Magnetic Radial Vortex Stabilization and Efficient Manipulation Driven by the Dzyaloshinskii-Moriya Interaction and Spin-Transfer Torque

Solitons are very promising for the design of the next generation of ultralow power devices for storage and computation. The key ingredient to achieving this goal is the fundamental understanding of their stabilization and manipulation. Here, we show how the interfacial Dzyaloshinskii-Moriya Interaction (IDMI) is able to lift the energy degeneracy of a magnetic vortex state by stabilizing a topological soliton with radial chirality, hereafter called radial vortex. It has a noninteger Skyrmion number $S$ ($0.5<|S|<1$) due to both the vortex core polarity and the magnetization tilting induced by the IDMI boundary conditions. Micromagnetic simulations predict that a magnetoresistive memory based on the radial vortex state in both free and polarizer layers can be efficiently switched by a threshold current density smaller than ${10}^6\mathrm{A}/{\mathrm{cm}}^2$. The switching processes occur via the nucleation of topologically connected vortices and vortex-antivortex pairs, followed by spin-wave emissions due to vortex-antivortex annihilations.

Figure 1

Spatial distribution of magnetization for different types of vortex with positive (top) and negative (bottom) polarity. (a) Counterclockwise (CCW) circular vortex. (b) Clockwise (CW) circular vortex. (c) Radial vortex. A color scale linked to the out-of-plane component of the magnetization is also shown (red positive, blue negative).

Figure 2

Equilibrium configurations of the magnetization as a function of $|D|$ at zero external field when (a) $T=0\mathrm{K}$ and (b) $T=300\mathrm{K}$. The snapshots are calculated for $|D|=0.0$, 0.5, 1.0, 1.5, 2.0, 2.5, and $3.0\mathrm{mJ}/{\mathrm{m}}^2$. For $|D|=1.0\mathrm{mJ}/{\mathrm{m}}^2$ in (a), the two represented magnetization configurations depend on the initial state. The colors refer to the $z$ component of the magnetization (blue negative, red positive). Left inset: the initial state can be radial or circular vortex, as well as the uniform state.

Figure 3

Skyrmion number as a function of $|D|$. Four different regions are indicated and separated by vertical dashed lines. Insets: examples of spatial distribution of the magnetization related to each region. The colors refer to the $z$ component of the magnetization (blue negative, red positive).

Figure 4

$x$ component of the normalized magnetization as a function of the external field applied along the positive $x$ direction for (a) the radial vortex, when $|D|=2.0\mathrm{mJ}/{\mathrm{m}}^2$, and (b) the circular vortex, when $|D|=0.0\mathrm{mJ}/{\mathrm{m}}^2$. Insets: spatial distributions of the magnetization where the colors indicate the $z$ component (blue negative, red positive). The snapshots for different fields are represented, and the direction of the applied in-plane field is illustrated.

Figure 5

Example of snapshots for the radial vortex switching at $J_{\mathrm{MTJ}}=5\mathrm{MA}/{\mathrm{cm}}^2$. (a) Initial state: radial vortex. (b) Topologically connected radial vortices together with an edge antiradial vortex. (c) Three antiradial vortex-antivortex pairs, together with an edge radial and antiradial vortex. (d) Configuration before the accomplishment of the switching: two antiradial vortex-antivortex pairs and one antiradial vortex are clearly observed. (e) Final state: antiradial vortex. The colors are linked to the $z$ component of the magnetization (red positive, blue negative). The acronyms TCRV, ARV, RV, AV, ERV, and EARV indicate the topologically connected radial vortices, antiradial vortex, radial vortex, antivortex, edge radial vortex, and edge antiradial vortex, respectively.

Figure 6

The main panel shows the switching time as a function of the current density for the radial vortex (RV) and the circular vortex (CV) at $T=0\mathrm{K}$ and $T=300\mathrm{K}$, as indicated in the legend. Inset: example of histogram related to 100 realizations performed for RV at $T=300\mathrm{K}$ for $J_{\mathrm{MTJ}}=0.5\mathrm{MA}/{\mathrm{cm}}^2$, and the corresponding Gaussian fit.