Spin splitting without symmetry: a nearly compensated ferrimagnet and the origin of altermagnetism

In the world of solid materials, electrons are the tiny messengers that carry electricity and magnetism. When these electrons move through a metal or an insulator, they usually behave in one of two familiar ways. In a standard magnet, like a fridge magnet, the electrons align their spins in the same direction, creating a strong, unified magnetic pull. In a conventional anti-magnet, the electrons pair up with opposite spins that perfectly cancel each other out, leaving the material with no net magnetic pull at all. For decades, scientists believed that if the spins canceled out, the energy levels of the electrons would also be identical, making the material magnetically silent in a very specific way.

However, a newer class of materials has recently challenged this simple picture. These materials, called altermagnets, manage to have their spins cancel out just like an anti-magnet, yet their electrons still show a distinct energy difference between the two spin directions. This hidden energy split is what makes them so interesting for future technology, as it could allow for faster, more efficient electronic devices. For a long time, the prevailing idea was that this energy split was created by the material's internal symmetry—its specific geometric arrangement of atoms, much like how a mirror reflects an image. The assumption was that without a special geometric rule connecting the opposite spins, this energy split could not exist.

A researcher at Sungkyunkwan University in South Korea has now shown that this assumption is incorrect. By studying a specific type of manganese oxide in its most basic, low-symmetry form, they discovered that the energy split does not come from the geometric rules of the crystal at all. Instead, it arises from the physical shape and orientation of the electron clouds and the atoms surrounding them. The researcher found that the crystal symmetry does not create the split; it merely organizes it. To prove this, they performed a delicate experiment where they kept the magnetic atoms exactly the same but slightly shifted the surrounding oxygen atoms. When they did this, the energy split vanished almost entirely, collapsing to a tiny fraction of its original size. This demonstrated that the split is generated by the specific arrangement of the atoms, not by the symmetry of the crystal structure.

The study begins by looking at a material called altermagnetism, which sits in a middle ground between a standard magnet and an anti-magnet. In these materials, the magnetic moments of the atoms cancel out, so the material does not act like a magnet in the usual sense. Yet, the electrons still show a clear separation in energy depending on their spin direction. This separation is not uniform; it changes as the electrons move through the material, creating a pattern that looks like a four-leaf clover in the way the energy shifts. Scientists had previously thought that this pattern was a direct result of the crystal's symmetry, specifically a rotation or a mirror reflection that linked the two sets of opposite spins. They believed that if you removed that symmetry, the energy split would disappear.

To test this, the researcher turned to a crystal system that has the lowest possible symmetry, known as triclinic. In this system, there are no mirrors, no rotations, and no center points that relate one part of the crystal to another. It is a structure where every atom is in a unique position relative to its neighbors. They constructed a model of a manganese oxide crystal in this triclinic state, where the two magnetic manganese atoms were different from each other and not connected by any symmetry rule. Despite having no symmetry to link them, the calculations showed that the electrons still exhibited a strong energy split across the entire material. This was a surprise because, according to the old view, the lack of symmetry should have meant no split at all.

The researcher then took this finding a step further to see what was actually causing the split. They kept the magnetic manganese atoms exactly where they were but carefully moved the surrounding oxygen atoms. They shifted these oxygen atoms just enough to create a perfect center of symmetry between the two manganese sites, effectively turning the crystal into a more symmetrical structure. When they did this, the strong energy split that had been present in the low-symmetry version collapsed. It shrank to a level roughly one hundred times smaller, essentially disappearing. This result was decisive: the only thing that changed was the physical arrangement of the oxygen atoms. The magnetic atoms remained the same, and the symmetry actually increased, yet the energy split vanished.

This experiment revealed that the energy split is not a gift from the crystal's symmetry. Instead, it is generated by the anisotropic arrangement of the magnetic orbitals—the specific shapes and directions of the electron clouds—and how they are held by their surrounding ligands, which are the oxygen atoms in this case. The researcher explained that the oxygen atoms create a distorted cage around the manganese. This distortion gives the electron clouds a specific direction or shape. When these shaped clouds are placed in a way that is different for the two sets of spins, it creates a difference in how the electrons hop between atoms, leading to the energy split. The symmetry of the crystal, if it exists, simply takes this pre-existing split and arranges it into a neat, predictable pattern. Without the symmetry, the split still exists, but it is unorganized and messy.

The paper further clarifies that symmetry plays a role, but it is a different one than previously thought. Symmetry acts as an organizer. It can force the energy split to be zero in certain directions, creating what are called nodal planes, which are like invisible walls where the energy difference disappears. It can also ensure that the split follows a specific pattern, like the four-leaf clover shape seen in higher-symmetry materials. However, symmetry cannot create the split from nothing. If the underlying arrangement of the atoms and orbitals does not provide the necessary difference, the symmetry has nothing to organize, and no split appears. The researcher showed that in materials where the symmetry is present, it is the arrangement of the atoms that actually does the heavy lifting to generate the energy difference.

This finding changes how scientists should look for new materials with these properties. Instead of searching only for crystals with specific symmetrical shapes, researchers should focus on the physical arrangement of the magnetic atoms and their surrounding ligands. The study suggests that even in materials with very low symmetry, or no symmetry at all, these energy splits can occur as long as the orbital arrangement is right. This opens up a much wider range of materials for potential use in technology. The researcher describes the relationship between the organized altermagnet and the unorganized, fully compensated ferrimagnet as two ends of the same spectrum. One end has a symmetry that organizes the split, while the other end has no symmetry, leaving the split to exist in a raw, unorganized form.

The work also addresses why this discovery was missed for so long. The scientific community had largely assumed that a material without symmetry would not show this kind of spin splitting, or that if it did, it would be a trivial result of having no rules to prevent it. This led to a blind spot where the most basic cases were ignored. By examining the triclinic case, the researcher exposed the true origin of the phenomenon. They showed that the arrangement of the orbitals is the primary driver, and symmetry is secondary. This distinction is crucial because it means that the search for these materials should focus on the microscopic details of how atoms are packed and how their electron clouds are shaped, rather than just looking for specific crystal classes.

In the end, the study provides a clear and systematic way to understand these magnetic materials. It establishes a hierarchy where the first question is whether the arrangement allows for a split, the second is which symmetry operations relate the spins, and the third is how those operations shape the split. The researcher found that the arrangement is the source, and the symmetry is the editor. This insight not only corrects a long-held misconception but also provides a practical guide for designing the next generation of magnetic materials. The ability to control the energy split by manipulating the physical arrangement of atoms, rather than just relying on the crystal's symmetry, offers a new and powerful tool for materials science. The findings suggest that the path forward lies in understanding the subtle, physical details of how atoms and their electron clouds interact, rather than just the geometric rules they follow.