Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry

TLDR

Research into novel magnetic quantum phases has relied on relativistic magnetic‑symmetry groups, yet these groups cannot separate non‑relativistic effects such as the unconventional spin physics observed in collinear antiferromagnets. The study introduces a third non‑relativistic collinear magnetic phase, altermagnetism, defined by zero net magnetization and alternating spin‑momentum locking in energy bands. The authors develop a spin‑group theory describing six types of altermagnetic spin‑momentum locking and employ first‑principles calculations to identify candidate materials. They demonstrate that altermagnetic bands exhibit an extraordinary spin‑splitting driven by local electric crystal fields, and the calculations reveal candidates ranging from insulators and metals to a cuprate‑superconductor parent, underscoring the promise of high‑temperature magnets for spintronics.

Abstract

The search for novel magnetic quantum phases, phenomena and functional materials has been guided by relativistic magnetic-symmetry groups in coupled spin and real space from the dawn of the field in 1950s to the modern era of topological matter. However, the magnetic groups cannot disentangle non-relativistic phases and effects, such as the recently reported unconventional spin physics in collinear antiferromagnets from the typically weak relativistic spin-orbit coupling phenomena. Here we discover that more general spin symmetries in decoupled spin and crystal space categorize non-relativistic collinear magnetism in three phases: conventional ferromagnets and antiferromagnets, and a third distinct phase combining zero net magnetization with an alternating spin-momentum locking in energy bands, which we dub "altermagnetic". For this third basic magnetic phase, which is omitted by the relativistic magnetic groups, we develop a spin-group theory describing six characteristic types of the altermagnetic spin-momentum locking. We demonstrate an extraordinary spin-splitting mechanism in altermagnetic bands originating from a local electric crystal field, which contrasts with the conventional magnetic or relativistic splitting by global magnetization or inversion asymmetry. Based on first-principles calculations, we identify altermagnetic candidates ranging from insulators and metals to a parent crystal of cuprate superconductor. Our results underpin emerging research of quantum phases and spintronics in high-temperature magnets with light elements, vanishing net magnetization, and strong spin-coherence.