FMR and voltage induced transport in normal metal-ferromagnet-superconductor trilayers

TL;DR

This paper investigates how bias voltage and magnetization precession influence charge and spin transport in normal metal-ferromagnet-superconductor trilayers, revealing that voltage-induced currents are unaffected by precession, while transverse spin currents depend on scattering details.

Contribution

It provides a theoretical analysis of non-equilibrium charge and spin currents in FMR-S trilayers, including a simplified formula for transverse spin current in certain structures.

Findings

Voltage-induced charge and longitudinal spin currents are unaffected by magnetization precession.

Transverse spin current depends on spin-dependent conductances and scattering matrix details.

Derived a simplified expression for transverse spin current in long ferromagnetic structures.

Abstract

We study the subgap spin and charge transport in normal metal-ferromagnet-superconductor trilayers induced by bias voltage and/or magnetization precession. Transport properties are discussed in terms of time-dependent scattering theory. We assume the superconducting gap is small on the energy scales set by the Fermi energy and the ferromagnetic exchange splitting, and compute the non-equilibrium charge and spin current response to first order in precession frequency, in the presence of a finite applied voltage. We find that the voltage-induced instantaneous charge current and longitudinal spin current are unaffected by the precessing magnetization, while the pumped transverse spin current is determined by spin-dependent conductances and details of the electron-hole scattering matrix. A simplified expression for the transverse spin current is derived for structures where the ferromagnet is longer than the transverse spin coherence length.