Fig. 1. (Color online) (a) Schematic illustration of the four-terminal non-local measurement scheme (not drawn to scale). (b) AFM image of the GaN channel between injection and detection electrodes. (c) Schematic diagram of Schottky barrier tunneling at various doping densities. A lower doping density of GaN channel (red conduction band case) has a thicker barrier which causes spin polarized electrons being trapped by interface states.

Fig. 2. (Color online) (a) The I–V characteristics of the injection circuit of the sample at various temperatures. The inset shows the differential conductance as a function of the bias voltage. (b) The zero-bias conductance as a function of temperature. The inset shows the ln(I/V²)–1/V curves for various temperatures.

Fig. 3. (Color online) (a) Magnetoresistance as a function of in-plane magnetic field under a constant injection current of I_inject = 40 μA at 1.7 K. (b) The injection current-dependent non-local voltage at 1.7 K. The non-local voltage peaks are always restricted in the range of ±(250–600)Oe as surrounded by four corresponding dotted lines. (c) The magnetoresistance difference extracted by non-local measurements at various injection currents. (d) The temperature dependent ΔR under 40 μA injection current.