It is widely accepted that spin-orbit coupling (SOC) generally locks spin and spatial degrees of freedom, as a result, the spin, despite being an axial vector, is fixed and cannot rotate independently, and the magnetic system should be described by magnetic space groups (MSGs). While as a new type of group, spin space groups (SSGs) have been introduced to approximately describe the symmetry of magnetic systems with negligible SOC, and received significant attention recently. In this work, we prove that in two cases of coplanar spin configurations, there are spin-only operations that strictly hold even with considerable Dzyaloshinskii-Moriya interaction (DMI), and the symmetry of their spin models could be described by the spin-coplanar SSG. In addition, we also find that for spin-collinear cases, regardless the strength of DMI, the magnon systems within the framework of linear spin wave theory (LSWT) also preserve the decoupled spin and spatial rotations, but the symmetry does not belong to the conventional definitions of collinear spin groups. We discuss the potential realization of these novel symmetries in rod, layer, and three-dimensional space groups. Our work extends the applicability of SSGs to magnetic materials with heavy elements, and reveals that the coexistence of DMI and SSG symmetries provides new opportunity for exploring novel magnon transport phenomena, and potential material realization had also been discussed.

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• Electronic structure
• Spin-orbit coupling
• Altermagnets
• Symmetries in condensed matter