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Magnetic Skyrmion Logic Gates: Conversion, Duplication and Merging of Skyrmions

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Magnetic Skyrmion Logic Gates: Conversion, Duplication and Merging of Skyrmions

Xichao Zhang et al. Sci Rep.

Abstract

Magnetic skyrmions, which are topological particle-like excitations in ferromagnets, have attracted a lot of attention recently. Skyrmionics is an attempt to use magnetic skyrmions as information carriers in next generation spintronic devices. Proposals of manipulations and operations of skyrmions are highly desired. Here, we show that the conversion, duplication and merging of isolated skyrmions with different chirality and topology are possible all in one system. We also demonstrate the conversion of a skyrmion into another form of a skyrmion, i.e., a bimeron. We design spin logic gates such as the AND and OR gates based on manipulations of skyrmions. These results provide important guidelines for utilizing the topology of nanoscale spin textures as information carriers in novel magnetic sensors and spin logic devices.

Figures

Figure 1
Figure 1. The basic design of the magnetic skyrmion logic gate system.
(a), Sketch of the simulated model: the red and green layers represent the nanowire and the substrate, respectively; the spin-polarized current is injected into the nanowire with the current-in-plane (CIP) geometry, through which electrons flow from the source to the drain, i.e., toward +x; the current density inside the wide part of the nanotrack is proportional to the current density inside the narrow part of the nanotrack with respect to the ratio of narrow width to wide width; a skyrmion is initially created at the input side and can be pushed into the output side by the current with the conversion between skyrmion and domain-wall pair in the junction geometry. (b), The top-view of the design of the 1-nm-thick skyrmion-conversion geometry: the width of the input and output sides is 150 nm, the width of the narrow channel is 12 nm, and the length of the sample is 450 nm; the interface connection angle is fixed at 45 degrees (similarly hereinafter); red and blue denote two regions with different parameters, where a gradient transition of parameter is used on the narrow channel. (c), The top-view of the design of the 1-nm-thick geometry for the skyrmion duplication: the width of all the input and output sides is 100 nm, and the length of the sample is 600 nm. (d), The top-view of the design of the 1-nm-thick geometry for the skyrmion merging and the logical OR gate: the geometry is the horizontally-flipped version of the one in c. e, The top-view of the design of the 1-nm-thick geometry for the logical AND gate: the geometry is similar to the one in d, except the horizontal branch of the Y-junction channel, of which the width is increased from 20 nm to 40 nm. The current density inside the output side is equal to the sum of that inside the two input sides. All the designed samples can connect to nanowires with matching width of the branch for application in integrated circuit devices.
Figure 2
Figure 2. Conversions between skyrmions and antiskyrmions.
The top panels show the snapshots of the magnetization configuration at four selected times corresponding to the vertical lines in the middle and bottom panels; the middle panels show the time evolution of the average spin components mx, my, mz; the bottom panels show the time evolution of the skyrmion number Qs. (a), Conversion between a skyrmion and a skyrmion with identical out-going helicity: the D in the sample is 3.5 mJ m−2; the background points +z; a current density of 3 × 1012 A m−2 (the value is of the input or output side, similarly hereinafter) is applied along −x for 0 ns < t < 0.56 ns followed by a relaxation (highlighted by the gray shadows) until t = 1 ns. (b), Conversion between a skyrmion and a skyrmion with opposite in-going helicity: the D is 3.5 mJ m−2 in the input side and −3.5 mJ m−2 in the output side, while a gradient transition from 3.5 mJ m−2 to −3.5 mJ m−2 is set in the narrow channel; the background points +z; a current density of 3 × 1012 A m−2 is applied along −x for 0 ns < t < 0.51 ns and then is the relaxation until t = 1 ns. (c), Conversion between a skyrmion and an anti-skyrmion with opposite in-going helicity: the D in the sample is 3.5 mJ m−2; the background of the input side points +z, while it points −z in the output side; a current density of 2.67 × 1012 A m−2 is applied along −x for 0 ns < t < 0.51 ns followed by a relaxation until t = 1 ns. (d), Conversion between a skyrmion and an anti-skyrmion with identical out-going helicity: the profile of D is the same as that in b and the profile of background is the same as that in c; a current density of 2.67 × 1012 A m−2 is applied along −x for 0 ns < t < 0.51 ns followed by a relaxation until t = 1 ns. The color scale has been used throughout this paper.
Figure 3
Figure 3. Conversion between a skyrmion and a bimeron.
The top panels show the snapshots of the magnetization configuration at six selected times corresponding to the vertical lines in the middle and bottom panels; the middle panels show the time evolution of the average spin components mx, my, mz; the bottom panels show the time evolution of the skyrmion number Qs. (a), Conversion between a skyrmion and an anti-bimeron: the D in the sample is 3.5 mJ m−2; the anisotropy K is 0.8 MJ m−3 in the input side and −0.8 MJ m−3 in the output side, while a gradient transition from 0.8 MJ m−3 to −0.8 MJ m−3 is set in the narrow channel, i.e. the plane of the input side is a hard plane, while the plane of the output side is an easy plane. The initial background magnetization of the input side points +z, while it is mostly aligned along −x direction in the output side; a current density of 9 × 1012 A m−2 (the value is of the input or output side, similarly hereinafter) is applied along −x direction for 0 ns < t < 0.17 ns followed by a relaxation without applying any current until t = 1 ns. (b), Conversion between a skyrmion and a bimeron: the D is 3.5 mJ m−2; the profile of the anisotropy is the same as that in a. The initial background magnetization of the input side points +z, while it is mostly aligned along +x direction in the right output side; a current density of 10 × 1012 A m−2 is applied along −x direction for 0 ns < t < 0.15 ns followed by a relaxation until t = 1 ns.
Figure 4
Figure 4. Duplication and merging of skyrmion.
The top panels show the snapshots of the magnetization configuration at eight selected times corresponding to the vertical lines in the middle and bottom panels; the middle panels show the time evolution of the average spin components mx, my, mz; the bottom panels show the time evolution of the skyrmion number Qs. (a), Duplication of a skyrmion: the D is 3.5 mJ m−2; the initial background magnetization of the sample points +z; a current density of 5 × 1012 A m−2 (the value is of the input side) is applied along −x direction for 0 ns < t < 0.49 ns followed by a relaxation without applying any current until t = 1 ns. (b), Merging of two skyrmions: the D is 3.5 mJ m−2; the initial background magnetization of the sample points +z; a current density of 4 × 1012 A m−2 (the value is of the output side) is applied along −x direction for 0 ns < t < 0.64 ns followed by a relaxation until t = 1 ns.
Figure 5
Figure 5. Skyrmion logical OR operation.
The skyrmion represents logical 1, and the ferromagnetic ground state represents logical 0. Left panel, the basic operation of OR gate 1 + 0 = 1: there is a skyrmion in the input A and no skyrmion in the input B at initial time, which represents input = 1 + 0; a current density of 7 × 1012 A m−2 (the value is of the output side, similarly hereinafter) is applied along −x direction for 0 ns < t < 0.39 ns followed by a relaxation without applying any current until t = 1 ns. At t = 1 ns, a stable skyrmion is in the output side, which represents output = 1. Middle panel, the basic operation of the OR gate 0 + 1 = 1: there is a skyrmion in the input B side and no skyrmion in the input A side at initial time, which represents input = 0 + 1; a current density of 7 × 1012 A m−2 is applied along −x direction for 0 ns < t < 0.39 ns followed by a relaxation without applying any current until t = 1 ns. At t = 1 ns, a stable skyrmion is in the output side, which represents output = 1. Right panel, the basic operation of the OR gate 1 + 1 = 1: there is a skyrmion in both the input A side and the input B side, which represents input = 1 + 1; a current density of 4 × 1012 A m−2 is applied along −x direction for 0 ns < t < 0.64 ns followed by a relaxation without applying any current until t = 1 ns. At t = 1 ns, a stable skyrmion is in the output side, which represents output = 1.
Figure 6
Figure 6. Skyrmion logical AND operation.
The skyrmion represents logical 1, and the ferromagnetic ground state represents logical 0. Left panel, the basic operation of AND gate 1 + 0 = 0: there is a skyrmion in the input A side and no skyrmion in the input B side at initial time, which represents input = 1 + 0; a current density of 4 × 1012 A m−2 (the value is of the output side, similarly hereinafter) is applied along −x direction for 0 ns < t < 0.81 ns followed by a relaxation without applying any current until t = 1 ns. At t = 1 ns, no skyrmion is in the output side, which represents output = 0. Middle panel, the basic operation of the AND gate 0 + 1 = 0: there is a skyrmion in the input B side and no skyrmion in the input A side at initial time, which represents input = 0 + 1; a current density of 4 × 1012 A m−2 is applied along −x direction for 0 ns < t < 0.81 ns followed by a relaxation without applying any current until t = 1 ns. At t = 1 ns, no skyrmion is in the output side, which represents output = 0. Right panel, the basic operation of the AND gate 1 + 1 = 1: there is a skyrmion in both the input A side and the input B side, which represents input = 1 + 1; a current density of 4 × 1012 A m−2 is applied along −x direction for 0 ns < t < 0.81 ns followed by a relaxation without applying any current until t = 1 ns. At t = 1 ns, a stable skyrmion is in the output side, which represents output = 1.

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