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The layered magnetic topological insulator MnBi$_2$Te$_4$ is a promising platform to realize the quantum anomalous Hall effect because its layers possess intrinsic ferromagnetism. However, it is not well understood why the high-spin $d^5$ magnetic ions Mn$^{2+}$ forming the Mn-Te-Mn spin exchange paths prefer ferromagnetic (FM) coupling, contrary to the prediction of the Goodenough-Kanamori rule that a TM-L-TM spin exchange, where TM and L are a transition-metal magnetic cation and a main group ligand, respectively, is antiferromagnetic (AFM) even when the bond angle of the exchange path is 90$^{\circ}$... (read more)
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