Antiferromagnets are commonly expected to produce no net magnetization because their atomic magnetic moments cancel one another. Yet some antiferromagnets exhibit spin-split electronic states, Hall currents or spin-orbit-induced magnetization, responses more commonly associated with ferromagnets.
These effects can coexist in the same material without sharing the same physical origin. Some are permitted by the arrangement of magnetic moments, referred to as the magnetic geometry. Others appear only when spin-orbit coupling links electron spin to the crystal lattice. Distinguishing these contributions is essential for understanding unconventional magnets and evaluating their potential for spin-based technologies.
Knowing which mechanism is responsible matters. It determines how a response may change when the magnetic order is rotated, switched or placed in a different crystal environment. It also helps researchers decide which materials are worth pursuing through more demanding calculations and experiments.
The research team led by Qihang Liu and Xiaobing Chen from the State Key Laboratory of Quantum Functional Materials, Department of Physics, Southern University of Science and Technology and Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area has developed FINDSPINGROUP to make this distinction systematically. The open-source online platform and its applications are reported in National Science Review.
One material, two symmetry maps
Symmetry offers a shortcut for studying material properties. Instead of calculating every possible response, researchers can first determine which responses the symmetry permits or forbids.
Magnetic materials, however, have required two different symmetry maps.
A spin space group describes the magnetic geometry in the absence of spin-orbit coupling. In this regime, operations acting on spins do not have to follow the corresponding rotations of the crystal lattice. A magnetic space group describes the regime with spin-orbit coupling, where spin and lattice operations are locked together.
Each map works in its own regime, but the two are not automatically aligned. A spin space group is unchanged when the entire spin frame is rotated, so it does not specify the physical orientation of its spin operations relative to the crystal. A magnetic space group already assumes that this relationship is fixed. Different choices of unit cell, basis and origin add further complications.
The oriented spin space group, or OSSG, aligns the two maps. It selects the material-specific orientation of the spin operations relative to crystallographic directions without itself introducing spin-orbit coupling. The full OSSG can then be used to analyze the material without spin-orbit coupling. The operations that remain compatible with spin-lattice locking form the corresponding magnetic space group and describe the symmetry with spin-orbit coupling.
“The important question is not only what symmetry a magnetic material has, but where each of its allowed responses comes from,” said Qihang Liu. “By placing magnetic geometry and spin-orbit effects in the same material-specific frame, the OSSG allows the two contributions to be compared directly.”
Asking the same material two questions
Applying this comparison to a real magnetic structure previously required researchers to identify and realign the two symmetry descriptions manually. FINDSPINGROUP turns the OSSG framework into an automated workflow.
A user supplies a magnetic structure in CIF, MCIF or SCIF format. FINDSPINGROUP identifies its material-specific OSSG, converts the result to a standard crystallographic setting, matches it to a canonical database representative and derives the corresponding magnetic space group in the same coordinate frame.
The platform then asks the same material two questions: What does its magnetic geometry permit without spin-orbit coupling? What additional responses become possible, or disappear, after spin-orbit coupling is included?
To answer them, FINDSPINGROUP produces standard magnetic cells, spin Wyckoff positions, spin site-symmetry groups, spin Brillouin zones and symmetry information at high-symmetry wave vectors. It evaluates whether magnetization, electric polarization, momentum-dependent spin polarization, spin texture, anomalous Hall conductivity and nonlinear-response tensors are allowed in each regime.
The answers are symmetry constraints, not numerical predictions. FINDSPINGROUP does not calculate how large a Hall current or electric polarization will be. It determines whether the response is possible, which directions or tensor components are allowed and whether its origin can be traced to magnetic geometry or spin-orbit coupling.
Three magnetic puzzles
The researchers tested the workflow on three materials, each posing a different question.
Does spin splitting always require spin-orbit coupling? The two-dimensional altermagnet V2Se2O shows that it does not. Its magnetic geometry already permits momentum-dependent spin splitting. FINDSPINGROUP then tracks how spin-orbit coupling lowers the symmetry, changes the allowed spin-polarization components and permits an additional magnetic response.
Can magnetic order create electric polarization? In MnSe2, the magnetic order breaks the inversion symmetry of the non-magnetic crystal and allows an electric polarization to emerge. The same order also permits momentum-dependent spin splitting. FINDSPINGROUP identifies symmetry-related magnetic states that can serve as candidate switching endpoints, revealing whether electric polarization and spin-dependent responses may reverse separately or together.
Can a Hall response exist even when the electronic bands remain spin degenerate? The non-coplanar antiferromagnet CoNb3S6 provides such a case. Its magnetic geometry permits an anomalous Hall response without spin-orbit coupling while forbidding spin polarization throughout the Brillouin zone. When spin-orbit coupling is included, additional spin polarization and magnetization become symmetry-allowed.
The examples show why observing a ferromagnetic-like response does not, by itself, reveal its origin. Similar effects can follow different symmetry rules and respond differently to external control.
Making the spin group symmetry information portable
To make the comparison reproducible and transferable, the study introduces the spin crystallographic information file, or SCIF. Like CIF and MCIF, SCIF stores the crystal structure together with its spin-group assignment, symmetry operations, coordinate transformations and metadata. The team is working with the IUCr Commission on Magnetic Structures to develop SCIF as a standard format for exchanging spin-group information (https://github.com/COMCIFS/spinCIF).
FINDSPINGROUP combines this format with an online service, open-source software and a searchable database. It can export standardized magnetic structures, wave-vector paths and SCIF files for visualization and tensor analysis, making the paired symmetry workflow applicable to individual materials and high-throughput screening. The platform is available at https://findspingroup.com, with its source code hosted at https://github.com/LiuQH-lab/FindSpinGroup.
National Science Review
Computational simulation/modeling