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

Abstract

Dynamics of charge-density fluctuations in a system of two tunnel-coupled wires contains two diffusion modes with dispersion iw=Dq^2 and iw =Dq^2+2/tau_t, where D is the diffusion coefficient and tau_t is the tunneling time between the wires. The dispersion of corresponding spin-density modes depends on magnetic field as a result of spin precession with Larmour frequency, w_L. The presence of two modes affects the shape of the Hanle curve describing the spin-dependent resistance, R, between ferromagnetic strips covering the non-magnetic wires. We demonstrate that the relative shapes of the R(w_L)-curves, one measured within the same wire and the other measured between the wires, depends on the ratio tau_t/tau_s, where tau_s 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 intra-wire and inter-wire 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/(D tau_s)^(1/2).