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Радиотехника и электроника / Journal of Communications Technology and Electronics

Nonlinear magnetization dynamics in Bose-Einstein condensation of magnons

A. D. Gasanov, A. A. Matveev, A. R. Safin, С. А. Никитов

Published Jan 1, 2025• 0 citations
Publisher

Abstract

An equation for the dynamics of a Bose-Einstein condensate of magnons in a ferromagnetic film is presented, derived from quantum-mechanical theory. The main interactions affecting the evolution of the condensed state are considered. The transition from the equation for the annihilation operator of condensed magnons to an autonomous system of first-order differential equations describing their amplitude and phase is made. Phase trajectories of such a system were studied by constructing phase portraits and determining the stability of stationary points.

DOI
10.7868/s3034590125040078

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An equation for the dynamics of a Bose-Einstein condensate of magnons in a ferromagnetic film is presented, derived from quantum-mechanical theory. The main interactions affecting the evolution of the condensed state are considered. The transition from the equation for the annihilation operator of condensed magnons to an autonomous system of first-order differential equations describing their amplitude and phase is made. Phase trajectories of such a system were studied by constructing phase portraits and determining the stability of stationary points.
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We propose a stabilizing mechanism for the Bose-Einstein condensation (BEC) of interacting magnons in ferrimagnets and ferromagnets. By studying the effects of the magnon-magnon interaction on the stability of the magnon BEC in a ferrimagnet and two ferromagnets, we show that the magnon BEC remains stable even in the presence of the magnon-magnon interaction in the ferrimagnet and ferromagnet with a sublattice structure, while it becomes unstable in the ferromagnet without a sublattice structure. This indicates that the existence of a sublattice structure is the key to stabilizing the BEC of interacting magnons, and the difference between the spin alignments of a ferrimagnet and a ferromagnet is irrelevant. Our result can resolve a contradiction between experiment and theory in the magnon BEC of yttrium iron garnet. Our theoretical framework may provide a starting point for understanding the physics of the magnon BEC including the interaction effects.
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We discuss the dynamics of a quantum phase transition in a spin-1 Bose–Einstein condensate when it is driven from the magnetized broken-symmetry phase to the unmagnetized 'symmetric' polar phase. We determine where the condensate goes out of equilibrium as it approaches the critical point, and compute the condensate magnetization at the critical point. This is done within a quantum Kibble–Zurek scheme traditionally employed in the context of symmetry-breaking quantum phase transitions. Then we study the influence of the non-equilibrium dynamics near a critical point on the condensate magnetization. In particular, when the quench stops at the critical point, nonlinear oscillations of magnetization occur. They are characterized by a period and an amplitude that are inversely proportional. If we keep driving the condensate far away from the critical point through the unmagnetized 'symmetric' polar phase, the amplitude of magnetization oscillations slowly decreases reaching a nonzero asymptotic value. That process is described by an equation that can be mapped onto the classical mechanical problem of a particle moving under the influence of harmonic and `anti-friction' forces whose interplay leads to surprisingly simple fixed-amplitude oscillations. We obtain several scaling results relating the condensate magnetization to the quench rate, and verify numerically all analytical predictions.
The properties of spin-1 Bose gases with ferromagnetic interactions in the presence of a nonzero magnetic field are studied. The equation of state and thermodynamic quantities are worked out with the help of a mean-field approximation. The phase diagram besides Bose-Einstein condensation contains a first-order transition where two values of the magnetization coexist. The dynamics is investigated with the help of the random phase approximation. The soft mode corresponding to the critical point of the magnetic phase transition is found to behave like in conventional theory.