# Chemical potential of an antiferromagnetic magnon gas

## TL;DR

This paper derives the chemical potential of antiferromagnetic magnons, revealing tunability via magnetic fields and proposing experimental detection methods, advancing understanding of magnetic quantum phenomena.

## Contribution

It introduces a theoretical framework for the chemical potential of antiferromagnetic magnons and suggests experimental testing using NV-center relaxometry.

## Key findings

- Magnon eigenmodes have equal and opposite chemical potentials.
- Chemical potential can be tuned with AC magnetic fields.
- Proposes NV-center relaxometry for experimental validation.

## Abstract

Understanding the statistics of quasi-particle excitations in magnetic systems is essential for exploring new magnetic phases and collective quantum phenomena. While the chemical potential of a ferromagnetic gas has been extensively investigated both theoretically and experimentally, its antiferromagnetic counterpart remains uncharted. Here, we derive the statistics of a two-component U(1)-symmetric Bose gas and apply our results to an axially-symmetric antiferromagnetic insulator. We find that the two magnon eigenmodes of the system are described by an equal and opposite chemical potential, in analogy with a particle-antiparticle pair. Furthermore, we derive the thermomagnonic torques describing the interaction between the coherent and incoherent antiferromagnetic spin dynamics. Our results show that the magnitude and sign of the chemical potential can be tuned via an AC magnetic field driving resonantly one of the magnon modes. Finally, we propose NV-center relaxometry as a method to experimentally test our predictions.