Anti-spin Laue groups: classification of anti-altermagnets and their representative minimal models

Abstract

Anti-altermagnets exhibit odd-parity nonrelativistic spin splitting, yet unlike even-parity altermagnets, their momentum-space symmetries lack a reduced classification analogous to spin Laue groups. Here, we introduce anti-spin Laue groups, organized into three distinct classes, and identify 21 groups describing the odd-parity partial wave character of this unconventional class. Together with the 10 spin Laue groups of altermagnets, they complete the classification of nonrelativistic unconventional magnets with collinear momentum-space spin polarization. Anti-spin Laue groups also provide a many-to-one reduction of spin space (point) groups by retaining only their action on the collinear momentum-space spin polarization, thereby directly encoding the symmetry-enforced nodal spin-splitting character. Based on this we develop a systematic model-construction algorithm yielding minimal, material-oriented four-band models. This framework places odd- and even-parity unconventional magnets on equal footing within a unified momentum-space symmetry description.