon stability, Curie temperature, and MAE (Xiao et al., 28 Aug 2025). The broader literature suggests two natural extensions: deeper integration of thermodynamic databases for composition–processing–phase relations in systems such as Ni–Mn–Ga (Tiwari et al., 2023), and broader inclusion of transport and compensated-magnet descriptors already demonstrated at scale in Heusler-wide screening (Xiao et al., 25 Feb 2025). This suggests that the long-term significance of DxMag lies not only in cataloging Heusler compounds, but in providing a unified queryable representation of stability, lattice distortion, magnetism, and functionality across the Heusler design space.