Manifestation of two-channel nonlocal spin transport in the shapes of Hanle curves

The dynamics of charge-density fluctuations in a system of two tunnel-coupled wires contains two diffusion modes with dispersion iω = Dq2 and iω = Dq2 + 2τt, where D is the diffusion coefficient and τt is the tunneling time between the wires. The dispersion of corresponding spin-density modes depends on magnetic field as a result of the spin precession with Larmour frequency ωL. The presence of two modes affects the shape of the Hanle curve describing the spin-dependent resistance R between the ferromagnetic strips covering the nonmagnetic wires. We demonstrate that the relative shapes of the R(ωL) curves, one measured within the same wire and the other measured between the wires, depends on the ratio τt /τs, where τs is the spin-diffusion time. If the coupling between the wires is local, i.e., only at the point x = 0, then the difference of the shapes of intrawire and interwire Hanle curves reflects the difference in statistics of diffusive trajectories, which "switch" or do not switch near x = 0. When one of the coupled wires is bent into a loop with a radius a, the shape of the Hanle curve reflects the statistics of random walks on the loop. This statistics is governed by the dimensionless parameter a/ √ Dτs .