Generation and annihilation of skyrmions and antiskyrmions in magnetic heterostructures

We demonstrate the controlled generation and annihilation of (anti)skyrmions with tunable chirality in magnetic heterostructures by means of micromagnetic simulations. By making use of magnetic (anti)vortices in a patterned ferromagnetic layer, we stabilize (anti)skyrmions in an underlying skyrmionic thin film in a reproducible manner. The stability of the (anti)skyrmion depends on the polarization of the (anti)vortex, whereas their chirality is given by those of the (anti)vortices. We investigate the influence of geometric parameters such as nanodisk radius and film thickness on the stability of the (anti)skyrmions. By introducing the interlayer Dzyaloshinskii-Moriya interaction into our modeling, we predict that the same coupling mechanism works also for chiral skyrmions. Furthermore, we demonstrate that the core coupling between the (anti)vortices and (anti)skyrmions allows deleting and writing of spin objects in a controlled fashion by applying short pulses of in-plane external magnetic fields or charge currents, representing a new key paradigm in skyrmionic devices.

Figure 1

Schematic illustration of the proposed heterostructures, (a) a vortex layer (VL, orange) is situated on top of a skyrmion host layer (SkL, blue). The arrows show the magnetization in the VL. In (a), we schematically show magnetic nanodisks. The radius $R$ of the nanodisks with thickness $t_{\mathrm{VL}}$ can be varied to arrange the skyrmions in the SkL with the desired periodicity. A further tuning parameter is the lattice constant $a$ that describes the disk center to disk center distance. In (b), we illustrate that the square lattice can be used as the VL, where following studies on frustrated spin systems, stable antivortices can be obtained by means of alternative field demagnetization protocols.

Figure 2

Representative illustration of a magnetic vortex. In (a) we illustrate the IP rotation of the magnetic vortex core via the color-coded color wheel, and in (b) we show the $m_z$ component of the vortex, where the vortex core has a negative polarity. The magnetization configuration of an antivortex stabilized in the VL is depicted in (c) and (d).

Figure 3

Simulated out-of-plane M-H hysteresis loop where the $m_z$ component of the magnetization is averaged over the SkL (red) or VL (blue). Magnetization configurations along the hysteresis loop are illustrated in the corresponding color panels at chosen magnetic fields. Scalebar corresponds to $500\mathrm{nm}$.

Figure 4

Cross-sectional view of a coupled vortex and skyrmion in the $xz$ plane at different OOP fields obtained from the hysteresis simulation shown in Fig. 3. The left panel shows only the $z\mathrm{component}$ of the magnetization, while the right panel uses the color-coded representation. The 3D coupled skyrmion-vortex texture can be stabilized with both polarities based on the direction of the applied magnetic field.

Figure 5

The same as Fig. 3 if a square permalloy lattice is the VL, and the initial magnetization state contains only the antivortex and antiferromagnetic arrangement of the lattice sites in the VL, as shown in the blue panel on the right with the color-coded magnetization configurations. Antiskyrmions are stable at the different magnetic fields in the SkL, as illustrated in the red panel.

Figure 6

The same as Fig. 4 but for an antiskyrmion that is coupled to the antivortex from the VL.

Figure 7

Phase diagrams describing the topological state of the single vortex-skyrmion structure after being subject to an IP magnetic field pulse of Gaussian shape, wherein (a) the topological number of the VL is shown as a function of the chosen constant OOP bias field $H_{\mathrm{bias}}$, and the amplitude of the IP magnetic field pulse $H_{\mathrm{pulse}}$, and in (b) the topological number of the SkL, where for values around $N=0$ the skyrmion is deleted via the vortex-core reversal. The temporal evolution of N for different magnitudes of the IP field pulse is shown in (c)–(f), where the amplitude of the bias field is written inside the figures.

Figure 8

Evolution of the magnetization configuration during the vortex core reversal process induced by a short IP magnetic field pulse. The upper panel illustrates the skyrmion vanishing after $t=2\mathrm{ns}$, and the lower panel depicts how the vortex core reverses its polarity $[-1$ (black) to $+1$ (white)] by nucleating an additional antivortex and subsequent vortex-antivortex-pair annihilation.

Figure 9

Same as Fig. 5 but for an antiskyrmion in the SkL and an antivortex in the VL using a square lattice.

Figure 10

Same as Fig. 6 but for the antiskyrmions deletion process in the SkL progresses via the antivortex core reversal in the VL above.