Finite-frequency spin susceptibility and spin pumping in superconductors with spin-orbit relaxation

Abstract

Static spin susceptibility of superconductors with spin-orbit relaxation has been calculated in the seminal work of A.A. Abrikosov and L.P. Gor'kov [Sov. Phys. JETP, {\bf 15}, 752 (1962)]. Surprisingly the generalization of this result to finite frequencies has not been done despite being quite important for the modern topic of superconducting spintronics. The present paper fills this gap by deriving the analytical expression for spin susceptibility. The time-dependent spin response is shown to be captured by the quasiclassical Eilenberger equation with collision integrals corresponding to the ordinary and spin-orbit scattering. Using the developed formalism we study the linear spin pumping effect between the ferromagnet and the adjacent superconducting film. The consequences for understanding recent experiments demonstrating the modification of Gilbert damping by the superconducting correlations are discussed.

References in corpus (10)

• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Theory of magnetic excitations in iron-based layered superconductors
• Neutron scattering as a probe of the Fe-pnicitide superconducting gap
• Enhanced DC Spin Pumping into a Fluctuating Ferromagnet near Tc
• Spin dynamics in a superconductor / ferromagnet proximity system
• Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impurities
• Microscopic theory of spin transport at the interface between the superconductor and a ferromagnetic insulator
• Magnetization dynamics in proximity-coupled superconductor/ferromagnet/superconductor multilayers
• Proximity effect-assisted absorption of spin currents in superconductors
• Abrikosov vortex nucleation and its detrimental effect on superconducting spin pumping in Pt/Nb/Ni80Fe20/Nb/Pt proximity structures

Cited by in corpus (21)

• Large enhancement of spin pumping due to the surface bound states in normal metal/superconductor structures
• Magnon spin current induced by triplet Cooper pair supercurrents
• Anisotropic superconducting spin transport at magnetic interfaces
• Anomalous Gilbert Damping and Duffing Features of the SFS {\boldmath ${\phi }_0$} Josephson Junction
• Dynamics of two ferromagnetic insulators coupled by superconducting spin current
• Magnon-Cooparons in magnet-superconductor hybrids
• Ferromagnetic resonance modulation in $d$-wave superconductor/ferromagnetic insulator bilayer systems
• Superconductivity provides a giant enhancement to the spin battery effect
• Multi-Particle Tunneling Transport at Strongly-Correlated Interfaces
• Spin-pumping in superconductor-antiferromagnetic insulator bilayers
• Renormalization of antiferromagnetic magnons by superconducting condensate and quasiparticles
• Magnetic eigenmodes in chains of coupled phi0-Josephson junctions with ferromagnetic weak links
• Dynamical Majorana Ising spin response in a topological superconductor-magnet hybrid by microwave irradiation
• Spin transport between polarized Fermi gases near the ferromagnetic phase transition
• Magnon influence on the superconducting density of states in superconductor$-$ferromagnetic-insulator bilayers
• Anisotropic spin-current spectroscopy of ferromagnetic superconducting gap symmetries
• Coupling the Higgs mode and ferromagnetic resonance in spin-split superconductors with Rashba spin-orbit coupling
• Magnonic spin current shot noise in an itinerant Fermi gas
• Spin Pumping into Carbon Nanotubes
• Spin Pumping into two-dimensional systems
• Spin pumping into quantum spin chains