  The magnetic coupling mechanisms underlying ferromagnetism and
magnetotransport phenomena in magnetically doped topological insulators have
been a central issue to gain controlled access to the magneto-topological
phenomena such as quantum anomalous Hall effect and topological axion
insulating state. Here, we focus on the role of bulk carriers in magnetism of
the family of magnetic topological insulators, in which the host material is
either Bi$_{2}$Te$_{3}$ or BiSbTe$_{3}$, containing Mn self-organized in
MnBi$_{2}$Te$_{4}$ septuple layers. We tune the Fermi level using the electron
irradiation technique and study how magnetic properties vary through the change
in carrier density, the role of the irradiation defects is also discussed.
Ferromagnetic resonance spectroscopy and magnetotransport measurements show no
effect of the Fermi level position on the magnetic anisotropy field and the
Curie temperature, respectively, excluding bulk magnetism based on a
carrier-mediated process. Furthermore, the magnetotransport measurements show
that the anomalous Hall effect is dominated by the intrinsic and
dissipationless Berry-phase driven mechanism, with the Hall resistivity
enhanced near the bottom/top of the conduction/valence band, due to the Berry
curvature which is concentrated near the avoided band crossings. These results
demonstrate that the anomalous Hall effect can be effectively managed,
maximized, or turned off, by adjusting the Fermi level.
