论文标题
强烈非线性注入锁定自旋扭矩振荡器的分叉分析
Bifurcation analysis of strongly nonlinear injection locked spin torque oscillators
论文作者
论文摘要
我们研究了注射锁定的平面内均匀旋转扭矩振荡器的动力学，以在大型驾驶振幅下进行多种强制构型。为了进行分析，旋转波振幅方程用于将动力学减少为一般振荡器方程，在该方程中，强迫是复杂的有价值函数$ f（p，ψ）\proptoε_1（p）cos（ψ）+iε_2（p）sin（ψ）$。假设振荡器是强烈的非等方形和/或由电源强迫迫使$（|νε_1/ε_2| \ gg 1）$，我们表明参数$ε_{1,2}（p）$控制Arnold Tongue图的主要Bifurciation the Arnold Tongue图的主要Bifurciation the Arnold tongue图：（i）lock insymmmets aSymmmetmemmmetry insymmetmetry insymmetmetry insimmmetmemmetry a （p）/dp $，（ii）取回的bogdanov分叉在功率阈值中发生，具体取决于$ε_{1,2}}（p）$和（iii）频率滞后范围与零匹配频率的共振频率通过谐振频率有关。然后，将模型与Macrospin模拟进行比较，以驱动磁场的驱动幅度至$ 10^0-10^3 A/m $，而电流密度的$ 10^{10} -10} -10^{12} a/m^2 $。正如模型所预测的那样，强迫构型（驾驶信号的性质，应用方向的性质，谐波顺序）会对振荡器动态产生重大影响。但是，观察到一些差异。特别是，如果粘滞边界的幅度级阶相同，则可能会误解频率和功率锁定范围边界的预测。此外，如果分叉为鞍节点或bogdanov，则可以根据两种不同类型的误解。这些效果是非局部自动振荡器中动力学复杂性的进一步表现。
We investigate the dynamics of an injection locked in-plane uniform spin torque oscillator for several forcing configurations at large driving amplitudes. For the analysis, the spin wave amplitude equation is used to reduce the dynamics to a general oscillator equation in which the forcing is a complex valued function $F(p,ψ)\proptoε_1 (p)cos(ψ)+iε_2 (p)sin(ψ)$. Assuming that the oscillator is strongly nonisochronous and/or forced by a power forcing $(|νε_1/ε_2 |\gg 1)$, we show that the parameters $ε_{1,2} (p)$ govern the main bifurcation features of the Arnold tongue diagram : (i) the locking range asymmetry is mainly controlled by $dε_1 (p)/dp$, (ii) the Taken-Bogdanov bifurcation occurs for a power threshold depending on $ε_{1,2} (p)$ and (iii) the frequency hysteretic range is related to the transient regime through the resonant frequency at zero mismatch frequency. Then, the model is compared with the macrospin simulation for driving amplitudes as large as $10^0-10^3 A/m$ for the magnetic field and $10^{10}-10^{12} A/m^2$ for the current density. As predicted by the model, the forcing configuration (nature of the driving signal, applied direction, the harmonic orders) affects substantially the oscillator dynamic. However, some discrepancies are observed. In particular, the prediction of the frequency and power locking range boundaries may be misestimated if the hysteretic boundaries are of same magnitude order. Moreover, the misestimation can be of two different types according if the bifurcation is Saddle node or Taken Bogdanov. These effects are a further manifestation of the complexity of the dynamics in nonisochronous auto-oscillators.
