Quantitative Multipole Analysis Advances Understanding of Altermagnetic Phenomena

Altermagnetism, a unique form of magnetism where spins align perpendicular to the magnetic field, challenges conventional understanding of magnetic order, and researchers are now establishing a clearer link between its origins and the distribution of charge and magnetism around individual atoms. Francesco Martinelli, Anouk Droux, and Claude Ederer, all from ETH Z ̈urich, demonstrate a quantitative relationship between altermagnetic spin splitting and higher-order multipoles, complex patterns of charge and magnetism, within materials. Their work moves beyond qualitative symmetry arguments by employing advanced electronic structure calculations to show that altermagnetism arises not from a single dominant multipole, but from the combined influence of several comparable contributions, suggesting a more complex order parameter is needed to fully describe this phenomenon. This discovery provides a crucial step towards predicting and designing new materials exhibiting this unusual magnetic behaviour, potentially opening avenues for novel spintronic devices.

The team employs first-principles-based electronic structure calculations to establish a clear quantitative relation between the strength of the altermagnetic spin splitting and the magnitude of certain local multipoles. They vary the magnitude of these multipoles either by applying an appropriate constraint on the charge density or by varying a corresponding structural distortion mode, utilising two simple perovskite materials, SrCrO3 and LaVO3, as model systems. The analysis indicates that, in general, the altermagnetic spin splitting is not exclusively determined by the lowest order nonzero magnetic multipole, but results from a superposition of contributions from different multipoles with comparable strength, suggesting the need for a multi-component order parameter.

Non-Collinear Magnetism and Orbital Moments Revealed

This is a fantastic and comprehensive collection of research related to altermagnetism. The papers together establish altermagnetism as a distinct magnetic order, different from ferromagnetism, antiferromagnetism, and ferrimagnetism. It is characterized by non-collinear magnetic moments that do not cancel out and give rise to a net magnetization through the interplay of spin and orbital moments. A key aspect of altermagnetism is its strong dependence on symmetry, as well as the role of spin–orbit coupling and crystal field effects in stabilizing this unconventional magnetic order.

A recurring theoretical theme across the papers is the importance of multipole interactions. Several studies emphasize that dipolar interactions alone are insufficient to explain altermagnetism, and instead highlight the role of higher-order multipoles such as quadrupoles and octupoles. Decomposing magnetic moments into these multipole components emerges as a powerful analytical approach. Closely related to this is the extensive use of group theory and symmetry analysis, which is central to identifying allowed magnetic structures and understanding how specific space groups and symmetry operations enable altermagnetic order. Orbital ordering also appears repeatedly as a crucial factor, as specific orbital arrangements can induce magnetic anisotropies and drive the non-collinear alignment of spins that characterizes altermagnetism.

On the materials and computational side, much of the research focuses on perovskite chromates, particularly SrCrO₃, which serves as a prototypical altermagnetic material. Density functional theory calculations are widely used to determine ground-state magnetic structures, analyze electronic band structures and densities of states, investigate the influence of spin–orbit coupling, and study the effects of strain and chemical composition. Beyond SrCrO₃, the scope of materials studied includes Ruddlesden–Popper chromates, BiFeO₃, and GdAlSi, each offering new perspectives on altermagnetism and its coexistence with other phenomena. Standard computational techniques such as PAW and projector augmented wave methods underpin much of this work.

Several key findings emerge across the collection. One of the most significant is the possibility of non-relativistic spin splitting in altermagnetic materials, which contrasts with conventional spin–orbit–driven effects and opens new avenues for spintronic applications. Some materials are also shown to exhibit topological properties, such as Weyl semimetal behavior, alongside altermagnetism, suggesting the presence of novel quantum phenomena. There are also indications of connections between altermagnetism and multiferroicity, hinting at potential magnetoelectric functionalities. From these studies, early design principles are beginning to form, including the importance of crystal symmetry, control of orbital ordering, and tuning of spin–orbit coupling through material choice or strain.

The papers build on one another in a clear progression. Early theoretical works establish the role of multipole interactions in magnetism, while advances in computational methods enable detailed modeling of complex materials. SrCrO₃ serves as a central test case, with successive studies refining understanding of its electronic and magnetic properties. More recent work expands the focus to additional materials and explores links between altermagnetism, topology, and other emergent phenomena. Overall, this body of research reflects a rapidly developing field with strong potential for both fundamental insights and technological innovation, particularly in the context of spintronics and quantum materials.

Altermagnetism Arises From Multipole Interactions and Distortions

This research establishes a clear link between altermagnetic spin splitting and the distribution of charge and magnetism around magnetic atoms within materials. By performing detailed electronic structure calculations on strontium chromite and lanthanum vanadate, scientists demonstrate that altermagnetism arises not from a single magnetic component, but from the combined influence of multiple magnetic multipoles, each with comparable strength. This finding suggests that a more complex, multi-component order parameter is needed to fully describe altermagnetic behaviour., The team further investigated how structural distortions contribute to this phenomenon, isolating specific modes of atomic displacement within lanthanum vanadate. They found that each distortion mode induces a particular multipole, and by selectively amplifying these modes, they could directly observe the emergence of non-reciprocal spin splitting.

Importantly, the observed spin splitting in fully distorted materials closely resembles that induced by individual distortion modes, indicating a dominant role for these structural features in driving altermagnetism., The authors acknowledge that while they have identified key relationships, the interplay between different multipoles and distortion modes is complex, and further research is needed to fully understand the nuances of altermagnetic materials. Future work could focus on exploring a wider range of materials and investigating the impact of external stimuli on these magnetic properties. These findings represent a significant step towards designing materials with tailored altermagnetic properties for potential applications in novel electronic devices.