Kinetics of Bose-Einstein condensation of magnons in Yttrium Iron Garnet films

TL;DR

This work addresses the nonequilibrium kinetics of magnon Bose-Einstein condensation (BEC) in YIG, showing that inter-minima equilibration is too slow for a quasi-equilibrium description. By formulating a Boltzmann kinetic equation with a dominant dipolar three-magnon collision channel, it derives inter-minima relaxation times, computes collision rates in the Born approximation, and explores practical solution schemes (Rayleigh-Jones step distributions and MEPP-based two-step temperatures) to relate pumping power to the effective magnon temperature. The results explain experimental observations of repulsive interactions and condensate splitting, and demonstrate that high effective temperatures for low-energy magnons arise from entropy-production optimization under pumping, providing a coherent kinetic framework for nonequilibrium magnon condensation in YIG. The approach clarifies the role of slow inter-minima dynamics in shaping the nonequilibrium steady state and offers quantitative links between pump parameters, relaxation processes, and observed condensate behavior.

Abstract

In this article, we explain the reason of the apparent contradiction between recent experiments [1] and [2] and earlier theoretical predictions [3] of strongly asymmetric condensate resulting in attractive interaction between the condensate magnons. We show that the relaxation time for equilibrium between two condensates at two minima of energy exceeds the time of experiment. Therefore, it should be described by Boltzmann kinetic equation. We develop the proper kinetic theory and find the relation between the critical pumping power and the effective temperature of over-condensate magnons.

Figures (5)

• Figure 1: Time evolution of the normalized condensate density after switching off the pumping. The density in the graph is normalized with respect to the initial density of condensate magnons. Without pumping the magnon density decreases exponentially in time. Each curve show the distribution of magnon density at a fixed time. The width of curves contracts with time or equivalently with the density that proves the repulsive interaction. Reprinted from Borisenko1. Used under https://creativecommons.org/licenses/by/4.0/.
• Figure 2: (a) A schematic representation of the experimental setup used in the study. (b) Following the application of a localized magnetic field pulse, the Bose-Einstein condensate (BEC) was observed to split into four distinct sub-clouds. Each sub-cloud propagated in a specific direction, determined by the condensate's initial wave vector and the slope of the relevant magnon dispersion branch. (c) The magnon dispersion relations were examined at two spatial locations: one at the center of the metal strip, where the magnetic field strength was $H_0+\Delta H$ and another at a more distant point with field strength $H_0$. Colored markers denote the spectral positions of the magnon states corresponding to the four sub-clouds after their separation. The associated group velocities, and thus their directions of motion in real space, are indicated schematically with arrows. Reprinted from Borisenko1. Used under https://creativecommons.org/licenses/by/4.0/.
• Figure 3: Compton scattering, consists of two consecutive 3-magnon processes. The scattering amplitude is proportional to the product of two 3rd order Hamiltonian verticis. Using the Fermi's golden rule for the inter-minima transition rate, we find the relaxation time $10^6\,s$, which is much longer than the lifetime of the condensate magnons, indicating that the condensate magnons are under-relaxed, not reaching their thermodynamic equilibrium.
• Figure 4: Direct 4-magnon processes, with amplitude proportional to the 4th order vertex. Using the Fermi's golden rule, we find the relaxation time $\sim 10^5\,\mathrm{s}$, which is also much longer than the lifetime of the condensate magnons and time of the experiment.
• Figure 5: The numerical results for the 1-step and 2-step function models. !-step function is shown by solid lines, the two-step function by thinner line . They demonstrate that the low energy magnons have higher temperature than the thermal magnons. We expect that the n-step diagram will asymptotically approach a continuous steady state curve, which characterizes the actual distribution of magnons accumulating near the ground state under pumping.