An NML in-plane Wire Crossing Structure Laysson Oliveira Luz † , Jos´ e Augusto M. Nacif § , Ricardo S. Ferreira ∓ , Omar P. Vilela Neto † § Science and Technology Institute, Federal University of Vic ¸osa, Florestal, Brazil ∓ Department of Informatics, Federal University of Vic ¸osa, Vic ¸osa, Brazil † Department of Computer Science, Federal University of Minas Gerais, Belo Horizonte, Brazil Email: {layssonluz,omar}@dcc.ufmg.br Abstract—The Nanomagnetic Logic (NML) is a promising new technology to build low-power devices at room temperature. Furthermore, this technology allows mixing logic and memory on the same device, providing area and power consumption optimizations. However, when designing complex nanomagnetic circuits, we often need to cross wires without needing to include extra layers of interacting nanomagnets that would make the synthesis process more complex. In this work, we propose and analyze the behavior of a new structure that allows an in- plane wire crossing that can be useful in designing complex NML circuits. The design was built based on a clocking scheme of 4 phases and simulated using the Landauer-Lifshitz-Gilbert equation through the NMLSim v2 simulator. Our design can implement horizontal and vertical wire crossings without any extra time delay by exploring the time-division multiplexing method. Index Terms—Nanomagnetic Logic, Wire Crossing, Time- Division Multiplexing, Nanotechnologies I. I NTRODUCTION Nanomagnetic logic (NML) is one promising alternative to aid the CMOS devices. The CMOS severe power dissipation associated with the limit of transistor shrinking is becoming a significant barrier for novel computing devices to continue to achieve the benefits of downsizing. The NML is a non- volatile and low-power architecture that applies magnetostatic interactions between single-domain devices to propagate and process signals. This technology allows the fabrication of circuits with high-density integration, low heat dissipation, and low power consumption [1]–[4]. The NML basic unit is a nanomagnet particle with an elongated shape and two stable states for magnetization orien- tation. That orientation is associated with the binary values ‘0’ and ‘1’, used to perform Boolean logic. NML circuits trans- mit information through ferromagnetic and antiferromagnetic couplings. Nanomagnets’ position and geometry define the coupling interaction, which affects the logic of the component. Some simple circuits have been experimentally demonstrated in the past years [5], [6], showing that the technology is capa- ble of performing majority logic and information propagation. The design of NML circuits is a nontrivial task since their functionality depends on the nanomagnet’s geometry and relative positions. Moreover, the technology limitation for the physical synthesis of NML circuits justifies the small logic gates and simple devices presented by current works. Thus, the evaluation of NML designs demands simulators, such as NMLSim [7] to avoid incorrect designs, from the high-abstraction description to the prototyping. Beyond, well- established technologies apply standard cells to facilitate the development of more complex circuits. These logic cells per- form specific functions, present similar geometric dimensions, and behave as building blocks for integrated designs. With this in mind, a recent work presented the NMLib [8], an NML standard cell library implemented as an extension of the NMLSim 2.0 simulator. It provides four logic cells to perform the primitive boolean functions and six interconnection cells. In the synthesis of NML circuits, different data flowing through different wires eventually get to a point where they need to swap, continuing their propagation along the adjacent wires. However, its physical implementation is a challenging design problem in NML. Some works have explored the multilayered approach to cross wires in different layers of nanomagnets. Other works propose different particles shapes, clock systems, or even special elements to change the magnetic couplings at the crossing point. This work proposes and simulates an efficient and straight- forward NML design working on a 4-phase clock system that allows in-plane information crossing. The proposed device presents the most negligible latency in literature, gathering the crossing output values in only one clock cycle. II. RELATED WORK This section discusses the proposed wire crossing designs presented in the literature. Niemier et al. presented a crossing device via a size- decreasing scheme of circular nanomagnets [9]. The authors show how to arrange a group of nanomagnets whose shape represents two bits of information simultaneously. The isolated device can correctly cross the data, but they did not present any circuit applying it. More recently, Rahmeier et al. [10] proposed and analyzed the behavior of a structure that also allows an in-plane crossing of information. The work shows simulation results of micromagnetic simulations, using the consolidated Object- Oriented Micro-Magnetic Framework (OOMMF) to prove the wire crossing structure. However, the work lacks test cases applying the design in circuits. Yang et al. investigated a crossing device for wires of elliptical nanomagnets with a clock system composed of piezo- electric layers [11]. In addition to the geometric limitation of nanomagnets, the crossing system needs seven clock signals to control information propagation.