Unidirectional Magneto-Resistance in Modulation-doped Magnetic Topological Insulators.

Nonlinear unidirectional spin Hall magneto resistance (USMR) has been reported in heavy metal/ferromagnet bilayers, which could be employed as an effective method in detecting the magnetization orientation in spintronic devices with two-terminal geometry. Recently, another unidirectional magnetoresistance (UMR) was reported in magnetic topological insulator (TI)-based hetero-structures at cryogenic temperature, whose amplitude is orders of magnitude larger than the USMR measured in heavy metal-based magnetic heterostructures at room temperature. Here, we report the UMR effect in the modulation-doped magnetic TI structures. This UMR arises due to the interplay between the magnetic dopant's magnetization and the current-induced surface spin polarization, when they are parallel or antiparallel to each other in the TI material. By varying the dopant's position in the structure, we reveal that the UMR is mainly originating from the interaction between the magnetization and the surface spin-polarized carriers (not bulk carriers). Furthermore, from the magnetic field-, the angular rotation-, and the temperature-dependence, we highlight the correlation between the UMR effect and the magnetism in the structures. The large UMR versus current ratio in TI-based magnetic bilayers promises the easy readout in TI-based spintronic devices with two-terminal geometry.