A theoretical study of switching energy efficiency in sub-10-nm spintronic devices

Spin-transfer torque (STT) magnetic tunnel junctions (MTJs) in the sub-10-nm size range have shown enhancement in energy efficiency. This improved switching energy efficiency means a longer spin relaxation time, a corresponding stronger spin accumulation, and a resulting lower switching current density. This improvement in switching energy efficiency stems from a reduction in damping as the device size is reduced. This can be seen by a reduction in the damping constant in the Landau-Lifshitz Gilbert (LLG) equation. This term can take a range of values, and this range depends on the different contributions from the surface relative to the bulk. Specifically, at such small sizes the damping constant differs from the bulk damping constant. In this study, a detailed equation defining this surface-to-volume relative contribution was developed. This theory was tested through simulations involving a sub-10-nm cobalt cube utilizing the Object Oriented Micromagnetic Framework (OOMMF). These simulations showed a longer spin relaxation time with a decrease in device size (defined by side length) as well as a reduction in switching current density with a decrease in side length. This reduction in switching current density was approximately logarithmic versus volume, surface area, and side length. Moreover, in the sub-5-nm range, this reduction was nearly linear with respect to side length. These results agree with theoretical predictions and they are aligned with the experimentally demonstrated quantum size effect.