Nonlocal spin correlations mediated by a superconductor

Nonlocal charge correlations induced in two normal metals contacted separately to a superconductor have been studied intensively in the past few years. Here we investigate nonlocal correlations induced by the transfer of pure spin currents through a superconductor on a scale comparable to the superconducting coherence length. As with charge currents, two processes contribute to the nonlocal spin signal: crossed Andreev reflection (CAR), where an electron with spin-up injected from one normal metal into the superconductor results in a hole with spin-down being injected into the second normal metal, and elastic cotunneling (EC), where the electron with spin-up injected from the first normal metal results in an electron with spin-up being injected into the second normal metal. Unlike charge currents, however, the spin currents associated with CAR and EC add due to the fact that the bulk superconductor cannot sustain a net spin current.

Figure 1

Schematic diagram of the device. The bias current is applied from a ferromagnet $F_1$ to a normal metal $N_1$ and nonlocal voltage is measured between $F_2$ and $N_2$.

Figure 2

Nonlocal correlations near the $N_{1}S{N}_2$ structure. Pure spin current is injected from $N_1$ and a finite spin current is generated in $N_2$ by CAR and EC. One should note that the direction of the spin currents attributed to CAR and EC are in the same direction and there is no net spin accumulation in the superconductor.