Odd-parity magnets (OPMs) have recently emerged as a new magnetic class, but their general symmetry criteria remain elusive. In this Letter, we establish these criteria through a comprehensive spin group symmetry analysis. Concretely, we identify eight distinct symmetry-driven cases that support OPMs with collinear, coplanar, or noncoplanar magnetic order. These are classified into three classes based on their spin textures: collinear (type-I), coplanar (type-II), and noncoplanar (type-III). From the Magndata database, we identify 33 candidate OPM materials and diagnose their spin-splitting character (p- or f-wave) by analyzing the representation of spin textures within an emergent Laue group derived from the spin space group, which reveals a variety of novel spin textures. To validate the symmetry criteria, we construct and analyze two theoretical models. Furthermore, we demonstrate that OPMs can host an intrinsic Z2 topology and propose a model for their realization. Our work provides a foundational framework for the future exploration of OPMs.
@article{arxiv.2510.05512,
title = {Spin Group Symmetry Criteria for Odd-parity Magnets},
author = {Xun-Jiang Luo and Jin-Xin Hu and Meng-Li Hu and K. T. Law},
journal= {arXiv preprint arXiv:2510.05512},
year = {2026}
}