# Nonadiabaticity in spin pumping under relaxation

## TL;DR

This paper investigates how nonadiabatic effects influence spin pumping in a quantum dot system, revealing that spin current arises solely from nonadiabaticity and depends on precession frequency.

## Contribution

It provides a detailed analysis of nonadiabatic spin pumping using full counting statistics, highlighting the frequency-dependent behavior of spin current.

## Key findings

- Spin current is absent in the adiabatic limit.
- Nonadiabatic spin current varies linearly with frequency at low frequencies.
- Oscillations in spin current occur at high frequencies, indicating potential for tuning spin pumping.

## Abstract

Using a minimum model consisting of a magnetic quantum dot and an electron lead, we investigate spin pumping by its precessing magnetization. Focusing on the "adiabaticity", which is quantified using a comparison between the frequency of precession and the relaxation rate of the relevant system, we investigate the role of nonadiabaticity in spin pumping by obtaining the dependence of the spin current generated on the frequency of precession using full counting statistics. This evaluation shows that the steady-state population of the quantum dot remains unchanged by the precession owing to the rotational symmetry about the axis of precession. This implies that in the adiabatic limit the spin current is absent and that spin pumping is entirely a nonadiabatic effect. We also find that the nonadiabatic spin current depends linearly on the frequency in the low-frequency regime and exhibits an oscillation in the high-frequency regime. The oscillation points to an enhancement of spin pumping by tuning the frequency of precession.