Since the early 1980s, most electronics have relied on the use of complementary metal-oxide-semiconductor (CMOS) transistors. However, the principles of CMOS operation, involving a switchable semiconductor conductance controlled by an insulating gate, have remained largely unchanged, even as transistors are miniaturized to sizes of 10 nanometres. We investigated what dimensionally scalable logic technology beyond CMOS could provide improvements in efficiency and performance for von Neumann architectures and enable growth in emerging computing such as artifical intelligence. Such a computing technology needs to allow progressive miniaturization, reduce switching energy, improve device interconnection and provide a complete logic and memory family. Here we propose a scalable spintronic logic device that operates via spin-orbit transduction (the coupling of an electron's angular momentum with its linear momentum) combined with magnetoelectric switching. The device uses advanced quantum materials, especially correlated oxides and topological states of matter, for collective switching and detection. We describe progress in magnetoelectric switching and spin-orbit detection of state, and show that in comparison with CMOS technology our device has superior switching energy (by a factor of 10 to 30), lower switching voltage (by a factor of 5) and enhanced logic density (by a factor of 5). In addition, its non-volatility enables ultralow standby power, which is critical to modern computing. The properties of our device indicate that the proposed technology could enable the development of multigenerational computing.