🔬 materials science

Bond, orbital and spin order in d4/d6/d7 perovskite oxides: successes and limitations of foundation interatomic potentials

This study evaluates the capabilities of foundation machine-learning interatomic potentials in modeling strongly correlated perovskite oxides, finding that while they successfully capture simple geometric orders like those in NdNiO3, they fail to reproduce symmetry-breaking vector orders in LaMnO3 and remain entirely unable to simulate purely local spin-state crossovers in LaCoO3.

Original authors: Swagata Acharya, Dimitar Pashov, Mark van Schilfgaarde, Alin M. Elena

Published 2026-07-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Swagata Acharya, Dimitar Pashov, Mark van Schilfgaarde, Alin M. Elena

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 you have a super-smart robot chef named Foundation. This chef has read millions of cookbooks (data from density-functional theory) and can now predict exactly how a kitchen (a crystal structure) will look and move when you turn up the heat, without ever needing to taste the food first. Scientists are excited because this chef can simulate cooking for a whole second (1 nanosecond), which is an eternity in the world of atoms.

But here's the catch: the chef only looks at the shape of the ingredients and how they bump into each other. It doesn't actually "see" the invisible electronic magic that happens inside the atoms. The paper tests this chef on three very specific, tricky recipes made of perovskite oxides: LaCoO₃, NdNiO₃, and LaMnO₃.

The researchers wanted to see if the chef could figure out the secret "dance moves" (order) these atoms do when it gets cold. They ran the simulation from 50 K to 300 K (that's from very cold to a warm summer day) using a giant kitchen with 80 atoms (and double-checked with a 160-atom kitchen to be sure).

Here is what the chef got right, what it got wrong, and why.

1. The Easy One: The Breathing Rock Salt (NdNiO₃)

The Recipe: This material is like a group of dancers holding hands in a checkerboard pattern. When they get cold, they start a "breathing" dance: some pairs pull close together, and others push far apart, alternating in a perfect pattern.
The Chef's Performance: The chef was pretty good at this! It saw the pattern of long and short bonds.

The Result: The chef noticed the bonds were alternating, with a "rocksalt order parameter" (a score for how well they alternate) sitting around -0.20 to -0.27. One version of the chef (called omol) got it perfect, locking the pattern in with a score of -1.000.
The Catch: The perfect score was a bit of a trick. The chef got stuck in one specific "dance groove" and didn't realize that in real life, this dance changes as the temperature changes. It saw the shape of the dance, but missed the thermodynamics (the reason the dance happens).

2. The Tricky One: The Spinning Top (LaMnO₃)

The Recipe: This material is like a room full of spinning tops (Jahn-Teller distortions). Each top has a long axis. In the real world, these tops don't all point the same way; they alternate in a specific "C-type" pattern (like a checkerboard of directions).
The Chef's Performance: The chef struggled here. It could see that the tops were wobbling (the bonds were stretching), but it couldn't figure out the direction they were pointing.

The Result: The chef saw the tops wobble, but they all pointed in the same direction (a "ferro-orbital" pattern) instead of alternating. One version (CHGNet) made the tops wobble with the right size (0.42 Å at 50 K, close to the real 0.39 Å), but they were all pointing the wrong way. The other versions barely saw the wobble at all (|Qstatic₂| ≤ 0.025 Å).
The Verdict: The chef knows the tops are moving, but it can't figure out the complex "alternating" choreography. It's like seeing a crowd of people waving flags, but thinking they are all waving them in the same direction.

3. The Impossible One: The Invisible Mood Swing (LaCoO₃)

The Recipe: This material is the hardest. Inside the atoms, the electrons are having a "mood swing," switching between a calm state (low-spin) and an excited state (high-spin) as it warms up.
The Chef's Performance: The chef failed completely.

The Result: The chef saw absolutely nothing. The bonds didn't change length, and the atoms didn't rearrange. The bond length stayed flat at ±0.003 Å.
The Verdict: This is because the "mood swing" happens inside the atom. It doesn't change the shape of the kitchen. Since the chef only looks at the shape of the room, it can't see the mood swing at all. The paper says this is fundamentally inaccessible to a chef that only looks at geometry.

The Big Lesson: A Hierarchy of Difficulty

The authors found a clear "ladder of difficulty" for these AI chefs:

Scalar (The Easy Step): If the electronic problem creates a simple "long vs. short" pattern (like the breathing rock salt), the chef can see it.
Vector (The Middle Step): If the problem requires knowing which direction is long (like the spinning tops), the chef gets the size right but the direction wrong. It needs more training on specific patterns to get the choreography right.
On-Site (The Top Step): If the problem is purely about the internal state of the atom with no shape change (like the mood swing), the chef is blind. No amount of looking at the room will help; you have to teach the chef to "feel" the electrons directly.

What the Paper Rules Out

The paper explicitly argues against the idea that these foundation models are a magic bullet for all correlated materials.

It rules out the idea that we can just use these models to study the "mood swing" in LaCoO₃ without changing how they work.
It rules out the idea that the models have "learned" the correct physics for the alternating patterns in LaMnO₃; they just got lucky with the size of the wobble but missed the pattern.

How Sure Are They?

The authors are very sure about what they simulated. They ran 1 nanosecond of molecular dynamics for each material at 6 different temperatures (50, 100, 150, 200, 250, 300 K). They checked their work with 160-atom kitchens to make sure the results weren't just a fluke of the small kitchen size.

They are suggesting that future models need to be "fine-tuned" with specific data (like knowing the spin state or the exact alternating pattern) to fix these errors. They aren't saying the models are broken forever, but they are saying: "If you want to solve these specific puzzles, you can't just use the generic recipe; you need to add these specific ingredients to the training data."

In short, the robot chef is great at seeing the furniture move, okay at seeing the furniture wobble, but completely blind to the invisible feelings inside the furniture. To fix that, we have to teach the chef a whole new way of seeing.

Technical Summary: Bond, Orbital, and Spin Order in $d^4/d^6/d^7$ Perovskite Oxides

Problem Statement
Foundation machine-learning interatomic potentials (MLIPs), trained on density-functional theory (DFT) total energies, forces, and stresses, are increasingly used to model structural and nuclear dynamics in correlated transition-metal oxides at finite temperatures. However, these models rely primarily on atomic numbers and local bonding environments as descriptors, lacking direct access to local multiplets, ligand-hole physics, or orbital occupation. The central question addressed is whether the skeletal structural information encoded in these foundation potentials is sufficient to capture the complex low-temperature orders arising from strongly correlated electronic channels, or if specific electronic instabilities remain inaccessible.

Methodology
The authors tested three foundation MLIPs—MACE with the matpes r2scan head (trained on Materials Project total energies), MACE with the omol head (trained on molecular data), and CHGNet (trained on Materials Project trajectories with explicit $+U$ and magnetic moment supervision)—against three isostructural $ABO_3$ perovskite oxides with distinct correlated ground states:

NdNiO $_3$ ( $d^7$ ): Exhibits a metal-insulator transition driven by a rocksalt breathing-mode distortion (scalar order parameter).
LaMnO $_3$ ( $d^4$ ): Features cooperative Jahn-Teller (JT) distortions with C-type antiferro-orbital order (vector order parameter).
LaCoO $_3$ ( $d^6$ ): Displays a low-spin to high-spin crossover with no spatial order parameter (on-site multiplet population shift).

Simulations were conducted using NVT molecular dynamics on 80-atom and 160-atom supercells across a temperature range of 50–300 K. No system-specific training was performed; the potentials were applied "out of the box." Structural analysis relied on a descriptor pipeline calculating per-site bond statistics, shell correlations, and specific order parameters: the rocksalt order parameter ( $Q_{RS}$ ), static JT amplitude ( $|Q^{\text{static}}_2|$ ), and orbital order parameters ( $M_{OO}$ , $M_{FO}$ ). Finite-size effects were ruled out by verifying consistency between 80- and 160-atom supercells.

Key Results
The study reveals a hierarchy of difficulty for foundation MLIPs in reproducing correlated electronic orders, categorized by the nature of the order parameter:

Scalar Class (NdNiO $_3$ ): The breathing-mode distortion, characterized by alternating long/short Ni-O bonds, is captured to varying degrees. The omol potential successfully reproduces the frozen rocksalt pattern ( $Q_{RS} \approx -1.0$ ), while matpes r2scan captures the precursor fluctuations ( $Q_{RS} \approx -0.27$ ), and CHGNet shows weaker correlation. This class is learnable from nearest-neighbor bond-length anti-correlations alone.
Vector Class (LaMnO $_3$ ): The cooperative JT order requires determining the specific Cartesian axis of the long bond (a vector field). All three potentials fail to reproduce the experimental C-type antiferro-orbital pattern. CHGNet captures the magnitude of the distortion but incorrectly predicts a ferro-orbital (FO) pattern where all long axes align. omol shows partial static distortion, and matpes r2scan yields only dynamical, non-cooperative distortions. The failure stems from the lack of training data containing the specific symmetry-breaking pattern required to lift the degeneracy of the long-axis direction.
On-Site Class (LaCoO $_3$ ): The spin-state crossover involves a shift in multiplet populations without a static structural order parameter. All three potentials correctly predict the absence of symmetry-breaking distortions, consistent with the experimental low-spin ground state. However, the underlying physics (the crossover itself) is inaccessible to structure-only models because the order parameter is not geometric; it manifests only as a subtle broadening of the bond-mean distribution (leptokurtic enhancement in omol), which the models cannot explicitly resolve as a spin transition.

Key Contributions

Structural-Footprint Criterion: The authors establish that a foundation MLIP can reliably reproduce the static low-temperature structural fingerprints of a correlated oxide if and only if the underlying electronic instability has condensed its order parameter onto a static lattice distortion present in the training-set ground-state relaxations.
Hierarchy of Architectural Difficulty: The paper defines a three-tiered difficulty scale for foundation models handling correlated oxides:
- Scalar: Learnable from bond-length correlations (e.g., breathing modes).
- Vector: Requires training sets that explicitly break long-axis degeneracy in the correct symmetry pattern (e.g., cooperative JT).
- On-Site: Fundamentally unreachable by structure-only models as the order parameter is not geometric (e.g., spin crossovers).
Diagnostic Framework: The study provides specific structural descriptors (e.g., $Q_{RS}$ , $|Q^{\text{static}}_2|$ , bimodality coefficients) to test the fidelity of MLIPs against experimental structural data, distinguishing between capturing magnitude versus capturing symmetry.

Significance and Claims
The paper claims that while foundation MLIPs are powerful for modeling structural ensembles, they are not universally sufficient for correlated systems. The "skeletal structural information" is sufficient for scalar collective modes (like the breathing mode in nickelates) but fails for vector orbital ordering (manganates) unless the training set explicitly includes the correct symmetry patterns. Crucially, the paper asserts that on-site multiplet crossovers (like in cobaltates) are "inaccessible to present-day MLIPs" because the order parameter is not a static structural distortion.

The authors conclude that correcting these failures requires material-specific strategies: adding per-site spin labels for scalar classes, including specific JT-active reference structures for vector classes, and incorporating explicit multiplet-resolved auxiliary inputs (trained against multi-reference methods like DMFT or GW) for on-site classes. The work serves as a diagnostic benchmark, demonstrating that the limitations of current foundation potentials are not merely a matter of data volume but of the fundamental mismatch between geometric descriptors and non-geometric electronic order parameters.