Magnetism induced by nonlocal spin-entangled electrons in a superconducting spin-valve

In the traditional view, the magnetic moment appearing in the superconducting region is induced by equal-spin triplet superconducting correlations in superconductor (S) ferromagnet (F) heterostructure with noncollinear magnetization. In this paper, we represent that in (N-normal-metal) spin-valve structure the induced magnetic moment emerging in both the S and N regions can also be generated by Cooper pair splitting: one electron coherently tunnels from the S layer into the F 1 layer, and the other one stays in the S layer or tunnels into the N layer. Two electrons are spatially separated from each other but their total spin ground state is entangled in this process. In contrast, the magnetic moment induced by the equal-spin triplet correlations hardly penetrates from the S layer into the N layer. In particular, by tuning the size of the exchange field and the thickness of the F 1 layer, one may control the direction of the induced magnetic moment in the N layer. This interesting phenomenon can be attributed to the phase-shift obtained by the spin-entangled electrons. Our theoretical proposal will offer an effective way to control the entanglement of the nonlocal electrons, and also may provide possible explanations for previous and recent experimental observations (Stamopoulos et al 2005 Phys. Rev. B 72 212514; Ovsyannikov et al 2016 J. Exp. Theor. Phys. 122 738; Flokstra et al 2016 Nat. Phys. 12 57).