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arXiv:1812.01787 · Physical review. B./Physical review. B

Controlling stability of Bose-Einstein condensation of interacting magnons in an antiferromagnet by an external magnetic field

Naoya Arakawa

Published Jan 7, 2019• 7 citations
arXivHTMLPDF

Abstract

We propose a mechanism for destabilizing or stabilizing Bose-Einstein condensation (BEC) of interacting magnons in an antiferromagnet. We study how the interaction between magnons affects the magnon BEC in a two-sublattice antiferromagnet without and with an external magnetic field. We show that in the absence of the magnetic field the magnon BEC is destabilized by the attractive interband interaction, which is larger than the repulsive intraband interaction. We also show that in the presence of the magnetic field the magnon BEC is stabilized only if the magnetic field is large enough to make the intraband interaction larger than the interband interaction. Our results provide the first step for understanding the interaction effects on the magnon BEC in antiferromagnets and may open interaction physics of multicomponent BEC of magnons in magnets.

DOI
10.1103/physrevb.99.014405

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We propose a mechanism for destabilizing or stabilizing Bose-Einstein condensation (BEC) of interacting magnons in an antiferromagnet. We study how the interaction between magnons affects the magnon BEC in a two-sublattice antiferromagnet without and with an external magnetic field. We show that in the absence of the magnetic field the magnon BEC is destabilized by the attractive interband interaction, which is larger than the repulsive intraband interaction. We also show that in the presence of the magnetic field the magnon BEC is stabilized only if the magnetic field is large enough to make the intraband interaction larger than the interband interaction. Our results provide the first step for understanding the interaction effects on the magnon BEC in antiferromagnets and may open interaction physics of multicomponent BEC of magnons in magnets.
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.
We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field HHH near saturation (Hc)({H}_{c})(Hc​). Because Hc{H}_{c}Hc​ is independent of FM couplings, magnetic materials of this type can have small Hc{H}_{c}Hc​ which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature ${T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}$ from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}=1$ in quasi-one-dimensional magnets, and from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}\ensuremath{\approx}1$ $({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)$ in quasi-two-dimensional ones.
In this paper, we theoretically investigate the stability of spin-wave solitons in Bose-Einstein condensates of repulsive magnons, confined by an inhomogeneous external magnetic field described by a Gaussian well. For this purpose, we use the quasi-one-dimensional Gross-Pitaevskii equation to describe the behavior of the condensate. In order to solve the Gross-Pitaevskii equation, we used two different approaches: one analytical (variational method) and another numerical (split-step Crank-Nicolson method). The stability of the solutions and the validation of the numerical results were confirmed, respectively, through the anti-VK criterion and the virial theorem. Furthermore, the simulations described the behavior of physical quantities of interest such as chemical potential, energy per magnon and central density as a function of the nonlinearity of the model (magnon-magnon interactions). The theoretical results provide subsidies for a better understanding of the nonlinear phenomena related to the Bose-Einstein condensates of magnons in ferromagnetic films.
The Bose-Einstein condensation (BEC) was predicted by Einstein in 1925 and this effect is characterized by the formation of a collective quantum state, when macroscopic number of particles is governed by a single wave function. The BEC of magnons was discovered experimentally in superfluid phase of 3 He. In the present work we report our progress on the BEC of magnons investigations in solid antiferromagnets at low temperatures by magnetic resonance methods. The duration of the FID signal in two samples of easy-plane antiferromagnets CsMnF 3 has been studied. Obtained data confirm the formation of magnon BEC in antiferromagnet CsMnF 3 .
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.
The Bose-Einstein condensate of magnons (mBEC) that is formed at room temperature in parametrically pumped magnetic films is doubly degenerate: it is formed simultaneously in two spectral minima corresponding to the lowest-energy magnons propagating in opposite directions along the in-plane bias magnetic field. In this work the interactions of magnons in the mBEC are studied both theoretically and experimentally. It is shown by direct calculation that the magnons residing in each of the degenerate spectral minima of mBEC form a practically ideal magnon gas, as the attractive self-interaction between these magnons is very weak. At the same time, the interaction between the magnons residing in different spectral minima, corresponding to opposite directions of the magnon wave vector, is relatively strong and repulsive, leading to a repulsive total intermagnon interaction. By measuring the spectral characteristics of the mBEC it is shown that with increased magnon density the energy per magnon in the mBECs increases, thus confirming experimentally that the net intermagnon interaction in a doubly degenerate mBEC is repulsive.