  Magnetic carbon nanostructures are currently under scrutiny for a wide
spectrum of applications. Here, we theoretically investigate armchair graphene
nanoribbons patterned with asymmetric edge extensions consisting of laterally
fused naphtho groups, as recently fabricated via on-surface synthesis. We show
that an individual edge extension acts as a spin-$\frac{1}{2}$ center and
develops a sizable spin-polarization of the conductance around the band edges.
The Heisenberg exchange coupling between a pair of edge extensions is dictated
by the position of the second naphtho group in the carbon backbone, thus
enabling ferromagnetic, antiferromagnetic, or non-magnetic states. The periodic
arrangement of edge extensions yields full spin-polarization at the band
extrema, and the accompanying ferromagnetic ground state can be driven into
non-magnetic or antiferromagnetic phases through external stimuli. Overall, our
work reveals precise tunability of the ${\pi}$-magnetism in graphene
nanoribbons induced by naphtho groups, thereby establishing these
one-dimensional architectures as suitable platforms for logic spintronics.
