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Applying electric or magnetic fields is widely used to not only create andmanipulate topological states but also facilitate their observations inexperiments. In this work, we show by first-principles calculations andtopological analysis that the time-reversal (TR) symmetry-broken quantum spinHall (QSH) state emerges in a two-dimensional ferromagnetic MnBi$_4$Te$_7$monolayer. This TR-symmetry broken QSH phase possesses a highly tunablenontrivial band gap under an external electric field (or tuning interlayerdistance). Furthermore, based on the Wannier-function-based tight-bindingapproach, we reveal that a topological phase transition from the TR-symmetrybroken QSH phase to the quantum anomalous Hall (QAH) phase occurs with theincrease of magnetic fields. Besides, we also find that a reverse electricfields can facilitate the realization of QAH phase. Our work not only uncoversthe ferromagnetic topological properties the MnBi$_4$Te$_7$ monolayer tuned byelectric and magnetic fields, but also can stimulate further applications tospintronics and topological devices.

Electric and magnetic fields tuned spin-polarized topological phases in two-dimensional ferromagnetic MnBi$_4$Te$_7$