🔬 materials science

Catalogue of Collinear Magnetic Structures in Stoichiometric Materials

This paper presents a comprehensive computational catalogue of 365,639 symmetry-allowed collinear magnetic structures for over 72,000 stoichiometric materials by leveraging spin space groups and maximal subgroups, ultimately identifying thousands of new magnetic topological materials to guide experimental characterization and spintronics applications.

Original authors: Liangliang Huang, Houhao Wang, Yuanze Song, Ruixi Pu, Xiangang Wan, Feng Tang

Published 2026-09-29

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CC BY 4.0

Original authors: Liangliang Huang, Houhao Wang, Yuanze Song, Ruixi Pu, Xiangang Wan, Feng Tang

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

Magnetism is a force that has shaped human history, from the ancient discovery of lodestones guiding compasses to the modern technology that stores our digital lives. At its core, magnetism arises from the tiny, intrinsic spins of electrons within atoms, which act like microscopic bar magnets. In most materials, these spins are either aligned in the same direction, creating a strong pull like a refrigerator magnet, or they point in opposite directions, canceling each other out so the material feels non-magnetic to the outside world. However, the internal arrangement of these spins is far more complex than just "up" or "down." The specific pattern they form, known as the magnetic structure, dictates how a material behaves, influencing everything from its ability to conduct electricity to its potential for storing data. For decades, scientists have relied on powerful experiments, such as firing neutrons at crystals, to map out these invisible patterns. Yet, for the vast library of known chemical compounds, these magnetic maps remain largely blank, leaving researchers to guess how the atoms inside might be arranged.

A team of researchers at Nanjing University has now filled in a massive portion of this missing map. By combining advanced mathematical symmetry rules with high-speed computer simulations, they have systematically predicted the magnetic structures for nearly 72,000 different chemical compounds. Their work focuses on a specific, common type of magnetism where the atomic spins line up in straight, parallel rows, rather than twisting into complex spirals. Using a sophisticated framework called spin space groups, which acts as a set of strict architectural rules for how these spins can arrange themselves, the team generated a catalogue of 365,639 possible magnetic configurations. They then used powerful computers to calculate the energy of these arrangements for thousands of materials, identifying which pattern nature actually prefers to settle into. The result is a comprehensive database that reveals the ground-state magnetic structure for over 7,800 materials, many of which were previously unknown to science.

The researchers began by acknowledging a gap in current knowledge: while databases exist for experimentally measured magnetic structures, they contain only a tiny fraction of the materials scientists have synthesized. To bridge this gap, the team turned to symmetry. Just as a snowflake's shape is dictated by the symmetry of its crystal lattice, the arrangement of magnetic spins is constrained by the underlying geometry of the material. The team utilized a mathematical tool called spin space groups to list every possible way spins could align in a straight line for any given crystal structure. This approach was far more efficient than previous methods, which often had to test countless random possibilities. By applying these rules to 72,075 non-magnetic crystal structures found in the Inorganic Crystal Structure Database, they narrowed down the possibilities to a manageable number of candidates for each material. In most cases, the symmetry rules left fewer than eight potential magnetic arrangements to consider, making it feasible to run detailed computer simulations on a massive scale.

The team then performed high-throughput first-principles calculations, essentially simulating the quantum behavior of electrons within these materials to find the lowest energy state. This process determined the actual magnetic structure that each material would adopt in its most stable form. They validated their method by comparing their predictions against known experimental data for hundreds of materials, finding that their approach correctly identified the magnetic structure in over 70 percent of cases. This success gave them the confidence to apply their method to the entire database of stoichiometric materials. The outcome was a list of 7,824 materials with confirmed collinear magnetic structures, including well-known compounds like manganese bismuth telluride and cobalt tin sulfide, as well as hundreds of new candidates. Among these, they identified 186 materials that are not only magnetic but also possess exotic electronic properties, such as the ability to conduct electricity without resistance along their surfaces or to host unique quantum particles.

This work does more than just catalog existing materials; it provides a roadmap for discovering new technologies. The researchers found that many of their predicted materials belong to a recently identified class called altermagnets. These are unusual magnets that have no net magnetic pull on the outside, like traditional antiferromagnets, but still exhibit strong internal spin effects that can be used for ultra-fast data processing. The study also highlighted materials that could serve as topological insulators, which are crucial for developing next-generation electronics that are faster and more energy-efficient. By providing a reliable, pre-screened list of candidates, the team has saved experimentalists from having to guess which materials to test. Instead of searching blindly, scientists can now look directly at this database to find materials with specific magnetic and topological properties tailored for applications in spintronics, quantum computing, and advanced sensors.

The significance of this achievement lies in its scale and precision. Before this work, predicting the magnetic structure of a new material was a slow, trial-and-error process that often required expensive and time-consuming experiments. The new database turns this into a systematic search, allowing researchers to instantly see what magnetic order is possible for a given chemical composition. The team has made this entire collection of data openly available, creating a resource that the global scientific community can use to accelerate the discovery of new functional materials. By revealing the hidden magnetic order within thousands of compounds, this study transforms our understanding of the magnetic landscape, turning a vast field of unknowns into a structured territory ready for exploration and application.

Technical Summary: Catalogue of Collinear Magnetic Structures in Stoichiometric Materials

Problem Statement
Magnetic materials are central to information technologies and the realization of novel quantum states, including quantum spin liquids, Weyl semimetals, and the recently predicted altermagnets (AM). However, the accurate determination of magnetic structures (MSs)—specifically the local magnetic moments (MMs) on magnetic ions—is often a bottleneck. While experimental techniques like neutron scattering are standard, they are resource-intensive. Conversely, while the Inorganic Crystal Structure Database (ICSD) contains over 70,000 nonmagnetic stoichiometric structures, the vast majority lack experimentally determined MSs. Traditional approaches using Magnetic Space Groups (MSGs) to constrain candidate MSs are often insufficient for large-scale screening because the symmetry reduction from a nonmagnetic Space Group (SG) to an MSG is abrupt, leading to a large number of candidate configurations. Furthermore, identifying the ground-state symmetry and predicting topological properties without prior knowledge of the MS direction remains challenging.

Methodology
The authors propose a framework based on Spin Space Groups (SSGs) to systematically enumerate and predict collinear MSs. The methodology proceeds in three main stages:

Group-Theoretical Enumeration:
- The authors utilize the 230 nonmagnetic Space Groups (SGs) to construct all possible maximal collinear Spin Space Groups (Max-SSGs). There are 2,078 such Max-SSGs (1,421 inequivalent), categorized into Ferromagnetic (FM), Altermagnetic (AM), and two types of Antiferromagnetic (AFM) structures ( $\tau T$ and $PT$ ).
- Unlike MSGs, SSGs explicitly separate spin and real-space operations. This allows for stricter symmetry constraints: for a given SG, Max-SSGs can often rule out candidate MSs that Max-MSGs would permit. For instance, in certain hexagonal symmetries, Max-SSGs require all MMs to vanish for specific subgroups, whereas Max-MSGs might allow non-collinear or coplanar configurations.
- Using these Max-SSGs, the authors exhaustively enumerate all symmetry-allowed collinear MSs for the 72,075 nonmagnetic stoichiometric structures in the ICSD. This process identifies the specific Wyckoff positions (WYPOs) that can host non-zero MMs and the allowed relationships between them.
High-Throughput First-Principles Screening:
- The enumeration is applied to the ICSD, yielding 365,639 possible collinear MSs. Notably, 92% of the structures possess no more than eight candidate MSs, making large-scale computational screening feasible.
- The authors select 21,315 materials (those with $\le$ 20 atoms per primitive cell) for high-throughput Density Functional Theory (DFT) calculations.
- Calculations are performed without Spin-Orbit Coupling (SOC) to determine the ground-state MS and SSG symmetry for various Hubbard $U$ values.
- For the identified ground states, SOC is subsequently included to determine the specific MM direction and the resulting Magnetic Space Group (MSG) symmetry.
Topological Classification:
- The predicted collinear magnets are classified based on their topological properties. The authors utilize the compatibility relations between SSGs and their MSG subgroups.
- In the weak-SOC limit, the topological diagnosis derived from SSG-based calculations (without SOC) can be extended to all possible MM directions in the presence of SOC.
- For materials where this approximation holds, or where full SOC calculations are performed, the band topology is diagnosed to identify magnetic topological insulators, Weyl semimetals, and nodal-line semimetals.

Key Contributions and Results

Comprehensive Database: The study generates a catalogue of 365,639 symmetry-constrained collinear MSs for 72,075 ICSD structures.
Ground-State Prediction: Through high-throughput calculations, the ground-state collinear MSs and SSG symmetries are determined for 7,824 materials.
Validation: The approach is benchmarked against the MAGNDATA database, which contains experimentally determined MSs.
- Max-SSGs successfully describe 83% (799 out of 962) of the collinear magnets in MAGNDATA, significantly outperforming Max-MSGs, which capture only 57% (549).
- For a subset of 173 materials, first-principles calculations without SOC correctly predict the SSG symmetry of the ground state in approximately 70% of cases.
- When compared to experimental MSs in MAGNDATA, 77 out of 137 overlapping materials show agreement between the calculated ground-state MS and experiment.
Discovery of Magnetic Topological Materials:
- The screening identifies 5,351 magnetic topological materials (without SOC) and 2,481 with SOC.
- The authors select 186 "nearly ideal" magnetic topological materials. These include known materials such as the magnetic topological insulator $MnBi_2Te_4$ , the Weyl semimetal $Co_3Sn_2S_2$ , and altermagnets like $MnTe$ and $CrSb$ .
- The study provides detailed nodal structures and surface states for representative examples, including $NaSe_2V$ (Weyl semimetal), $NiPt$ (Dirac semimetal), and $FeInO_3$ (nodal-line semimetal).

Significance
The paper claims that the experimentally determined MSs in MAGNDATA represent only the "tip of the iceberg" compared to the computational database generated in this work. The primary significance lies in providing a systematic, symmetry-guided route to determine magnetic structures without relying solely on experimental trial-and-error. By leveraging SSGs, the authors demonstrate that the complexity of determining collinear MSs can be drastically reduced, enabling the prediction of ground-state magnetic orders and their associated topological properties on a large scale. The resulting database serves as a resource for experimentalists to guide MS characterization and for the discovery of new materials for spintronic applications, particularly those involving altermagnetism and magnetic topology. The work also establishes a framework where SSG symmetry classification can potentially be extended to other microscopic orders, such as charge-density waves.

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