Lateral diffusive spin transport in layered structures

A one-dimensional (1D) theory of lateral spin-polarized transport is derived from the two-dimensional flow in the vertical cross section of a stack of ferromagnetic and paramagnetic layers. This takes into account the influence of the lead on the lateral current underneath, in contrast to the conventional 1D modeling by the collinear configuration of lead/channel/lead. Our theory is convenient and appropriate for the current in-plane configuration of an all-metallic spintronics structure as well as for the planar structure of a semiconductor with ferromagnetic contacts. For both systems we predict the optimal contact width for maximal magnetoresistance and propose an electrical measurement of the spin-diffusion length for a wide range of materials.

Figure 1

(Color online) A two-dimensional sketch of a planar system with ferromagnetic and normal materials. $A\text{–}D$ represent boundaries which may be connected to the external circuit. All of the labeled lengths enter into our 1D transport equations.

Figure 2

(a) Magnetoresistance effect versus the contact width of a GaAs channel at 300 K. The solid (dashed) line denotes a confined (open) structure. The dots are the results of a 2D numerical computation in the confined geometry. (b) Magnetoresistive effect versus $\alpha$ for three cases of spin selectivity, $\beta ∕\alpha$ in the confined geometry, calculated for the optimal contact width corresponding to the same $\alpha$ value shown in (c).

Figure 3

(a) The magnetoresistive effect versus the right contact width in the $\mathrm{Al}∕\mathrm{Co}$ system at 300 K. (b) The current density profile in the Al layer for a parallel magnetic configuration at the optimal contact width. Solid (dash) lines denote spin-up (down) current components. The total current is constant where in the dip regions along the $\mathrm{Al}∕\mathrm{Co}$ interfaces currents propagate in both layers. (c) Same as (b) for the antiparallel magnetic configuration.