The recent experimental observation of the quantum anomalous Hall effect^1,2,3,4,5 has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi₂Te₃, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements^6,7,8. However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi₂(Se_xTe_1−x)₃, a magnetic quantum phase transition tuned by the actual chemical composition has been reported⁸. From an application-oriented perspective, the relevance of these results hinges on the possibility to manipulate magnetism and electronic band topology by external perturbations such as an electric field generated by gate electrodes—similar to what has been achieved in conventional diluted magnetic semiconductors⁹. Here, we investigate the magneto-transport properties of Cr-doped Bi₂(Se_xTe_1−x)₃ with different compositions under the effect of a gate voltage. The electric field has a negligible effect on magnetic order for all investigated compositions, with the remarkable exception of the sample close to the topological quantum critical point, where the gate voltage reversibly drives a ferromagnetic-to-paramagnetic phase transition. Theoretical calculations show that a perpendicular electric field causes a shift in the electronic energy levels due to the Stark effect, which induces a topological quantum phase transition and, in turn, a magnetic phase transition.

最近对量子异常霍尔效应^1,2,3,4,5的实验观察已引起磁性拓扑绝缘体的极大关注。在常规拓扑绝缘体（例如Bi ₂ Te ₃）的这些磁性对等体中，可以通过对过渡金属元素^6,7,8进行化学掺杂来建立长距离铁磁状态。但是，可以出现更丰富的电子相图，并且在特定的Cr掺杂Bi ₂（Se _x Te _{1- x}）_3情况下，已经报道了通过实际化学成分调整的磁量子相变^8。。从面向应用的角度来看，这些结果的相关性取决于通过外部扰动（例如栅电极产生的电场）来操纵磁性和电子能带拓扑的可能性，这与传统的稀释磁半导体⁹相似。在这里，我们研究了Cr掺杂的Bi ₂（Se _x Te _{1- x}）₃的磁输运性质。在栅极电压的作用下具有不同的成分。电场对所有研究的成分的磁序的影响都可以忽略不计，除了接近拓扑量子临界点的样品（栅极电压可逆地驱动铁磁至顺磁的相变）外，电场的影响显着。理论计算表明，由于斯塔克效应，垂直电场导致电子能级发生位移，从而引起拓扑量子相变，进而引起磁相变。