Current-control of chaos and effects of thermal fluctuations in magnetic tunnel junctions

Abstract

We theoretically investigate the chaotic behavior of spin-torque ferromagnetic resonance in magnetic tunnel junctions (MTJs) with perpendicular magnetic anisotropy under thermal fluctuations. By calculating the Lyapunov exponent based on the Landau-Lifshitz-Gilbert equation, we demonstrate that an MTJ characterized by a double-well potential, composed of uniaxial magnetic anisotropy and an external magnetic field, exhibits chaotic magnetization dynamics that can be controlled by means of the DC current bias. Furthermore, we find that thermal fluctuations help to induce these chaotic magnetization dynamics, which can be regarded as noise-induced chaos. This research provides a basis for brain-inspired computing using spintronic devices and advances the understanding of the interplay between thermal fluctuations and chaos in magnetization dynamics.

Figures (6)

• Figure 1: (a) Schematic illustration of the system. The MTJ consists of a free layer and a reference layer underneath. An external DC magnetic field $B_x$ is applied along the $x$-axis and the uniaxial magnetic anisotropy field $B_K$ is oriented along the $z$-axis. The polar and azimuth angles of the magnetization vector in the free layer, $\bm{m}$, are denoted by $\theta$ and $\varphi$. The magnetization vector pointing along the $y$-axis in the reference layer is represented by $\bm{p}$. The applied AC and DC currents along the $z$ direction generate spin-transfer torque. (b) Hamiltonian ($\mathcal{H}$) landscape of the MTJ for $B_x = 32$ mT and $B_\mathrm{ani} = 41.9$ mT. The red energy contour line is the homoclinic orbits, which starts from and end at the same saddle point.
• Figure 2: Heatmaps of the Lyapunov exponent $\lambda$ as functions of the DC current density $j_\mathrm{dc}$ and the amplitude of AC current density $j_\mathrm{ac}$ for (a) $\sigma = 0$ and (b) $\sigma = 0.366$ (corresponding to room temperature).
• Figure 3: Magnetization dynamics and corresponding Fourier spectrum. The magnetization trajectory in the phase space of $\theta$ and $\varphi$ is shown in the left panel. The central panel displays the trajectory in three dimensional real space represented by $(m_x, m_y, m_z)$. The right panel shows the Fourier spectrum of the $y$-component of the magnetization $m_y$. The parameters are as follows: (a), (c) $j_{\mathrm{ac}} = 1.2 \times 10^{12}$$\mathrm{Am^{-2}}$, $j_{\mathrm{dc}} = 0$; (b), (d) $j_{\mathrm{ac}} = 1.2 \times 10^{12}$$\mathrm{Am^{-2}}$, $j_{\mathrm{dc}} = 2.9 \times 10^{11}$$\mathrm{Am^{-2}}$; and (e), (f) $j_{\mathrm{ac}} = 1.75 \times 10^{12}$$\mathrm{Am^{-2}}$, $j_{\mathrm{dc}} = 2.9 \times 10^{11}$$\mathrm{Am^{-2}}$, respectively. Panels (a), (b) and (e) show the results without thermal fluctuations ($\sigma = 0$), whereas panels (c), (d) and (f) include thermal fluctuations at room temperature ($\sigma = 0.366$).
• Figure 4: Magnetization dynamics driven solely by stochastic forces. (a) Lyapunov exponent $\lambda$ as a function of the noise strength $\sigma$. The dynamics exhibits chaotic behaviors for $\sigma \gtrsim 0.6$. (b),(c) Magnetization trajectory and the corresponding Fourier spectrum at (b) $\sigma = 0.5$ for the radius of the free layer being $88$$\mathrm{nm}$ and (c) $\sigma = 0.8$ for the radius with $55$$\mathrm{nm}$.
• Figure 5: Heatmaps of the Lyapunov exponent $\lambda$ as functions of the amplitude of AC current density $j_{\mathrm{ac}}$ and the frequency of AC current $f$.