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

Abstract

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