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Based on the first-principles electronic structure calculations, weinvestigate the magnetic and electronic properties of transition-metal-dopedPb$_{10}$(PO$_4$)$_6$O with the Pb atom substituted by various transitionmetals. The $3d$ orbitals of the doped transition metals are distributed nearthe Fermi energy and exhibit strong spin-polarization, resulting in the localmagnetic moment. With the doped metal varying from V, Cr, Mn, Fe, Co, Ni, Cu,to Zn, the moment changes gradually from 3.0, 4.0, 5.0, 4.0, 3.0, 2.0, 1.0, to0 $\mu_B$, while the electronic structure is modulated progressively due to thecontinuous change of total charge. Moreover, the flat bands near the Fermienergy are also found in the V, Cr, and Fe-doped lead-apatite, similar to theCu-doped system. Our work not only provides the critical comparativeinformation for investigating the Cu-doped lead-apatite, but also suggest acategory of diluted magnetic semiconductor.

Modulating magnetic and electronic properties of lead-apatite Pb$_{10}$(PO$_4$)$_6$O via different transition metal doping