Coupling the Higgs mode and ferromagnetic resonance in spin-split superconductors with Rashba spin-orbit coupling

We consider the Higgs mode at nonzero momentum in superconductors and demonstrate that in the presence of Rashba spin-orbit coupling, it couples linearly with an external exchange field. The Higgs-spin coupling dramatically modifies the spin susceptibility near the superconducting critical temperature and consequently enhances the spin pumping effect in a ferromagnetic insulator/superconductor bilayer system. We show that this effect can be detected by measuring the magnon-induced voltage generated by the inverse spin Hall effect.