Complex dynamics of nano-oscillators with dual vortex free layers mutually coupled via spin-torques

Abstract

Spin-torque vortex oscillators (STVOs) have been shown to exhibit rich and complex dynamical regimes, which are strongly dependent on the polarizer's configuration. Here, we give an overview of the dynamics in an STVO comprising two vortex free layers, where each layer serves as a dynamic polarizer for the other, increasing the number of degrees of freedom and therefore, the complexity of the system. The dynamics are studied through extensive micromagnetic simulations, performed using our own implementation of the coupled equations of motion, implemented in the open-source micromagnetics code Mumax3. We explore the roles of relative vortex configurations and layer asymmetry on the current-driven dynamics, and find several complex regimes, including self-modulated gyration, the emergence of C-state dynamics, as well as chaotic transitions between regular gyration and this C-state.

Figures (7)

• Figure 1: (a) Schematic of the two free layers for $p_{0}=p_{1}=$1 and $c_{0}=c_{1}=$-1. $d_0$, $d_1$ and $r_\mathrm{d}$ are the layers dimensions. $I$ is the current passing through the oscillator. Layer 0 (1) favors an antiparallel (parallel) configuration in respect to layer 1 (0) due to STT. (b), (c) and (d) show the three studied relative vortex configurations. (b) opposite polarities configuration with $p_{0}=1$, $p_{1}=-1$ and $c_{0}=c_{1}=$-1. (c) identical vortices configuration with $p_{0}=p_{1}=-1$ and $c_{0}=c_{1}=$-1. (d) opposite chiralities configuration with $p_{0}=p_{1}=-1$ and $c_{0}=1$, and $c_{1}=-1$.
• Figure 2: (a) Power spectral density map of the gyration frequency of the vortex in layer 0 as a function of the applied dc current $I$ in the case of opposite polarities. (b) Average gyration orbit radii as a function of the current applied to the system for layers 0 (dark) and 1 (light) are represented in solid markers. The standard deviation is also given in the form of a semi-transparent envelope for both layers. (c)G-state schematic, where the vortex core gyrates inside the disk. (d) C-state schematic, where the virtual vortex core gyrates outside the disk.
• Figure 3: (a) Power spectral density map of the gyration frequency of the vortex in layer 0 as a function of the applied dc current $I$ in the case of identical vortices. (b) Average gyration orbit radii as a function of the current applied to the system for layers 0 (dark) and 1 (light) are represented in solid markers. The standard deviation is also given in the form of a semi-transparent envelope for both layers.
• Figure 4: Topological charge, $Q_0$, and magnetization component along $x$ axis, $m_\mathrm{x,0}$, in layer 0 (bottom layer) as a function of time for fully identical vortices under applied currents of (a) $11$ mA, (b) $15$ mA, and (c) $19$ mA. (d) Profiles of the topological charge density $q_0 (x,y)$ (left) and $m_\mathrm{z,0}$ (right). At $t=24.55$ ns, vortex/antivortex pairs are generated in the disk, in addition to the original vortex core. At $t = 24.70$ ns the original core interacts with vortex antivortex pair. At 24.95 ns the original core and the antivortex annihilate, leaving a new core of opposite polarity. (e) Normalized standard deviations for $Q_0$ and $r_{gyr,0}$, computed over the first $125$ ns of the simulation, as a function of current.
• Figure 5: (a) Power spectral density map of the gyration frequency of the vortex in layer 0 as a function of the applied dc current $I$ in the case of opposite chiralities. (b) Average gyration orbit radii as a function of the current applied to the system for layers 0 (dark) and 1 (light) are represented in solid markers. The standard deviation is also given in the form of a semi-transparent envelope for both layers.