Constrained DFT-based magnetic machine-learning potentials for magnetic alloys - a case study of Fe–Al

Aug 4, 2026

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A machine-learning interatomic potential is developed for multi-component magnetic materials by treating magnetic moments as explicit degrees of freedom alongside atomic positions, atomic types, and lattice vectors. A training set is constructed using constrained DFT (cDFT) to include configurations with non-equilibrium (excited) magnetic moments, enabling reliable predictions throughout an extended configurational space. The trained potential is validated on bcc Fe–Al across different concentrations and atomic occupations, matching DFT for formation energies, equilibrium lattice parameters, and total magnetic moments. It also reproduces the experimentally observed anomalous volume–composition dependence in Fe–Al.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages10

Reading Time25 min

AccessFree to download

Introduction

Motivation: explicit magnetism in alloys

Challenge: excited states vs DFT ground-state nature

Method

Constrained DFT training set construction

Machine-learning interatomic potential design

Validation and Results

bcc Fe–Al test cases (concentration and site occupation)

Agreement with DFT: energies, lattice parameters, magnetic moments

Reproduction of anomalous volume–composition behavior

[www. nature.com/scientificreports](www. nature.com/scientificreports) OPEN Constrained DFT‑based magnetic machine‑learning potentials for magnetic alloys: a case study of Fe–Al Alexey S. Kotykhov1,2, Konstantin Gubaev3, Max Hodapp4, Christian Tantardini5,6,7*, Alexander V. Shapeev 1 & Ivan S. Novikov1,2* We propose a machine‑learning interatomic potential for multi‑component magnetic materials. In this potential we consider magnetic moments as degrees of freedom (features) along with atomic positions, atomic types, and lattice vectors. We create a training set with constrained DFT (cDFT) that allows us to calculate energies of configurations with non‑equilibrium (excited) magnetic momentsand, thus, it is possible to construct the training set in a wide configuration space with great variety of non‑equilibrium atomic positions, magnetic moments, and lattice vectors. Such a training set makes possible to fit reliable potentials that will allow us to predict properties of configurations in the excited states (including the ones with non‑equilibrium magnetic moments). We verify the trained potentialson the system of bcc Fe–Al with different concentrations ofAl and Fe and different ways Al and Fe atoms occupy the supercell sites. Here, we show that the formation energies, the equilibrium lattice parameters, and the total magnetic moments ofthe unit cell for different Fe–Al structures calculated with machine‑learning potentials are in good correspondence with the ones obtained with DFT. We also demonstrate that the theoretical calculations conducted in this study qualitatively reproduce the experimentally‑observed anomalous volume‑composition dependence in the Fe–Al system. Magnetism is important to be explicitly taken into account for the successful computational prediction of many properties in single-component metals1–6 and multi-component alloys7–15. In particular, magnetic properties of the constituting elements of alloys affect the phase stability7–10. Furthermore, magnetism can be responsible for the unusual properties like negative thermal expansion11, 12, anomalous volume-composition dependence13, and the so-called “half-metallic behavior” in perovskites14 or full-Heusler alloys15. In such multi-component alloys not only magnetism is a more complex physical phenomenon as compared to the single-component materials, the presence of magnetism in multi-component alloys also leads to extra difficulties for its computational studies. Steel, a workhorse of heavy industry, is an example of such a material; it has immense variety of applications and corresponding sub-types, possessing magnetic properties due to Fe being presented in their content. Steels, as well as other Fe-based alloys, can be characterized by different magnetic orders for which the electronic ground state can be substantially different. One of the most widely used methods for simulations of ground state properties of condensed matter is density functional theory (DFT) . In magnetism, however, we are are often interested in excited state properties (e.g., excited magnetic moments), while, strictly speaking, DFT is a theory for the electronic ground state: the fundamental theorem of DFT relies on a minimization of the energy in the functional space of many-body electronic wavefunction, which is the Slater determinant that avoid the electronic localization due to the spreading of all electrons on the entire orbitals (i.e., Kohn–Sham equations) . 1Skolkovo Institute of Science and Technology, Skolkovo Innovation Center, Bolshoy Boulevard 30, Moscow 143026, Russian Federation. 2Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region 141701, Russian Federation. 3University of Stuttgart, Postfach 10 60 37, 70049 Stuttgart, Germany. 4Materials Center Leoben Forschung GmbH (MCL), Leoben, Austria. 5Hylleraas Center, Department of Chemistry, UiT The Arctic University of Norway, Langnes, PO Box 6050, 9037 Tromsø, Norway. 6Depa

FAQs

How does the method incorporate magnetism into the machine-learning interatomic potential?

Magnetic moments are included as additional degrees of freedom (features) together with atomic positions, atomic types, and lattice vectors during potential construction.

Why is constrained DFT (cDFT) used for training?

cDFT enables generating a training set that spans non-equilibrium (excited) magnetic moments, allowing the model to predict energies for excited magnetic states.

What properties are verified for bcc Fe–Al and how do the predictions compare to DFT?

The potential reproduces formation energies, equilibrium lattice parameters, and total magnetic moments of unit cells across different Fe–Al structures, showing good correspondence with DFT.

Aug 4, 2026

Upload by Liam