## Work Package B: Task 2

Micromagnetic simulation of magnon BEC in AFM systems. Investigation of stability of
BEC phase.

Finding equations of motion for magnon superfluids.

Our goal is to introduce the concept of chiral supermagnonics in AFM systems: chiral magnon BEC and chiral spin superfluidity. We consider an AFM system in the presence of homogeneous and inhomogeneous DMIs and an external DC magnetic field. We intend to study the formation and stability of chiral magnon BEC.

In principle, using micromagnetic simulations, we wish to show that thermal magnons can be amplified using parametric pumping technique. Tuning system parameters, we expect to find the criteria for magnon BEC in real space and a magnon BEC state with only one magnon helicity.

We will investigate the temporal evolution of parametrically generated magnons and condensed magnons, numerically. Additionally, we will focus on the case of large magnon densities, where magnon-magnon scatterings become relevant. These scatterings are crucial for the magnon thermalization and stability of the BEC phase. Since dipolar interaction is negligible in AFM systems, four-magnon scatterings are dominant scattering processes. Thus, it is essential to understand the nature of four-magnon scatterings in this system.

The last question is about the possibility of magnon supercurrent. As soon as magnon BEC is created in a part of the sample, applying a temperature gradient leads to the motion of condensed magnons. We will study this effect using a two-fluid theory in which the system under sconsideration is described as a mixture of normal thermal magnons and a frictionless superfluid. One of the advantages of AFM systems respect to their FM counterparts, among other things, is that thermal AFM magnons do not carry spin angular momentum, and then all detected spin angular momentums are carried by superfluid magnons.