Proposal for quantum spin tomography in ferromagnet-normal conductors

We present a theory for a complete reconstruction of nonlocal spin correlations in ferromagnet-normal conductors. This quantum spin tomography is based on cross-correlation measurements of electric currents into ferromagnetic terminals with controllable magnetization directions. For normal injectors, nonlocal spin correlations are universal and strong. The correlations are suppressed by spin-flip scattering and, for ferromagnetic injectors, by increasing injector polarization.

Figure 1

(Color online) (a) A normal conductor is connected to an injector biased at voltage $V$ and two detector nodes $A$ and $B$. The node $A$ $\left(B\right)$ is coupled to grounded ferromagnetic detector terminals $A1$ and $A2$ ($B1$ and $B2$). (b) Node $A$ is connected to the normal conductor, as well as nodes $A1$ and $A2$ via tunnel conductances $G_A$, $G_{A1}$, and $G_{A2}$, respectively. The polarizations ${\mathbf{P}}_{A1}$ and ${\mathbf{P}}_{A2}$ of the contacts to the ferromagnetic terminals are in opposite directions.