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In this study, the structural and magnetic properties of group-IV-dopedmonolayer GaN were systematically investigated by first-principlescalculations. Among all the group-IV dopants, only Ge and Sn atoms prefer tosubstitute the Ga atom of monolayer GaN and form a buckling structure with amagnetic moment of 1 $\mu_B$ per dopant. The N-rich growth conditions are moredesirable for such a substitution process than the Ga-rich grow conditions.With a large diffusion barrier vertical to the monolayer GaN, both Ge and Snatoms tend to stay on the same side of monolayer GaN with an antiferromagneticcoupling between them. When intrinsic vacancies exist in monolayer GaN, themagnetic moments of group-IV dopants vanish due to the charge transferring fromthe dopants to Ga or N vacancies. The precondition creation of Ga vacancies, aplentiful supply of Ge or Sn dopants, and the N-rich conditions can be adoptedto maintain the magnetic properties of group-IV-doped monolayer GaN. Thesetheoretical results help to promote the applications of 2D GaN-based materialsin spintronics.

The unexpected magnetism in 2D group-IV-doped GaN for spintronic applications