磁斯格明子是一种具有准粒子特性的磁涡旋结构，有望成为新型自旋电子学器件的信息载体。其中，基于斯格明子的纳米振荡器因其在微波通信和神经形态计算中的应用潜力而备受关注。此前的研究主要集中于单个斯格明子振荡器，其输出功率和执行的功能有限，难以满足实际应用的需要。

Fig. 1 Nonlinear dynamics in coupled SFiM-skyrmion-based STNOs.

一种可能的解决方案是构建由耦合振荡器组成的网络，通过振荡器之间的非线性效应实现信号放大。最近研究发现，亚铁磁斯格明子振荡器具有可扩展优势，为振荡器之间的非线性物理研究提供了条件。然而，相互耦合的亚铁磁斯格明子振荡器的具体动力学行为及其可调控性尚不清楚。

Fig. 2 Frequency spectra for different oscillator spacings.

来自北京师范大学物理学系高等量子研究中心的沈卡教授团队，利用微磁模拟和有效动力学方程求解，研究了相互作用亚铁磁斯格明子振荡器的动力学行为，证明了不同振荡器中斯格明子运动的同步、频率梳等非线性效应。

Fig. 3 Nonmonotonic variation of oscillation frequency with the oscillator spacing.

他们的研究表明：当振荡器之间耦合较弱时，振荡器彼此独立；随着耦合增强，系统的频谱出现等间距的峰，实现频率梳特征；随着耦合进一步增强至某一临界值以上，不同振荡器中的斯格明子以相同的频率振荡，进入同步态。

Fig. 4 Phase difference from effective potentials.

作者发现，从频率梳到同步态的转变与斯格明子间的有效势能在不同耦合强度下的演化有关。该研究不仅证明了亚铁磁斯格明子振荡器在非线性物理研究中的应用，还揭示了其非线性动力学背后的物理。该文近期发表于npj Computational Materials 10:48 (2024)。手机阅读原文，请点击本文底部左下角“阅读原文”，进入后亦可下载全文PDF文件。

Fig. 5 Tunability of critical distance.

Editorial Summary

Nonlinear dynamics of skyrmions: Synchronization and frequency comb

Magnetic skyrmions, swirling magnetic textures with particle-like properties, are promising candidates as information carriers for advanced spintronic devices. In particular, skyrmion-based nano-oscillators have received much attention due to their potential applications in microwave communication and neuromorphic computing. Previous proposals are mainly based on single skyrmion oscillators, which lead to relatively low output power and limited functions and therefore are not suitable for practical applications. One solution is then to use the nonlinear effects in a network of coupled oscillators. Recent theoretical work demonstrated that boundary-free spin torque nano-oscillators based on ferrimagnetic skyrmions could be a suitable platform for studying nonlinear physics of coupled oscillators. However, the specific dynamical behaviors of such interacting oscillators as well as their tunability remain to be explored.

Fig. 6 Current control in STNO array.

A team led by Prof. Ka Shen from the Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, China, investigated the dynamical behaviors of ferrimagnetic-skyrmion-based interacting oscillators through the micromagnetic simulation and the numerical solution of the effective kinetic equation. They demonstrated nonlinear effects of skyrmions in coupled oscillators, including synchronization and frequency comb. Their results showed that for a relatively weak coupling between the oscillators, the oscillators keep nearly individual. As the coupling strength increases, equally spaced discrete frequencies gradually appear in the Fourier spectrum of the dynamic quantities, corresponding to a frequency comb. Once the coupling strength exceeds a critical value, the skyrmions in different oscillators move at the same frequency, achieving a synchronization state. Moreover, the authors found that the transition from frequency comb to synchronization is related to the evolution of the effective potential energies of skyrmions under different coupling strengths. These findings not only demonstrate the potential application of ferrimagnetic-skyrmion-based oscillators in nonlinear physics research, but also reveal the underlying physics behind their nonlinear dynamics. Thisarticle was recently published in npj Computational Materials 10: 48 (2024).

原文Abstract及其翻译

Nonlinear dynamics of directly coupled skyrmions in ferrimagnetic spin torque nano-oscillators (亚铁磁振荡器中直接耦合的斯格明子非线性动力学)

Laichuan Shen,Lei Qiu & Ka Shen

AbstractNonlinear spin torque nano-oscillators have received substantial attentions due to their important applications in microwave communication and neuromorphic computing. Here we investigate the dynamical behaviors of directly coupled skyrmion oscillators in a synthetic ferrimagnet. We demonstrate through the micromagnetic simulation and Thiele’s equation that the skyrmion oscillators can present either synchronization or frequency comb, depending on the strength of interactions between the skyrmions. The underlying physics of the transition between the two scenarios are unveiled based on a quantitative analysis of the effective potentials, which also successfully interprets the dependence of the transition on parameters. By further demonstrating the tunability of the nonlinear dynamics by the driving current of the oscillators, our work reveals the great potentials of ferrimagnetic-skyrmion-based interacting oscillators for nonlinear applications.

摘要由于在微波通信和神经形态计算中的应用前景，非线性自旋矩纳米振荡器受到广泛关注。在本文中，我们研究了合成亚铁磁中直接耦合的斯格明子振荡器的动力学行为。通过微磁模拟和Thiele方程求解，我们证明了振荡器中的多个斯格明子在不同相互作用强度下可以实现同步或频率梳。基于有效势能的定量分析揭示了两种动力学之间转变的物理本质，并成功解释了模拟中观察到的参数依赖。进一步，我们证明了驱动电流对两种非线性动力学的调控。这些结果表明相互耦合的亚铁磁斯格明子振荡器在非线性应用中的巨大潜力。