Bias dependences of in-plane and out-of-plane spin-transfer torques in symmetric MgO-based magnetic tunnel junctions

We investigate the bias dependences of in-plane and out-of-plane spin-transfer torque by employing magnetic noise measurement in symmetric MgO-based magnetic tunneling junction devices. The measured power spectra densities of magnetic noise are successfully analyzed by the fluctuation-dissipation theorem with an imaginary part of transverse susceptibility including spin-transfer torque contributions. We find that the in-plane component has a linear dependence of the bias voltage, while the out-of-plane component has a quadratic dependence. These results are well consistent with the noise amplitude analysis, neglecting the Joule heating effect with small bias voltage.