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The research on emergent particles in condensed matters has been attractingtremendous interest, and recently it is extended to magnetic systems. Here, westudy the emergent particles stabilized by the symmetries of type-IV magneticspace groups (MSGs). Type-IV MSGs feature a special time reversal symmetry$\{\mathcal{T}|\boldsymbol{t}_0\}$, namely, the time reversal operationfollowed by a half lattice translation, which significantly alters the symmetryconditions for stabilizing the band degeneracies. In this work, based onsymmetry analysis and modeling, we present a complete classification ofemergent particles in type-IV MSGs by studying all possible (spinless andspinful, essential and accidental) particles in each of the 517 type-IV MSGs.Particularly, the detailed correspondence between the emergent particles andthe type-IV MSGs that can host them are given in easily accessed interactivetables, where the basic information of the emergent particles, including thesymmetry conditions, the effective Hamiltonian, the band dispersion and thetopological characters can be found. According to the established encyclopedia,we find that several emergent particles that are previously believed to existonly in spinless systems will occur in spinful systems here, and vice versa,due to the $\{{\cal T}|\boldsymbol{t}_{0}\}$ symmetry. Our work not onlydeepens the understanding of the symmetry conditions for realizing emergentparticles but also provides specific guidance for searching and designingmaterials with target particles.

Encyclopedia of emergent particles in type-IV magnetic space groups