# Microscopic theory of spin transport at the interface between the superconductor and a ferromagnetic insulator

## TL;DR

This paper develops a theoretical framework for understanding spin transport at the interface between a superconductor and a ferromagnetic insulator, highlighting the effects of superconducting coherence and noise characteristics.

## Contribution

It introduces formulas for spin current and noise at FI-SC interfaces considering microwave and thermal effects, advancing understanding of spin transport in superconductor-based systems.

## Key findings

- Superconducting coherence influences temperature dependence of spin current.
- Derived formulas for spin current and noise under microwave and thermal stimuli.
- Quantitative comparison of spin-current noise in equilibrium and non-equilibrium states.

## Abstract

We theoretically investigate spin transport at the interface between the ferromagnetic insulator(FI) and a superconductor(SC). Considering a simple FI-SC interface model, we derive formulas for the spin current and spin-current noise induced by microwave irradiation (spin pumping) or the temperature gradient (the spin Seebeck effect). We show how the superconducting coherence factor affects the temperature dependence of the spin current. We also calculate the spin-current noise in thermal equilibrium and in non-equilibrium states induced by the spin pumping, and compare them quantitatively for an yttrium-iron-garnet-NbN interface.