Electrical spin injection through dual ferromagnetic electrodes in nonlocal spin valves

Spin injection efficiency has been a key factor for designing spintronic devices based on the lateral nonlocal spin valve. Here, we suggest a type of nonlocal spin valve in which the spin is injected electrically via dual ferromagnetic electrodes similar to a vertical spin valve and the spin detection is done by another ferromagnetic electrode. Using spin drift-diffusion theory, we study the spin injection, transport, and detection analytically and numerically. The results show that the spin injection efficiency can be enhanced significantly compared to the usual single ferromagnetic electrode injection, and thus the detected spin signal is increased greatly. Besides, by controlling the magnetization orientations of the two injecting ferromagnetic electrodes as well as the magnetization direction of the detection electrode, one can switch on and off the spin injection and thus form three or four output spin states. This feature is used for designing all spin-based three-state logic devices.