Skyrmion size-tuning in two-dimensional antiferromagnetic monolayers by applying local spin-polarized current-induced spin-transfer torque

Reconfigurable Skyrmion-Based Logic Gates: Versatile Design and Full-Scale Implementation

“…The energy barriers in this context are determined by the PMA values on both sides, represented as K u (1) and K u (2) . These constants are related to each other through K u (VCMA), where K u (2) = K u (1) + K u (VCMA). , Consequently, setting V b to −2.66 V leads to a 5% increase in the anisotropy, resulting in K u (2) = 1.05 K u (1) within the VCMA gate. If the PMA on the left side is greater than that on the right side, we represent it as a negative barrier (−Δ E b ); otherwise, it is a positive barrier.…”

“…The dynamics of the AFM skyrmion is realized by applying a current density through the HM, generating SOTs in the AFM layer. The equation describing the skyrmion dynamics driven by SOTs is given by ,− normald m i normald t = prefix− γ 0 ( bold-italicm bold-italici × bold-italicH boldeff ) + α ( m i × normald m i normald t ) − γ 0 m i × ( m i × ℏ θ SHE J HM 2 μ 0 e M s d e y ) Here, m i represents the normalized magnetization, H eff is the effective field, γ is the gyromagnetic ratio, α is the Gilbert damping, θ SHE is the spin Hall angle (SHA), J HM is the pulsed current density flowing in the negative x -axis along the HM layer, μ 0 is the vacuum permeability, e is the elementary electron charge, M s is the saturation magnetization, and d is the AFM layer thickness.…”

“…This discretization technique allows us to precisely capture the intricate nanoscale behavior . By making the grid size small enough, we can numerically mimic the atomistic model conditions to effectively simulate antiferromagnetic systems , (see Supporting Movie S1). As shown in Figure d, the two-dimensional layer is stabilized in an AFM ground state consisting of two sublattices with opposite polarities to serve as the fundamental element for implementing AFM skyrmion-based logic operations.…”

“…To incorporate VCMA into the system, we introduced an additional anisotropy energy term corresponding to the VCMA effect. The VCMA is based on a linear relationship; thus, it is implemented in the simulation using the equation − K u (2) = K u (1) + K u (VCMA), where K u (VCMA) = V b ξ/ d gate d AFM and ξ represents the VCMA coefficient and V b is the bias voltage. ,, The detailed implementation of the VCMA effect in Mumax3 can be found in references. , This modification enables us to fine-tune the effective field within the simulation as a function of the applied voltage, thus influencing the anisotropy barrier. Therefore, H eff in the LLG equation exhibits a significant dependency on the bias voltage V b via the anisotropy term H anis ( V b ).…”

“…The interplay between VCMA and SOTs is carefully balanced to achieve reliable and accurate results. The magnetic parameters adopted in the micromagnetic model are as follows: the interfacial DMI strength D = 3.1 mJ/m 2 , exchange stiffness A exch = 15 PJ/m, interlayer exchange coupling constant J int = −5 mJ/m 2 , PMA constant K u (1) = 0.65 MJ/m 3 , saturation magnetization M s = 580 kA/m, gyromagnetic ratio γ = −2.21 × Mm/As, positive SHA θ SHE = 15°, Gilbert damping coefficient α = 0.20, and VCMA coefficient ξ is assumed to be 30 fJ/Vm. ,− …”