Magnetic quantum phase transition in Cr-doped Bi₂ (Se_x Te_1-x)₃ driven by the Stark effect

The recent experimental observation of the quantum anomalous Hall effect has cast significant attention on magnetic topological insulators. In these magnetic counterparts of conventional topological insulators such as Bi 2 Te 3, a long-range ferromagnetic state can be established by chemical doping with transition-metal elements. However, a much richer electronic phase diagram can emerge and, in the specific case of Cr-doped Bi₂ (Se_x Te_1-x)₃, a magnetic quantum phase transition tuned by the actual chemical composition has been reported. 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 semiconductors. Here, we investigate the magneto-transport properties of Cr-doped Bi₂ (Se_x Te_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.