🔬 materials science

Development of a magnetic interatomic potential for cubic anti-ferromagnets: the case of NiO

This paper presents a novel methodology for developing magnetic interatomic potentials for cubic antiferromagnets by integrating Heisenberg exchange and Néel models, successfully applying it to NiO to create validated potentials that enable large-scale molecular dynamics simulations of coupled magnetoelastic phenomena.

Original authors: Ievgeniia Korniienko, Pablo Nieves, Jakub Sebesta, Roberto Iglesias, Dominik Legut

Published 2026-07-20

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CC BY 4.0

Original authors: Ievgeniia Korniienko, Pablo Nieves, Jakub Sebesta, Roberto Iglesias, Dominik Legut

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the invisible world inside a solid object, like a tiny, bustling city made of atoms. In this city, the atoms aren't just sitting still; they are constantly jiggling, bumping into each other, and holding hands in specific ways. But in some special materials, these atoms have a secret superpower: they act like tiny magnets. Usually, when we think of magnets, we picture a fridge magnet that sticks to metal. But in a different kind of material called an "antiferromagnet," the neighbors are like a game of tug-of-war where everyone pulls in opposite directions. One atom points "up," its neighbor points "down," and they cancel each other out so the whole block doesn't act like a magnet to the outside world.

Scientists are super interested in these materials because they can change shape when you apply a magnetic field, or change their magnetism when you squeeze them. This is called "magnetoelasticity." It's like if you squeezed a stress ball and it suddenly decided to point north, or if you waved a magnet near it and it squished itself. To understand how this happens, researchers use powerful computer simulations. They build a "recipe" called an interatomic potential, which is basically a set of instructions telling the computer how atoms should push, pull, and react to magnetic forces. The tricky part is that for these tug-of-war materials, the recipes have been missing a crucial ingredient: the magnetic rules. Without them, the computer simulations are like trying to predict the weather without knowing about wind.

This paper is about finally writing that missing recipe book for a specific material called Nickel Oxide (NiO), which is the "poster child" for these tug-of-war magnets. The researchers, a team of scientists from the Czech Republic and Spain, developed a new way to mix the rules of magnetism with the rules of how atoms move and stretch. They created two different versions of this recipe. One version is based on a classic idea about how ionic solids (like salt) behave, and the other is a brand-new, custom-made recipe built from scratch using high-level computer calculations.

The team tested their new recipes by simulating a huge city of over 85,000 atoms. They checked if the simulated material would shrink or expand just the right amount when the magnetic order changed, and if it would react to pressure in the correct way. The results were promising: both recipes predicted the material's behavior with excellent accuracy, matching the complex calculations done by supercomputers. Specifically, they found that the material shrinks by about 0.14% when it orders its magnetic spins, and they successfully recreated the material's resistance to being squished in different directions.

However, the authors are careful to note that these results are currently valid for simulations at zero temperature (a theoretical state where atoms stop jiggling). While the models work beautifully in the computer, the scientists suggest that more work is needed to see how these materials behave in the real, warm world. They also point out that while their new custom recipe (called RF-MEAM) is better at predicting how the material resists twisting than the older recipe, there is still some mystery about exactly how strong the material's magnetic stretching is compared to other studies.

In short, this paper doesn't claim to have solved all the mysteries of magnetic materials, but it has built a very strong, reliable bridge for future explorers. By successfully combining magnetic rules with movement rules for Nickel Oxide, they have opened the door for much larger and more detailed simulations. This means that in the future, scientists might be able to design better sensors, actuators, or even quantum technologies that use these clever, shape-shifting magnets, all because they finally have a good map of how the atoms dance together.

Problem Statement
Interatomic potentials are fundamental for molecular dynamics (MD) simulations of magnetic materials; however, incorporating magnetic features into potentials for complex antiferromagnets (AFM) remains a significant challenge. While spin-lattice models combining classical spin and MD (SD-MD) have been successfully formulated and validated for cubic ferromagnets (FM), extending these to AFM systems is difficult. The core difficulty lies in the requirement for the model to simultaneously reproduce magnetic dynamics under variable interatomic distances and elastic properties governed by the interatomic potential in the presence of magnetic interactions. Currently, available interatomic potentials for the prototypical cubic AFM material, Nickel Oxide (NiO), can describe charge and electric field responses but lack magnetic interactions. This limitation hinders the study of coupled electric and magnetic field phenomena, such as magnetoelasticity and magnetoelectric effects, in metal oxides.

Methodology
The authors propose a methodology to integrate magnetic properties into interatomic potentials for cubic AFMs by adding a magnetic Hamiltonian to the standard interatomic potential. The total Hamiltonian ( $H_{sl}$ ) includes kinetic energy, a non-magnetic interatomic potential ( $V$ ), and a magnetic potential ( $V_{mag}$ ).

Magnetic Hamiltonian: The magnetic term includes the Heisenberg exchange interaction and the Néel interaction ( $H_{N\acute{e}el}$ ). The Néel interaction accounts for magnetic anisotropy via dipole ( $l$ ) and quadrupole ( $q$ ) terms, which describe anisotropic magnetostriction and magnetocrystalline anisotropy (MCA), respectively.
Bethe-Slater Parameterization: The spatial dependence of the exchange ( $J$ ), dipole ( $l$ ), and quadrupole ( $q$ ) parameters is modeled using Bethe-Slater curves. For the AFM case, the authors derive specific expressions for these parameters based on the Néel model for a simple cubic (SC) structure with antiparallel spins.
NiO Specifics: Given the complexity of the NiO unit cell (face-centered cubic Ni sublattice with mixed parallel and antiparallel nearest neighbors), the model simplifies the interactions by focusing exclusively on the second nearest neighbors (NNN) of Ni atoms. This choice is justified because the NNN exchange interaction is stronger than nearest-neighbor interactions in NiO, and the NNN Ni sublattice forms a simple cubic structure where all spins are antiparallel, simplifying parameter derivation.
Potential Construction: Two distinct interatomic potentials were constructed to validate the methodology:
- SD-MD 1: Based on the Born model of ionic solids (Fisher and Matsubara), utilizing a Buckingham potential for short-range interactions.
- SD-MD 2: Based on a reference-free modified embedded atom method (RF-MEAM), fitted to a dataset of 45 distorted NiO crystal structures calculated via Density Functional Theory (DFT) with Hubbard correction.
Input Parameters: Key parameters for the Bethe-Slater curves (Néel temperature, elastic constants, volume magnetostriction, anisotropic magnetoelastic constants, and MCA constants) were derived from a combination of experimental data and ab initio calculations (using VASP and MAELAS codes).

Key Contributions

Methodological Framework: The paper establishes a general procedure for developing interatomic potentials for cubic AFMs that include both Heisenberg exchange and Néel interactions, specifically addressing the challenge of modeling antiparallel spin configurations.
Dual-Potential Validation: The authors successfully applied this framework to NiO, creating two distinct models (SD-MD 1 and SD-MD 2) that incorporate magnetoelastic interactions.
Parameter Derivation: The work provides a detailed derivation of Bethe-Slater parameters for AFM systems, linking them to macroscopic properties like the Néel temperature, spontaneous volume magnetostriction, and anisotropic magnetoelastic constants.
Custom Potential Development: The study demonstrates the creation of a custom RF-MEAM potential for NiO, which offers improved agreement with DFT-calculated elastic constants (specifically $C_{44}$ ) compared to the traditional Born model potential.

Results
The developed models were validated against DFT calculations and experimental data at zero temperature:

Mechanical and Magnetic Properties: Both SD-MD models showed excellent agreement with DFT and experimental values for mechanical properties (elastic constants $C_{11}, C_{12}, C_{44}$ , bulk modulus) and magnetic properties (Néel temperature, spontaneous volume magnetostriction $\omega_s$ , and magnetocrystalline anisotropy constant $K_1$ ).
Magnetostriction: The models accurately reproduced the input volume magnetostriction ( $\omega_s \approx -0.0014$ ) and anisotropic magnetostrictive constants ( $\lambda_{100}, \lambda_{111}$ ).
Pressure Dependence: The models correctly captured the linear dependence of the magnetocrystalline anisotropy constant $K_1$ on hydrostatic pressure, matching the slope derived from DFT calculations.
Comparison of Potentials: The RF-MEAM based model (SD-MD 2) demonstrated superior performance in reproducing the shear elastic constant $C_{44}$ and the resulting magnetostrictive coefficients compared to the Born model (SD-MD 1), addressing known limitations of the latter for NiO.

Significance
The paper presents a "first attempt" at developing interatomic potentials that include magnetic properties specifically for cubic symmetry antiferromagnets. The authors claim this work serves as a proof of concept for the methodology at zero temperature. The primary significance lies in enabling large-scale molecular dynamics simulations of magnetoelastic phenomena in antiferromagnets, a capability previously limited by the lack of suitable potentials. The authors suggest these models open avenues for studying coupled electric and magnetic field effects in metal oxides, magnetoelastic and magnetoelectric coupling, shape effects in magnetic nanostructures, and magnon-phonon dynamics. The work is modest in its claims, noting that results should be interpreted with caution regarding finite-temperature studies, which require further detailed investigation.

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