Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling

Understand

Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry.

• More symmetry invariants exist in discrete point groups than the full rotation group $\mathrm{O(3)}$, leading to new quasiparticles restricted to lattices that do not have any counterpart in a vacuum.
• We focus on the fermionic quasiparticle excitations under ``spin-space group'' symmetries, applicable to materials where long-range magnetic order and itinerant electrons coexist.
• We provide a list of 218 classes of new quasiparticles that can only be realized in the spin-space groups.