Modeling the Oblique Spin Precession in Lateral Spin Valves for Accurate Determination of Spin Lifetime Anisotropy: Effect of Finite Contact Resistance and Channel Length

摘要

The spin lifetime anisotropy is an important quantity for investigating thespin relaxation mechanisms in graphene and in heterostructures oftwo-dimensional materials. We generalize the diffusive spin transport equationsof oblique spin precession in a lateral spin valve with finite contactresistance. This yields a method to determine the spin lifetime anisotropyratio {\xi}={\tau}$_{\perp}$/{\tau}$_{\parallel}$, which is the ratio betweenlifetimes of spin polarized perpendicular and parallel to the graphene surface.By solving the steady-state Bloch equations, we show that the line-shape of theoblique spin precession signal can be described with six dimensionlessparameters, which can be solved analytically. We demonstrate that theanisotropic spin precession characteristics can be strongly suppressed bycontact induced spin relaxation originating from conductance mismatch betweenthe channel material and electrodes. To extract the spin lifetime anisotropyratio accurately, we develop a closed form equation that includes the effect offinite contact resistance. Furthermore, we demonstrate that in the high contactresistance regime, the minimum channel length required for accuratelydetermining the spin lifetime anisotropy for a sufficiently low externalmagnetic field is only determined by the diffusion coefficient of the channelmaterial, as opposed to the spin diffusion length. Our work provides anaccurate model to extract the spin lifetime anisotropy ratio from the obliquespin precession measurement, and can be used to guide the device design forsuch measurements.