Field-free programmable spin logics based on spin Hall effect

Spin logics provide a shortcut toward logic-in-memory architectures. Here, using a T-type magnetic stack with a perpendicular magnetic layer, an in-plane layer, and a spacing layer in between, we can switch both the in-plane and perpendicular layers and independently control their magnetization without an external magnetic field. By initializing magnetization of the in-plane layer, we can further control chirality (clockwise and counterclockwise) of the current-dependence of perpendicular magnetization. Based on these properties and the majority gate theory, we experimentally construct five Boolean logic gates in a single device in the desired field-free condition, which steps forward to practical spin–orbit torque logics.