  Grain boundaries (GBs) are structural imperfections that typically degrade
the performance of materials. Here we show that dislocations and GBs in
two-dimensional (2D) metal dichalcogenides MX2 (M = Mo, W; X = S, Se) can
actually improve the material by giving it a qualitatively new physical
property: magnetism. The dislocations studied all have a substantial magnetic
moment of ~1 Bohr magneton. In contrast, dislocations in other well-studied 2D
materials are typically non-magnetic. GBs composed of pentagon-heptagon pairs
interact ferromagnetically and transition from semiconductor to half-metal or
metal as a function of tilt angle and/or doping level. When the tilt angle
exceeds 47{\deg} the structural energetics favor square-octagon pairs and the
GB becomes an antiferromagnetic semiconductor. These exceptional magnetic
properties arise from an interplay of dislocation-induced localized states,
doping, and locally unbalanced stoichiometry. Purposeful engineering of
topological GBs may be able to convert MX2 into a promising 2D magnetic
semiconductor.
