Magnetoelectronic Spin Echo

We predict a spin echo in electron transport through layered ferromagnetic-normal-ferromagnetic metal structures: whereas a spin current polarized perpendicular to the magnetization direction decays when traversing a single homogeneous ferromagnet on the scale of the ferromagnetic spin-coherence length, it partially reappears by adding a second identical but antiparallel ferromagnet. This reentrant transverse spin current resembles the spin-echo effect in the magnetization of nuclei under pulsed excitations. We propose an experimental setup to measure the spin echo.

Figure 1

(a) The scattering region couples the left (1) and right (2) normal-metal nodes with nonequilibrium chemical potentials ${\widehat{\mu }}^{(1)}$ and ${\widehat{\mu }}^{(2)}$. (b) The scattering region consists of one uniform ferromagnet and normal metals. (c) The scattering region consists of two identical antiferromagnetically aligned ferromagnets separated by a normal metal. A partial electron spin echo can be seen in transport in this configuration.

Figure 2

Proposed experiment to observe the spin echo. Grey areas denote ferromagnetic layers. The spin echo is measured via the angular dependence of the potential $U(\theta )$ (or simply by its drop when $\theta$ is changed from $0$ to $\pi$).