# Spin backflow: a non-Markovian effect on spin pumping

## TL;DR

This paper investigates how non-Markovian effects, specifically spin backflow, influence spin pumping in nanoscale devices, revealing that backflow reduces spin current at high frequencies and prevents unphysical divergences.

## Contribution

It introduces the concept of spin backflow as a non-Markovian effect in spin pumping, providing a quantifier and demonstrating its impact on spin current generation.

## Key findings

- Non-Markovian dynamics cause a temporal backflow of spin.
- Spin backflow reduces spin current at high precession frequencies.
- The effect prevents divergence of spin current in the high frequency limit.

## Abstract

The miniaturization of spintronic devices, specifically, nanoscale devices employing spintronics, has attracted intensive attention from a scientific as well as engineering perspective. In this paper, we study non-Markovian effect on spin pumping to describe spin current generation driven by arbitrary precession frequency of magnetization in a quantum dot attached to an electron lead. Although the Markovian approximation can be used when driving is sufficiently slow compared with relaxation times in electron tunneling, recent developments in nano-spintronic devices show that we need to include non-Markovian effects. In contrast to the one-way-only nature of the spin current generation under the Markovian dynamics, we find that the non-Markovian dynamics exhibits a temporal backflow of spin, call spin backflow for brevity. We capture the phenomenon by introducing its quantifier, and show that the backflow significantly reduces the amount of spin current when the frequency exceeds the relaxation rate. This prevents unphysical divergence of the spin current in the high frequency limit that occurs under the Markovian approximation. We believe our analysis provides an understanding of the spin pumping particularly in regard to producing a more efficient spin current generation over shorter time scales by going beyond the conventional Markovian approximation.