Spin-transfer effects in MgO-based tunnel junctions with an out-of-plane free layer and in-plane polarizer: static states and steady-state precession

Spin-torque nano-oscillators (STNOs) are novel devices which may be exploited for wireless communication applications. In particular, it has recently been demonstrated that STNOs utilizing an in-plane (IP) magnetized polarizer and out-of-plane (OOP) magnetized free layer allow for the full parallel (P)-to-antiparallel (AP) resistance variation to be exploited in the limit of 90° precession angle, thereby maximizing the output power. However, for this specific geometry, steady-state precession can only be sustained if the spin-transfer torque exhibits an asymmetric dependence on the angle between the free and the polarizing layer, such as in the case of fully metallic devices. Nevertheless, it has recently been reported that dynamics have been experimentally observed in similarly designed MgO-based MTJs under constant applied electrical current, in spite of the fact that such devices do not exhibit any asymmetry in the spin-torque angular dependence. These results have so far been interpreted based on the formalism for metallic devices, including the spin-torque angular dependence. Here, we explore potential mechanisms for sustaining steady-state precession in MgO-based MTJs with an IP polarizer and an OOP free layer. To this end, we analytically and numerically solve the Landau-Lifshitz-Gilbert-Slonczewski equation for a nano-pillar MTJ with circular cross-section, under a constant perpendicular applied current and field. Since for realistic current range, the field-like torque is negligible compared to effective field acting along z axis, we take into account only the in-plane spin-torque term. To sustain steady-state precession, the energy supplied by the in-plane spin-torque term and energy dissipated through damping must compensate over a full precession period. In an MgO-MTJ, the magnitude of the STT is determined not by the current, but by the corresponding voltage across the barrier. As the magnetization of the free layer precesses around the z axis, the angle between the magnetic moments of the two layers changes and through the magnetoresistance effect the voltage changes if the Experiment is conducted at constant applied current. This cosine-like angular dependence of the MTJ resistance effectively introduces a spin-torque angle dependence asymmetry. In addition, even for a given angle, the resistance exhibits a specific bias dependence, with the resistance of the AP state decreasing approximately linearly with the bias, while remaining mostly constant in the P configuration. In this work, we demonstrate that the spin-torque angular asymmetry exhibited in such systems is sufficient to sustain STT-driven dynamics.