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We combine low energy muon spin rotation (LE-$\mu$SR) and soft-X-rayangle-resolved photoemission spectroscopy (SX-ARPES) to study the magnetic andelectronic properties of magnetically doped topological insulators,(Bi,Sb)$_2$Te$_3$. We find that one achieves a full magnetic volume fraction insamples of (V/Cr)$_x$(Bi,Sb)$_{2-x}$Te$_3$ at doping levels x $\gtrsim$ 0.16.The observed magnetic transition is not sharp in temperature indicating agradual magnetic ordering. We find that the evolution of magnetic ordering isconsistent with formation of ferromagnetic islands which increase in numberand/or volume with decreasing temperature. Resonant ARPES at the V $L_3$ edgereveals a nondispersing impurity band close to the Fermi level as well as Vweight integrated into the host band structure. Calculations within thecoherent potential approximation of the V contribution to the spectral functionconfirm that this impurity band is caused by V in substitutional sites. Theimplications of our results on the observation of the quantum anomalous Halleffect at mK temperatures are discussed.

Spectroscopic perspective on the interplay between electronic and magnetic properties of magnetically doped topological insulators