1,2(STT) allows the electrical control of magnetic states in nanostructures [3][4][5] . The STT in magnetic tunnel junctions (MTJs) is of particular importance owing to its potential for device applications 6,7 . It has been demonstrated [8][9][10][11] that the MTJ has a sizable perpendicular STT (τ ⊥ , field-like torque), which substantially affects STT-driven magnetization dynamics. In contrast to symmetric MTJs where the bias dependence of τ ⊥ is quadratic [8][9][10]12,13 , it is theoretically predicted that the symmetry breaking of the system causes an extra linear bias dependence
11. Here, we report experimental results that are consistent with the predicted linear bias dependence in asymmetric MTJs. The linear contribution is quite significant and its sign changes from positive to negative as the asymmetry is modified. This result opens a way to design the bias dependence of the field-like term, which is useful for device applications by allowing, in particular, the suppression of the abnormal switching-back phenomena.The STT is composed of two vector components (Fig. 1a): the in-plane torque (τ ) and the perpendicular torque (τ ⊥ , also called 'field-like torque') normal to τ . Whereas τ ⊥ in fully metallic nanopillars is negligible and has been ignored in the analysis of experimental data 14 , τ ⊥ in MgO-based MTJs can be 10 ∼ 30% of τ (refs 8-10). Previous theoretical 12,13 and experimental 8-10 studies indicate that τ ⊥ is a symmetric function of the voltage V at low voltages;where the bias-independent contribution C 0 is also known as the interlayer exchange coupling 15,16 . A more recent theoretical study 11 indicates however that the symmetric bias dependence is expected only in symmetric MTJs and that extra antisymmetric components may appear ( (MTJ2) is 175%/117% (195%/123%) at 4.2 K/300 K (Fig. 1b). Owing to the asymmetry in the MTJs, the current-voltage characteristics are not symmetric even in the parallel magnetic configuration (P state) (Fig. 1c). Note that (d 2 I /dV 2 ) P at V = 0 has opposite sign for the MTJ1 and MTJ2, reflecting the different asymmetries in the two MTJs.To determine the bias dependence of τ ⊥ , we used the thermal activation model 17,18 ,where the upper (lower) signs apply to the antiparallel-to-parallel (parallel-to-antiparallel) switching, t ± is the relaxation time, f 0 is the attempt frequency (= 10 9 s −1 ), k B is the Boltzmann constant, T * is the junction temperature taking into account the bias-induced heating and V ± C is the critical voltage for magnetization switching at T * = 0 K. Here, the factor (1 ∓ V /|V ± C |) arises from the voltage dependence of the energy barrier due to the in-plane torque τ . The junction temperature T * is obtained from commonly used estimation methods (see the Methods section and Supplementary Note S1). Here, E ± B readswhere E 0 B is the intrinsic energy barrier, H ext is the external magnetic field applied along the easy axis, H sh is the shift field owing to the orange-peel coupling 19 as well as the interlayer exchange couplin...
