Stray Field Dependence of Threshold Current in a Spin-Torque Oscillator With a Perpendicular Spin Polarizer

We theoretically investigate the effect of stray field on the current-induced magnetization dynamics in a nanopillar with a perpendicular spin polarizer. The threshold current to excite out-of-plane (OP) magnetization procession is analytically calculated based on a simple Newton-like dynamic equation. The numerical calculations of this analytical expression are confirmed by macrospin simulations, revealing that the critical current linearly depends on the stray field. The stray field versus current phase diagram of magnetization oscillation states in such a device is presented, showing three regions of magnetization dynamics including parallel, antiparallel, and OP precession states. The physical insight of the phase transitions between the three states can be explained by calculating the energy profiles as well as the phase portraits of the free layer.