A generic dual d-band model for interlayer ferromagnetic coupling in a transition-metal doped MnBi 2 Te 4 family of materials.

Realization of ferromagnetic (FM) interlayer coupling in magnetic topological insulators (TIs) of the MnBi 2 Te 4 family of materials (MBTs) may pave the way for realizing the high-temperature quantum anomalous Hall effect (high- T QAHE). Here we propose a generic dual d-band (DDB) model to elucidate the energy difference (Δ E = E AFM - E FM ) between the AFM and FM coupling in transition-metal (TM)-doped MBTs, where the valence of TMs splits into d-t 2g and d-e g sub-bands. Remarkably, the DDB shows that Δ E is universally determined by the relative position of the dopant (X) and Mn d-e g / t 2g bands, . If Δ E d > 0, then Δ E > 0 and the desired FM coupling is favored. This surprisingly simple rule is confirmed by first-principles calculations of hole-type 3d and 4d TM dopants. Significantly, by applying the DDB model, we predict the high- T QAHE in the V-doped Mn 2 Bi 2 Te 5 , where the Curie temperature is enhanced by doubling of the MnTe layer, while the topological order mitigated by doping can be restored by strain.