Leveraging Magnetic Distortion Symmetry Groups to Elucidate the Multiferroic Origins of Altermagnetism

Altermagnets—materials exhibiting crystal-compensated magnetic order and non-relativistic spin splitting—have gained attention for their unconventional physics and technological promise [1]. In altermagnets, crystallographic rotations connect opposite spin sublattices, distinguishing them from antiferromagnets and ferromagnets under the spin group classification scheme [2]. While their unique symmetry permits non-relativistic piezomagnetism that is odd in the Néel vector (N) [3], many of their properties of interest, such as odd-in-N anomalous Hall conductivity, are mediated by spin–orbit coupling (SOC) [4]. The symmetries of such properties must therefore be predicted by the magnetic symmetry groups, which do not differentiate between altermagnetic and purely relativistic effects [5]. Moreover, it is still debated whether altermagnetism is a third phase of collinear magnetism alongside ferromagnetism and antiferromagnetism. In this work, we demonstrate that altermagnets are not a fundamental magnetic class, but rather a primary class of multiferroics analogous to magneto-electrics. To this end, we present a new framework for identifying altermagnetism, leveraging a new formalism for capturing the latent symmetries of structural distortions with respect to a parent crystal [6]. By assigning a magnetic distortion point group (MDPG) to a material, we can determine if it hosts a nonrelativistic coupling between antiferromagnetic order and staggered distortions that break both translation-time (Tt) and parity-time (PT) symmetries. With the same MDPGs, we can also predict the symmetries of SOC-mediated altermagnetic properties and distinguish them from purely relativistic effects based on how they couple to distortions. To demonstrate the power of our approach, we discuss a case study where we uncovers hidden altermagnetic order parameters and reveal the altermagnetic origins of experimentally observed SOC-mediated phenomena. Our work provides valuable insights into the synergetic relationships between multiferroicity, altermagnetism, and spin-orbit coupling—and affirms the MDPG formalism as a powerful tool for identifying and characterizing multiferroics.