---
title: DxMag Heusler Database
url: https://www.emergentmind.com/topics/dxmag-heusler-database
type: topic
---

# DxMag Heusler Database

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 [2508.20556].

## 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 [2508.20556].

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 [2508.20556].

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 [2502.17946].

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 [1706.01840]. 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 \(\Delta H\) as thermodynamic labels in screening [2508.20556].

| Property or label | Dataset size | Stated scope |
|---|---:|---|
| Local magnetic moments (\(lmm\)) | 27,864 | ground-state entries |
| Phonon minimum frequency (\(mpf\)) | 8,198 | thermodynamically stable ground states |
| Curie temperature (\(T_c\)) | 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
\[
\mathrm{MAE} = E_{\perp} - E_{\parallel},
\]
where \(E_{\perp}\) and \(E_{\parallel}\) are energies for magnetization perpendicular and parallel to the reference axis, respectively [2508.20556].

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 \(\omega_{\min}\), while magnetic ordering temperature is estimated from exchange constants through
\[
T_C=\frac{2}{3k_B}J_{\max}.
\]
The same study further identifies **47 low-moment ferrimagnets** using
\[
\sum_i |\mathbf{m}_i| > 0.5\ \mu_B,\qquad \left|\sum_i \mathbf{m}_i\right| < 0.5\ \mu_B,
\]
and supplements structural and magnetic labels with spin polarization, anomalous Hall conductivity, and anomalous Nernst conductivity [2502.17946]. 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 \(\Delta E\) and \(\Delta H\) 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 [2508.20556].

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: \(a,b,c\) are scaled by \(\pm 10\%\) and \(\pm 30\%\), while the \(c\)-axis alone is scaled by \(\pm 10\%, \pm 20\%, \pm 30\%, \pm 40\%, \pm 50\%\). 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 [2508.20556].

The operational thermodynamic and functional thresholds are likewise stated explicitly. In the DxMag-centered workflow, the principal thresholds are
\[
\Delta E < 0.0 \ \text{eV/atom}, \qquad \Delta H < 0.22 \ \text{eV/atom},
\]
magnetic classification by
\[
\sum_i |\mathbf{m}_i| > 0.1 \ \mu_B/\mathrm{f.u.},
\]
dynamical stability by
\[
\omega_{\min} > -10 \ \mathrm{cm}^{-1},
\]
magnetic stability by
\[
T_c > 300 \ \mathrm{K},
\]
and anisotropy selection by
\[
|\mathrm{MAE}| > 1\ \mathrm{MJ/m}^3.
\]
These definitions make the database directly queryable for room-temperature magnetic materials with robust anisotropy and acceptable dynamical stability [2508.20556].

A related Heusler-wide phonon-aware screening study uses a similar but not identical logic. It treats **\(\Delta E < 0.0\ \text{eV/atom}\)**, **\(\Delta H < 0.3\ \text{eV/atom}\)**, and **\(\omega_{\min}=0\)** as a practical combined criterion, while also discussing alternative thresholds such as \(\Delta E<0.2\) eV/atom and \(\Delta H<0.22\) eV/atom for improved recall, or \(\Delta E<0.0\), \(\Delta H<0.10\) eV/atom, and \(\omega_{\min}=0\) for improved precision [2502.17946]. One common misconception is that formation energy alone is an adequate stability filter. The combined use of \(\Delta E\), \(\Delta H\), 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-\(n\)**, and performance improves as the number of frozen layers increases up to **\(n=7\)**, 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 [2508.20556].

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 \(R^2 = 0.990\) for local magnetic moments, \(R^2 = 0.986\) for total magnetization \(m_{\mathrm{total}}\), \(R^2 = 0.990\) for \(\sum |\mathbf{m}_i|\), \(R^2 = 0.750\) for minimum phonon frequency, \(R^2 = 0.910\) and classification accuracy \(0.910\) for \(T_c\), and \(R^2 = 0.680\) for MAE. For structure optimization and thermodynamic quantities, eSEN achieves \(R^2 = 0.994\) for \(a\), \(R^2 = 0.995\) for formation energy, and \(R^2 = 0.980\) for hull distance [2508.20556].

The screening results provide an application-level benchmark. The final workflow produced **366 conventional quaternary candidates** and **924 all-\(d\) candidates**; another summary in the same work reports **334 conventional quaternary Heusler compounds** and **924 all-\(d\) Heusler compounds**. DFT validation indicates that **99.1%** of quaternary candidates and **97.8%** of all-\(d\) candidates satisfy \(\Delta E_{\mathrm{DFT}} < 0\), while **96.4%** and **98.8%** satisfy \(\Delta H_{\mathrm{DFT}} < 0.22\) eV/atom. Magnetic classification by local moments achieves **100% precision**; \(\mathrm{mpf}\) validation reaches **89.2%** for quaternary and **93.1%** for all-\(d\); \(T_c > 300\) K validation reaches **81.7%** and **80.4%**; and \(|\mathrm{MAE}| > 1\) MJ/m\(^3\) validation reaches **82.0%** and **68.2%** [2508.20556].

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 \(Z\) site in all-\(d\) compounds samples environments absent from the training set [2508.20556].

## 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 \(X_3Z\) systems identifies **631 magnetic compounds with \(T_C>300\) K** as promising room-temperature candidates, including **240 regular**, **291 inverse**, **24 \(X_3Z\)**, and **76 half-Heusler** structures. It also reports that among **490 stable inverse compounds**, **390 (80%)** lie in a region characterized by \(\chi^X-\chi^Y<0.15\) and \(|r^X_{\mathrm{cov}}-r^Y_{\mathrm{cov}}|<0.20\ \text{\AA}\), and that when \(DOS(\text{cubic},E_F) > 3\) eV\(^{-1}\), the probability of tetragonal distortion exceeds **80%** for \(X_2YZ\) and **70%** for half-Heuslers [2502.17946]. 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 \(\gamma\)** phase field and coexistence regions such as \(\gamma + \mathrm{NiGa}\), \(\gamma + \mathrm{Ni_3Ga}\), and \(L + \mathrm{Ni_2Ga_3}\), which is directly relevant to composition selection for magnetocaloric applications [2309.02694]. 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\(_{2-x}\)Mn\(_{1+x}\)Ga predict that a magnetic martensitic transformation is possible for all studied compositions \(x = 0, 0.25, 0.5, 0.75, 1\), with tetragonal minima near \(c/a \approx 1.3\) 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\(_2\)MnGa, Pt\(_{1.75}\)Mn\(_{1.25}\)Ga, Pt\(_{1.25}\)Mn\(_{1.75}\)Ga, and Mn\(_2\)PtGa [1403.7318]. In database terms, this is a case where total energy versus \(c/a\), magnetic moment changes under distortion, and electronic-structure signatures near \(E_F\) 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** \(XYZ\) 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 \(M_{tot}=N_V-18\) for half-metallic moments [1610.02444]. A separate high-throughput study of all-3d tetragonal Heuslers for permanent magnets identifies Fe\(_2\)NiZn, Fe\(_2\)NiTi, and Ni\(_2\)CoFe as the best candidates, with out-of-plane MAE values of **1.23**, **0.97**, and **0.82 MJ/m\(^3\)** and Curie temperatures more than **200 K** above room temperature [2212.07845]. 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 \(Z\) should be a main-group element for thermodynamic stability; within that framework, Co\(_2\)FeSi reaches magnetization values up to **1.2 T**, while the Cu\(_2\)Fe\(Z\) family offers approximately **0.65 T** as a cost-effective class [1706.01840]. 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 \(T_C\), 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-\(d\) systems is attributed to domain shift because the all-\(d\) chemical environments contain \(Z\)-site \(d\)-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 [2508.20556]. 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 [2212.07845]. 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 \(\Delta E<0\) and \(\Delta H<0.3\) eV/atom recover **159 of 169 \(X_2YZ\)** 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 [2502.17946]. 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 [2508.20556]. The broader literature suggests two natural extensions: deeper integration of thermodynamic databases for composition–processing–phase relations in systems such as Ni–Mn–Ga [2309.02694], and broader inclusion of transport and compensated-magnet descriptors already demonstrated at scale in Heusler-wide screening [2502.17946]. 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.

Source: https://www.emergentmind.com/topics/dxmag-heusler-database