Skyrmion-Based Programmable Logic Device with Complete Boolean Logic Functions

A skyrmionic programmable logic device (SPLD) with complete Boolean logic functions is proposed and analyzed by micromagnetic simulations. The SPLD is based on an antiferromagnet-ferromagnet bilayer structure, in which the antiferromagnetic layer supports the interfacial Dzyaloshinskii-Moriya interaction and the out-of-plane exchange-bias field for stabilizing a zero-field skyrmion. By varying the local exchange-bias field, artificial pinning sites are introduced to trap skyrmions. Depending on the input currents and initial position of skyrmions at different pinning sites, different logic functions can be realized. Micromagnetic simulations show that the proposed SPLD has a robust performance, even under thermal fluctuations and inhomogeneity effects. Our work can provide insights for the design of programmable spin-logic devices.

Figure 1

Setup of device and motion of skyrmions under input current. (a) Illustration of the device configuration in FM-AFM bilayer. AFM layer (blue) is patterned into cross-shaped Hall bar, and FM layer (gray) cover the center region. Two orthogonal currents with identical amplitude, I₁ and I₂, are injected into AFM layer as input signals. Four magnetic tunnel junctions (MTJs), marked as A, B, C, and D, are used for writing skyrmions. MTJ D is also used for reading output voltage. (b),(c) Spin structures in MTJ of parallel (P) and antiparallel (AP) states, respectively. Spins in AFM layer are reoriented into local in-plane order, resulting in local exchange-bias field and pinning sites (PSs). (d) Layout of pinning sites and MTJs. (e)–(h) Skyrmion motion in FM layer under different input currents. J represents overall current direction, and v represents skyrmion velocity. I₁= 0 and I₂= 0 indicate no input current (or equivalently, input 0), leading to no skyrmion motion. I₁= 0 (I₁= 1) and I₂= 1 (I₂= 0) indicate applied in-plane current flowing along y (x) axis and skyrmion moving along vector (−1, 1) [(1, 1)]. I₁= 1 and I₂= 1 indicate current flow along vector (1, 1) and skyrmion moving along y axis.

Figure 2

Simulated logic device with xor function. Complete process includes four sets of inputs, (a) I₁= 0 and I₂= 0, (b) I₁= 0 and I₂= 1, (c) I₁= 1 and I₂= 0, (d) I₁= 1 and I₂= 1, and four operations, clean, initialization (initial for short), input, and read. (a1)–(d1) “Clean” operation wipes out all skyrmions in FM layers by using a large current pulse. (a2)–(d2) “Initialization” operation creates skyrmions in specified pinning sites to initialize specific logic function. (a3)–(d3) “Input” operation injects input signals (currents) and drives skyrmion motion. Black arrows indicate input currents. Arrows in green, red, and blue show the trajectory of skyrmions after injecting current. (a4)–(d4) “Read” operation reads output voltage signal from MTJ D. Output signals, R, are indicated by dashed arrows.

Figure 3

Simulated results of different logic functions. Function is configured by setting skyrmions in specified pinning sites. Corresponding initial states and logic functions (written in brackets) are shown in the first row. 1” and 0 indicate output signals from MTJ D. Arrows in green, red, and blue show trajectory of skyrmions after injecting different input currents.

Figure 4

Duration of input current (t_p) as a function of current amplitude (J_p) for various ${\theta }_{\mathrm{SHE}}$. Curves are plotted according to Eq. (6) with different values of ${\theta }_{\mathrm{SHE}}$ marked by blue 0.02 for Fe-Mn [49], green (0.3 for ${\mathrm{IrMn}}_3$ [35]), and black (0.08 for $\mathrm{Pt-Mn}$ [34]).

Figure 5

Sketch of the layout of pinning sites and MTJs in different skyrmion Hall angle. (a)–(c),(e)–(g) Skyrmion motion with small and large skyrmion Hall angles, respectively. (d),(h) Layouts of pinning sites and MTJs. Solid blue lines in (c),(g) are parallel to those in (d),(h).

Figure 6

Simulation results for xor gate with damping α = 0.01.

Figure 7

Simulation results for xor gate with sample size 800 × 800 × 1 nm³ under open boundary conditions.