Arun R, Gopal R, Chandrasekar V K, Lakshmanan M
Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620024, India.
Department of Physics, Centre for Nonlinear Science & Engineering, School of Electrical & Electronics Engineering, SASTRA Deemed University, Thanjavur 613 401, India.
Chaos. 2024 Jan 1;34(1). doi: 10.1063/5.0173943.
We investigate the influence of field-like torque and the direction of the external magnetic field on a one-dimensional array of serially connected spin-torque nano oscillators (STNOs), having free layers with perpendicular anisotropy, to achieve complete synchronization between them by analyzing the associated Landau-Lifshitz-Gilbert-Slonczewski equation. The obtained results for synchronization are discussed for the cases of 2, 10, and 100 oscillators separately. The roles of the field-like torque and the direction of the external field on the synchronization of the STNOs are explored through the Kuramoto order parameter. While the field-like torque alone is sufficient to bring out global synchronization in the system made up of a small number of STNOs, the direction of the external field is also needed to be slightly tuned to synchronize the one-dimensional array of a large number of STNOs. The formation of complete synchronization through the construction of clusters within the system is identified for the 100 oscillators. The large amplitude synchronized oscillations are obtained for small to large numbers of oscillators. Moreover, the tunability in frequency for a wide range of currents is shown for the synchronized oscillations up to 100 spin-torque oscillators. In addition to achieving synchronization, the field-like torque increases the frequency of the synchronized oscillations. The transverse Lyapunov exponents are deduced to confirm the stable synchronization in coupled STNOs due to the field-like torque and to validate the results obtained in the numerical simulations. The output power of the array is estimated to be enhanced substantially due to complete synchronization by the combined effect of field-like torque and tunability of the field-angle.
我们研究类场转矩和外磁场方向对具有垂直各向异性自由层的串联自旋扭矩纳米振荡器（STNO）一维阵列的影响，通过分析相关的朗道-里夫希茨-吉尔伯特-斯隆切夫斯基方程来实现它们之间的完全同步。分别针对2个、10个和100个振荡器的情况讨论了同步的所得结果。通过Kuramoto序参量探究类场转矩和外场方向对STNO同步的作用。虽然仅类场转矩就足以在由少量STNO组成的系统中实现全局同步，但还需要对外场方向进行微调，以使大量STNO的一维阵列同步。对于100个振荡器，确定了通过在系统内形成簇来实现完全同步。对于少量到大量的振荡器都获得了大幅同步振荡。此外，对于多达100个自旋扭矩振荡器的同步振荡，展示了在很宽的电流范围内频率的可调性。除了实现同步外，类场转矩还增加了同步振荡的频率。推导横向李雅普诺夫指数以确认由于类场转矩在耦合STNO中实现的稳定同步，并验证数值模拟中获得的结果。由于类场转矩的综合作用和场角的可调性导致的完全同步，估计阵列的输出功率会大幅提高。
