# Mechanism for a Chemical Potential of Nonequilibrium Magnons in Parametric Parallel Pumping

## TL;DR

This paper theoretically demonstrates the generation of a magnon chemical potential in a nonequilibrium steady state induced by parametric parallel pumping, explaining experimental observations and advancing understanding of nonequilibrium magnon properties.

## Contribution

It provides the first theoretical demonstration of magnon chemical potential generation via parametric parallel pumping, highlighting a distinct distribution function with potential experimental relevance.

## Key findings

- Magnon distribution becomes Bose with μ=ω_p/2
- Distinct from standard theory, explains experimental generation
- Advances understanding of nonequilibrium magnon properties

## Abstract

We demonstrate how a magnon chemical potential is generated in parametric parallel pumping. We study how a time-periodic magnetic field of this pumping affects magnon properties of a ferrimagnet in a nonequilibrium steady state. We show that the magnon distribution function of our nonequilibrium steady state becomes the Bose distribution function with $\mu=\omega_{\textrm{p}}/2$, where $\mu$ is the magnon chemical potential and $\omega_{\textrm{p}}$ is the pumping frequency. This result is distinct from the absence of the magnon chemical potential in the standard theory and can qualitatively explain its generation in experiments. We believe our result is a first theoretical demonstration of the generation of the magnon chemical potential in the parametric parallel pumping, providing an important step towards a thorough understanding of properties of nonequilibrium magnons.