Janus skyrmion: Interfacial quasiparticle with two-faced helicity

Abstract

Janus particles are functional particles with at least two surfaces showing asymmetric properties. We show at the interface between two magnetic regions with different antisymmetric exchange interactions, an alternative species of two-dimensional topological quasiparticles can emerge, in which different helicity structures can coexist. We name such an interfacial quasiparticle a "Janus skyrmion," in analogy to the Janus particle. As the Janus skyrmion shows helicity asymmetry, its size could vary with both the in-plane and out-of-plane magnetic fields. A vertical spin current could drive the Janus skyrmion into one-dimensional motion along the interface without showing the skyrmion Hall effect, at a speed which depends on both the in-plane spin-polarization direction and current density. Thermal fluctuations could also lead to one-dimensional random walk of a Brownian Janus skyrmion. This work uncovers unique dynamics intrinsic to interfacial quasiparticles with exotic helicity, which may be realized in interface-engineered magnetic layers.

Figures (5)

• Figure 1: Janus skyrmion quasiparticle with two-faced asymmetric helicity at the interface. (a) A basic Janus particle has two distinct surfaces, that is, the left side A and right side B, which show different or asymmetric properties. (b) The statue of the two-faced god Janus Bifrons, the ancient Roman god of beginnings and transitions, who is able to look at opposite directions. The image is a cropped version from wikipedia.org, licensed under the https://creativecommons.org/licenses/by-sa/3.0. (c) Top view of various relaxed Néel-type, Bloch-type, and Janus skyrmions with $Q=-1$. Skyrmions are fully relaxed at the center of a square magnetic layer with the same or two different types of DM interactions. The length, width, and thickness of the monolayer are equal to $40$ nm, $40$ nm, and $1$ nm, respectively. The cell size is $1\times 1\times 1$ nm$^{3}$. No external magnetic field is applied. For Néel-type and Bloch-type skyrmions, the DM interaction is uniform and of the same type in the model. For Janus skyrmions, the value of Néel-type DM interaction in the left region ($x=0-20$ nm) is fixed at $D_{\text{L}}=\pm 3.7$ mJ m$^{-2}$, and the strength of Bloch-type DM interaction in the right region ($x=20-40$ nm) is set to $|D_{\text{R}}|=|D_{\text{L}}|$. The type and sign of $D_{\text{L}}$ and $D_{\text{R}}$ are indicated beyond each skyrmion configuration. A minimum value of $|D_{\text{R}}|=|D_{\text{L}}|=3.1$ mJ m$^{-2}$ is required to stabilize the Janus skyrmion. The color scale represents the reduced out-of-plane ($m_z$) or in-plane ($m_x$) spin component. The spin configurations are indicated by black arrows. (d) A basic Janus skyrmion has two distinct helicity structures. For example, the left half is with Néel-type helicity, and the right half is with Bloch-type helicity. The shape of the Janus skyrmion is thus like a heart, which is in stark contrast to a conventional skyrmion with centrosymmetric helicity. (e) Topological mapping of the spin configurations of a 2D Janus skyrmion with $Q=-1$ [(d)] onto a three-dimensional (3D) $2$-sphere.
• Figure 2: Manipulation of a static Janus skyrmion by in-plane or out-of-plane magnetic field. (a) Reduced out-of-plane magnetization ($m_z$) of the model as functions of applied external magnetic fields. The magnetic field is applied in the $x$, $y$, or $z$ direction, which scans from $-200$ mT to $+200$ mT. (b) Snapshots of the Janus skyrmion at $B_x=\pm 200$ mT. (c) Snapshots of the Janus skyrmion at $B_y=\pm 200$ mT. (d) Snapshots of the Janus skyrmion at $B_z=\pm 200$ mT. Here, the Janus skyrmion is stabilized at the interface between Néel-type (left) and Bloch-type (right) DM interactions. $D_{\text{L}}=D_{\text{R}}=3.5$ mJ m$^{-2}$. The model size is $100\times 100\times 1$ nm$^{3}$. Other parameters are given in Fig. \ref{['FIG1']} caption.
• Figure 3: Current-induced dynamics of a Janus skyrmion at the interface ($\theta$ dependence). (a) The velocity of the Janus skyrmion along the interface (i.e., $\pm y$ directions) as functions of the spin polarization angle ($\theta$). Symbols are simulation results, and curves show theoretical solutions. (b) The $\theta$-dependent speed of the Janus skyrmion moving along the interface. The current density $j$ is fixed at $1$ or $3$ MA cm$^{-2}$. Only simulation results are shown. Here, the Janus skyrmion is stabilized at the interface between Néel-type (left) and Bloch-type (right) DM interactions. $D_{\text{L}}=D_{\text{R}}=3.5$ mJ m$^{-2}$. The model size is $100\times 100\times 1$ nm$^{3}$. Other parameters are given in Fig. \ref{['FIG1']} caption.
• Figure 4: Current-induced dynamics of a Janus skyrmion at the interface ($j$ dependence). (a) Left: The velocity of the Janus skyrmion along the interface (i.e., $\pm y$ directions) as a function of the current density ($j$). Right: The reduced out-of-plane magnetization of the system obtained during the stable motion ($m_z^s$) as a function of $j$. The spin polarization angle is fixed at $\theta=270$ degrees (i.e., $\boldsymbol{p}=-\hat{y}$). (b) The time-dependent $m_z$ during the motion of a Janus skyrmion driven by different current densities ($j=1-10$ MA cm$^{-2}$). See Fig. \ref{['FIG3']} caption for other parameters.
• Figure 5: 1D Brownian random walk of a Janus skyrmion at the interface. (a) Time-dependent position of the Janus skyrmion in the $x$ dimension. (b) Time-dependent position of the Janus skyrmion in the $y$ dimension. (c) Time-dependent $m_z$ of the model. Here, the Brownian dynamics of the Janus skyrmion is simulated at three different temperatures ($T=10$, $50$, and $100$ K). See Fig. \ref{['FIG3']} caption for other parameters.