Generation of pure superconducting spin current in magnetic heterostructures via non-locally induced magnetism due to Landau Fermi-liquid effects

Abstract: We propose a mechanism for the generation of pure superconducting spin-current carried by equal-spin triplet Cooper pairs in a superconductor (S) sandwiched between a ferromagnet (F) and a normal metal (N${\rm so}$) with intrinsic spin-orbit coupling. We show that in the presence of Landau Fermi-liquid interactions the superconducting proximity effect can induce non-locally a ferromagnetic exchange field in the normal layer, which disappears above the superconducting transition temperature of the structure. The internal Landau Fermi-liquid exchange field leads to the onset of a spin supercurrent associated with the generation of long-range spin-triplet superconducting correlations in the trilayer. We demonstrate that the magnitude of the spin supercurrent as well as the induced magnetic order in the N${\rm so}$ layer depends critically on the superconducting proximity effect between the S layer and the F and N$_{\rm so}$ layers and the magnitude of the relevant Landau Fermi-liquid interaction parameter. We investigate the effect of spin flip processes on this mechanism. Our results demonstrate the crucial role of Landau Fermi-liquid interaction in combination with spin-orbit coupling for the creation of spin supercurrent in superconducting spintronics, and give a possible explanation of a recent experiment utilizing spin-pumping via ferromagnetic resonance [Jeon $\it{ et}$ $\it{al.}$, Nat. Mat. ${\bf 17}$, 499 (2018)].