Interconnects for All-Spin Logic Using Automotion of Domain Walls

Abstract

In this paper, an interconnect scheme based on automotion of domain walls for all-spin logic has been proposed. The proposed interconnect is analyzed using a comprehensive numerical model including an equivalent circuit for all-spin logic operations [1], the one-dimensional Landau-Lifshitz-Gilbert equation for domain wall creation, reflection, and disappearance at the boundaries. Analytical expressions for domain wall transport [2][3][4] along the wire are also presented. From the model, it is found that the reflection of the domain wall can be eliminated by using a material with high Gilbert damping coefficient at the end, the energy dissipation can be independent of the interconnect length, and domain wall displacement and energy dissipation can be further improved using a material with a low damping factor and saturation magnetization. Furthermore, the interconnect reliability is also studied by applying the thermal random noise analysis on the dynamics of domain walls, and it is found that thermal fluctuations can have a significant impact on the interconnect performance; thus, the interconnect with a low Gilbert damping factor is desired to suppress the thermal noise effects.

Low-power Spin Valve Logic using Spin-transfer Torque with Automotion of Domain Walls

“…Nd) at the end of the FM wire [21]. Making the input highly damped can also ensure that the DW can disappear at the end of the wire and thus no data reflection occurs in the interconnect [14]. In addition to the local enhancement of damping coefficient, the non-reciprocity can also be further improved by varying charge current density at both input and output, which strongly influence the magnitude of STT in the device (see Supplementary Materials for analytical derivations).…”

“…Similar to Ref. [14], a self-consistent numerical iteration between spin circuits and the LLG equation is required to describe the time evolution of the system. In this section, the theoretical approach to model the proposed scheme is presented in detail.…”

“…The overall conductance matrix for a single device, [G] 4N ×4N , can be obtained using a nodal analysis similar to Ref. [14], where a set of equations are established by the fact that the net current at each node is zero and satisfies the following equation:…”

“…where all the internal fields are defined the same as those in Ref. [14], and A is the exchange constant. Note that since the width and the thickness of FM wires are quite small, magentizations in both y and z directions are assumed to be uniform and thus the exchange field is only dependent on the x direction.…”

“…On the other hand, the general concept of using FM wires as interconnects has been proposed, in which the shape-anisotropy-driven DW motion, also known as DW automotion [12], is used to update the bit inside the wire [13]. Recently, devices in the form of NLSVs connected by FM wires based on automotion of DW has been proposed due to full metallic structures and the possibility of energyfree propagation of DW once it is created [14]. In contrast, in NLSVs, only part of injected spins contribute STT to DW creation in the interconnect, and STT becomes much weaker as the shunt path in the device is reduced [15].…”