Research towards brain-inspired computing based on beyond CMOS devices has gained momentum in recent years. The motivation beyond this vigorous research prevails in exploitation of the resemblance between the computing principles and the device characteristics. To this end, the devices are used to perform otherwise time-consuming and power hungry tasks required for brain-inspired computing. Due to their miniaturized dimensions, zero leakage and nonvolatility, spintronic devices are among the most promising class of beyond CMOS devices for this purpose. In this paper, we propose a novel spintronic structure based on antiferrromagnetically coupled domain walls. The device structure enables dedicated terminology for synaptic and neuron connections. This characteristic enables more efficient design of neuromorphic systems by allowing larger design space for designers. Furthermore, thanks to the coupling between the domain walls, the device can potentially operate at higher speeds; this higher speed contributes to improved performance of the neuromorphic system. In order to evaluate our proposed device structure, we developed a cross-layer simulation framework. Our simulation framework analyzes the neuromorphic system at the device, circuit and algorithm levels. Our simulation results show an order of magnitude improvement in the energy consumption compared to CMOS and analog neurons and up to 2X performance improvement as well as 8% improvement in the energy over state-of-the-art neuromorphic platforms using spintronic devices.