  We theoretically study magnetic ground states of doped zigzag graphene
nanoribbons and the emergence of topological domain walls. Using the
Hartree-Fock mean-field approach and an effective continuum model, we
demonstrated that the carrier doping stabilizes a magnetic structure with
alternating antiferromagnetic domains, where the doped carriers are
accommodated in topological bound states localized at the domain wall. The
energy spectrum exhibits a Hofstadter-like fractal spectral evolution as a
function of the carrier density, where minigaps are characterized by the Chern
number associated with the adiabatic charge pump in moving domain walls. A
systematic analysis for nanoribbons with different widths revealed that the
ferromagnetic domain-wall phase emerges in relatively wide ribbons, while the
colinear domain-wall phase arises in narrower ribbons.
