  The alkali-adsorbed graphene nanoribbons exhibit the feature-rich electronic
and magnetic properties. From the first-principles calculations, there are only
few adatom-dominated conduction bands, and the other conduction and valence
bands are caused by carbon atoms. A lot of free electrons are revealed in the
occupied alkali- and carbon-dependent conduction bands. Energy bands are
sensitive to the concentration, distribution and kind of adatom and the edge
structure, while the total linear free carrier density only relies on the first
one. These mainly arise from a single $s-2p_z$ orbital hybridization in the
adatom-carbon bond. Specifically, zigzag systems can present the
anti-ferromagnetic ordering across two edges, ferromagnetic ordering along one
edge and non-magnetism, being reflected in the edge-localized energy bands with
or without spin splitting. The diverse energy dispersions contribute many
special peaks in density of states. The critical chemical bonding and the
distinct spin configuration could be verified from the experimental
measurements.
