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arXiv:2212.06085

Slow inter-minima relaxation and its consequence for BEC of magnons

Gang Li, Haichen Jia, V. L. Pokrovsky

Published Dec 12, 2022• 0 citations
arXivHTMLPDF

Abstract

Two recent articles of the Munster University experimental team led by S.O. Demokritov displayed several important facts related to the Bose-Einstein condensation of magnons (BECM) under permanent pumping first discovered in 2006. They contradicted existing theories of this phenomenon, which predict the attractive interaction between magnons and strong spontaneous violation of the reflection symmetry. In this article, we show that these theories implicitly assumed all relaxation processes to be fast compared with the lifetime of the magnons, whereas one of them -- relaxation between two minima of energy -- is slow. We classify processes responsible for the inter-minima relaxation and present their analytic theory. We analyze how the slow inter-minima relaxation modifies the anticipated properties of a ferromagnet with the magnon condensate.

DOI
10.48550/arxiv.2212.06085

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Two recent articles of the Munster University experimental team led by S.O. Demokritov displayed several important facts related to the Bose-Einstein condensation of magnons (BECM) under permanent pumping first discovered in 2006. They contradicted existing theories of this phenomenon, which predict the attractive interaction between magnons and strong spontaneous violation of the reflection symmetry. In this article, we show that these theories implicitly assumed all relaxation processes to be fast compared with the lifetime of the magnons, whereas one of them -- relaxation between two minima of energy -- is slow. We classify processes responsible for the inter-minima relaxation and present their analytic theory. We analyze how the slow inter-minima relaxation modifies the anticipated properties of a ferromagnet with the magnon condensate.
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.
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.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The magnon BEC is manifested as the spontaneously emerging state of the precessing spins, in which all spins precess with the same frequency and phase even in an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.
Experimental evidence for Bose–Einstein condensation (BEC) of magnons at room temperature in a thin film of yttrium iron garnet (YIG) excited by parallel pumping is already available and different features of the experimental results have been explained qualitatively [Nature 443, 430 (2006)]. In the present work, we explain quantitatively different aspects of this experimental observation through spin wave treatment. In the case of parallel pumping field, we have developed a formula for the time required for the formation of magnon BEC in a thin film of ferromagnetic material. This relation is found to be in good agreement with known experimental results. In a similar treatment we predict the condition for the formation of BEC of magnons in the case of perpendicular pumping.
A quantised spin wave – magnon – in magnetic films can undergo Bose-Einstein condensation (BEC) into two energetically degenerate lowest-energy quantum states with nonzero wave vectors ±k BEC . This corresponds to two interfering condensates forming spontaneously in momentum space. Brillouin Light Scattering studies for a microwavepumped film with submicrometer spatial resolution experimentally confirm the existence of the two wavefunctions and show that their interference results in a nonuniform ground state of the condensate with the density oscillating in space. Moreover, fork dislocations in the density fringes provide direct experimental evidence for the formation of pinned half-quantum vortices in the magnon condensate. The measured amplitude of the density oscillation implies the formation of a nonsymmetric state that corresponds to nonequal occupation of two energy minima. We discuss the experimental findings and consider the theory of magnon condensates, which includes, to leading order, the contribution from the noncondensed magnons. The effect of the noncondensed magnon cloud is to increase the contrast of the asymmetric state and to bring about the experimental measurements. Introduction Magnons are quasiparticles corresponding to quantised spin waves that describe the collective motion of spins [1]. In recent years, it has become possible to realise a BEC of magnons in two remarkably different systems: in superfluid phases of an isotope of helium – Helium-3 at ultralow temperatures [2, 3] and in ferrimagnetic insulators [4, 5, 6, 7]. In the normal, noncondensed state, these magnetic materials exhibit a magnetically ordered state with a gas of magnons whose phases are not correlated. However, once condensation occurs, spins develop phase coherence resulting in a common global frequency and phase of precession. At room temperature, ferrimagnetic insulators, such as yttrium-iron garnet (YIG) films, together with a combination of an in-plane magnetic field and microwave radiation, are required for the magnon condensation [4, 5, 6, 7]. Therefore, in analogy with exciton– polariton condensates, this provides yet another example of a BEC of quasiparticle excitations in a solid-state system. Experimental Realisation of a Bose-Einstein Condensate of Magnons in an Epitaxial YIG-film A room-temperature Bose-Einstein condensate of magnons was created in an epitaxial YIG-film using an experimental setup shown in Fig. 25.1a, which, in general, is similar to that used in our previous studies [4, 5]. Given that magnons are quasiparticle excitations, their number is not conserved and, therefore, the chemical potential is zero.
The Spin Supercurrent and Bose-Einstein condensation of magnons, similar to an atomic BEC, was observed in 1984 in superfluid 3He-B. The same phenomena should exist in solid magnetic systems. We describe here the first observation of magnon BEC in solid easy plain antiferromagnets CsMnF3 and MnCO3. We have observed magnon BEC on a mode of coupled Nuclear-Electron precession. The dynamical properties of this mode have many similarities with NMR of superfluid 3He-A. The frequency changes with deflection of nuclear magnetization. Furthermore, the involvement of electron ordered subsystem gives the magnon-magnon interaction, spin waves and spin supercurrent, while the nuclear subsystem gives the relatively long time of relaxation.