Abstract
The anomalous Hall effect (AHE) around the flux state in square double-exchange model is investigated. By introducing the lattice distortion and local chirality, the system can break the parity symmetry and time-reversal symmetry spontaneously, and thus generate a topological nontriviality in the band structure associated with the AHE. Moreover, a possible realization of this AHE in multiferroic ${\text{TbMnO}}_{3}$ is discussed.
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