  We present a systematic classification of emergent particles in all 528
magnetic layer groups and 394 magnetic rod groups, which describe
two-dimensional and one-dimensional crystals respectively. Our approach is via
constructing a correspondence between a given magnetic layer/rod group and one
of the magnetic space group, such that all irreducible representations of the
layer/rod group can be derived from those of the corresponding space group.
Based on these group representations, we explicitly construct the effective
models for possible band degeneracies and identify all emergent particles,
including both spinless and spinful cases. We find that there are six kinds of
particles protected by magnetic layer groups and three kinds by magnetic rod
groups. Our work provides a useful reference for the search and design of
emergent particles in lower dimensional crystals.
