Spin-torque nano-oscillators (STNOs) have become one of the emerging and novel microwave devices with the high performance and tunability of GHz range frequency. The nanopillar structure with an out-of-plane (OP) spin polarizer and an in-plane (IP) magnetized free layer (FL) has been considered as a good candidate for the STNOs. Using the local rotational coordinate transformation, a nonstationary process describing magnetization dynamics in the laboratory frame is therefore transformed into a stationary one in the rotating frame. In this way, the state phase diagram of this type of STNOs is well established as a function of an applied current and external field, which is also evidenced by the macrospin simulations. Also, we show that the frequency tunability of the STNOs through electrical current can be well elevated by applying a static magnetic field anti-parallel to the spin-polarizer vector.

中文翻译：

---

自旋扭矩纳米振荡器在旋转框架中的稳定性分析

自旋扭矩纳米振荡器（STNO）已成为新兴的新型微波器件之一，具有GHz范围频率的高性能和可调性。具有面外（OP）自旋偏振器和面内（IP）磁化自由层（FL）的纳米柱结构被认为是STNO的良好候选者。使用局部旋转坐标变换，在实验室框架中描述磁化动力学的非平稳过程因此被转换为旋转框架中的静止过程。通过这种方式，这种类型的 STNO 的状态相图可以很好地建立为施加电流和外部场的函数，宏自旋模拟也证明了这一点。还，