Interplay between different magnetisms in Cr-doped topological insulators

Breaking the time-reversal-symmetry of topological insulators through magnetic doping has led to exotic physical discoveries. Here, we report the gate-dependent magneto-transport measurements on the Cr-doped (Bi _xSb_1-x)₂Te₃ thin films. With effective top-gate modulations, we demonstrate the presence of both the hole-mediated RKKY coupling and carrier-independent van Vleck magnetism in the magnetic TI systems. Most importantly, by varying the Cr doping concentrations from 2% to 20%, we unveil the interplay between the two magnetic orders and establish the valid approach to either enhance or suppress each individual contribution. The electric-field-controlled ferromagnetisms identified in the Cr-doped TI materials will serve as the fundamental step to further explore the TRS-breaking TI systems, and it may also help to expand the functionality of TI-based device for spintronics applications.