  The surfaces of intrinsic magnetic topological insulators (TIs) host magnetic
moments exchange-coupled to Dirac electrons. We study the magnetic phases
arising from tuning the electron density using variational and exact
diagonalization approaches. In the dilute limit, we find that magnetic
skrymions are formed which bind to electrons leading to a skyrmion crystal /
Wigner crystal phase while at higher densities spin spirals accompanied by
chiral 1d channels of electrons are formed. The binding of electrons to
textures raises the possibility of manipulating textures with electrostatic
gating. We determine the phase diagram capturing the competition of intrinsic
spin-spin interactions and carrier density and comment on the possible
application to experiments in magnetic TIs and spintronic devices such as
skyrmion-based memory.
