  Graphene nanomeshes (GNMs), formed by creating a superlattice of pores in
graphene, possess rich physical and chemical properties. Many of these
properties are determined by the pore geometry. In this work, we use first
principles calculations to study the magnetic and electronic properties of
metal-doped nitrogen-passivated GNMs. We find that the magnetic behaviour is
dependent on the pore shape (trigonal vs. hexagonal) as dictated by the number
of covalent bonds formed between the 3$d$ metal and the passivating N atoms. We
also find that Cr and V doped trigonal-pore GNMs, and Ti doped GNMs are the
most favourable for spintronic applications. The calculated magnetic properties
of Fe-doped GNMs compare well with recent experimental observations. The
studied systems are useful as spin filters and chemical sensors.
