Static, periodic, and chaotic magnetization behavior induced by spin-transfer torque in magnetic nanopillars

The magnetization dynamics of a square magnet in a pillar structure under the influence of a dc spin current is studied by micromagnetic simulation based on the modified Landau-Lifshitz-Gilbert equation. Even in the situation with neither external field perturbation nor thermal activation, the magnetization exhibits intricate behaviors ranging from static configurations to periodic domain wall rotations to chaotic processes. It arises from the nonlinearity of the spin-transfer torque and is explained by the excitation of nonlinear spin waves in the magnet.

Figure 1

Schematic of the pillar structure in Cartesian coordinates. Note that the graphic arrow shows the direction of the electrical current. Electron flow is in the opposite direction.

Figure 2

(a) Leaf state magnetization configuration for magnet ${\mathrm{FM}}_2$ at equilibrium in the absence of an electrical current. (b) $\mathrm{S}$-state magnetization configuration at equilibrium, (c) trajectory of $⟨\mathbf{m}⟩$ in the $x\text{−}y$ plane, and (d) time dependence of $⟨m_x⟩$ and $⟨m_z⟩$ for $I=2.75\mathrm{mA}$. (e) Magnetization configuration, (f) trajectory of $⟨\mathbf{m}⟩$ in the $x\text{−}y$ plane, (g) time dependence of $⟨m_x⟩$ and $⟨m_z⟩$, and (h) frequency spectrum of $⟨m_x⟩$ for $I=11.0\mathrm{mA}$. (i) Magnetization configuration, (j) trajectory of $⟨\mathbf{m}⟩$ in the $x\text{−}y$ plane, (k) time dependence of $⟨m_x⟩$ and $⟨m_z⟩$, and (l) frequency spectrum of $⟨m_x⟩$ for $I=27.5\mathrm{mA}$. The damping constant $\alpha$ is 0.10.

Figure 3

(a) Time-varying $⟨m_x⟩$ and (b) static vortex magnetization configuration of the square magnet at $t=9\mathrm{ns}$ for $I=6.9\mathrm{mA}$. (c) Time-varying $⟨m_x⟩$ and (d) chaotic magnetization configuration of the square magnet at $t=9\mathrm{ns}$ for $I=20.7\mathrm{mA}$ for comparison. The damping constant $\alpha$ is 0.01.

Figure 4

Dependence of ${\sigma }_x$ and ${⟨m_z⟩}_0$ on current $I$. The inset shows the distribution of $⟨m_x⟩$ is fit to a Gaussian function for $I=20.7\mathrm{mA}$. The damping constant $\alpha$ is 0.01.