Skyrmion generation by current

Skyrmions, once a hypothesized field-theoretical object believed to describe the nature of elementary particles, became common sightings in recent years among several noncentrosymmetric metallic ferromagnets. For more practical applications of Skyrmionic matter as a carrier of information, thus realizing the prospect of “Skyrmionics,” it is necessary to have the means to create and manipulate Skyrmions individually. We show through extensive simulation of the Landau-Lifshitz-Gilbert equation that a circulating current imparted to the metallic chiral ferromagnetic system can create isolated Skyrmionic spin texture without the aid of external magnetic field.

Figure 1

Skyrmion generation by circulating spin current source in the FM${}^{\prime }$ background. (a) Time dependence of the total Skyrmion number $Q\left(t\right)$. $Q\left(0\right)\approx -2$ is nonzero from the residual anti-Skyrmions in the ferromagnetic background. Blue (red) colored curves correspond to CW (CCW) circulating current with the $j_0$ value indicated for each curve. (b)–(l) Time-dependent snapshots of the spin configuration over the green-circled time interval in (a). Adjacent spins are separated by the distance $a$. The circle at the center of (b) indicates $R_c$, the extent of the current source. Residual anti-Skyrmions lie outside the field of view. Red and blue refer to positive and negative Skyrmion densities, respectively. Time at which the snapshot is taken and the change in the Skyrmion number are given as $(t/t_0,Q\left(t\right)-Q\left(0\right))$ above each figure. Skyrmion number is seen to decrease by one, and later by three. Threshold value $j_{0c}$ lies between 2.35 and 2.4 for CW spin current.

Figure 2

Skyrmion generation by circulating spin current source in the H background. (a) Time dependence of the total Skyrmion number $Q\left(t\right)$ for various $j_0$ values. Initial Skyrmion number is zero for the helical spin. Same color convention as in Fig. 1 applies throughout this figure. (b)–(l) Two sets of snapshots corresponding to $Q=0\to 1$ and $Q=1\to 2$ corresponding to two green circles in (a).

Figure 3

Influence of Gilbert damping on Skyrmion generation. (a), (b) Plot of Skyrmion number $Q\left(t\right)$ with $b=0$ (H background) for different Gilbert damping constants $\alpha$. $\left|Q\right(t\left)\right|$ increases monotonically with $\alpha$ without showing signs of quantization when $\alpha$ is small. At a larger damping, $0.3<\alpha <0.5$, quantization of Skyrmion number begins to occur. The time span of each integer plateau becomes longer, and the production rate of Skyrmions becomes less, with increasing $\alpha$. (c), (d) Plot of the Skyrmion number $Q\left(t\right)$ with FM${}^{\prime }$ background. Numbers in the inset are the Gilbert damping constants. $(j_0,R_c)=(-1.5,3.0)$ was used for (a) and (b), and $(j_0,R_c)=(-2.5,3.0)$ for (c) and (d).

Figure 4

Skyrmion generation by pulse current. (a), (b) Pulse current of size $j_0=5$ is applied for $0<t_1/t_0<50$ over the helical spin state and then turned off. (c), (d) $j_0=15$ for $0<t_1/t_0<15$ over the FM${}^{\prime }$ state. Dotted vertical line in (b) and (d) indicates the termination of the applied current. Top row: The spin configuration and Skyrmion number $Q\left(t\right)-Q\left(0\right)$ when a sufficiently long time has elapsed after the current is turned off. Bottom row: Time dependence of the Skyrmion number $Q\left(t\right)-Q\left(0\right)$. All current directions are CCW with $R_c=3$ and $\alpha =0.1$.

Figure 5

Skyrmion creation by radial current source. Current pulse with $j_0=10$ lasting for $t/t_0=10$ was given. The numbers above each figure indicate $(t/t_0,Q\left(t\right)-Q\left(0\right))$. (a) Right at the turn-off, one finds a swarm of positive and negative Skyrmion fragments. (b) After some time has passed, most of the Skyrmions and anti-Skyrmions have annihilated each other, leaving behind a predominant anti-Skyrmion density due to the external magnetic field. (c) Final state shows one anti-Skyrmion.

Figure 6

Schematic plot of the Skyrmion trajectory for uniform current when $\beta$ varies.