Journal of Experimental and Theoretical Physics Letters
Reply to Comment on “Bose–Einstein Condensation and Spin Superfluidity of Magnons in a Perpendicularly Magnetized Yttrium Iron Garnet Film” (JETP Letters 112, 299 (2020))
The unity of the laws of physics makes it possible to apply a unified approach to various physical systems. Bose–Einstein condensation of magnons (mBEC) and related magnon superfluidity were discovered almost four decades ago in antiferromagnetic superfluid 3He. Bose–Einstein condensation was then detected in a gas of ultracold atoms, a gas of exciton-polaritons, etc. A magnon BEC was then detected in antiferromagnets with coupled nuclear–electron precession and in yttrium iron garnet (YIG) films. Moreover, the properties of the magnon BEC in films are fundamentally different when the magnetic field is oriented along and across the film plane. In this short article, the main properties of mBEC and, in particular, the difference between the “classical” mBEC for magnons with zero momentum and “exotic” mBEC for magnons with nonzero momentum are highlighted.
The unity of the laws of physics makes it possible to apply a unified approach to various physical systems. Bose–Einstein condensation of magnons (mBEC) and related magnon superfluidity were discovered almost four decades ago in antiferromagnetic superfluid 3He. Bose–Einstein condensation was then detected in a gas of ultracold atoms, a gas of exciton-polaritons, etc. A magnon BEC was then detected in antiferromagnets with coupled nuclear–electron precession and in yttrium iron garnet (YIG) films. Moreover, the properties of the magnon BEC in films are fundamentally different when the magnetic field is oriented along and across the film plane. In this short article, the main properties of mBEC and, in particular, the difference between the “classical” mBEC for magnons with zero momentum and “exotic” mBEC for magnons with nonzero momentum are highlighted.
The conventional magnon Bose-Einstein condensation (BEC of magnons with k = 0) is a coherent state of excited magnons described by a common wave function. It was observed first in antiferromagnetic superfluid states of 3He. Here we report on the discovery of a very similar magnon BEC in ferrimagnetic film at room temperature. The experiments were performed in Yttrium Iron Garnet (YIG) films at a magnetic field oriented perpendicular to the film. The high-density quasiequilibrium state of excited magnon was formed by methods of pulse and/or Continuous Waves (CW) magnetic resonance. We have observed a Long Lived Induction Decay Signals (LLIDS), well known as a signature of spin superfluidity. We demonstrate that the BEC state may maintain permanently by continuous replenishment of magnons with a small radiofrequency (RF) field. Our finding opens the way for development of potential supermagnonic applications at an ambient conditions.
Under suitable experimental conditions, collective spin-wave excitations, magnons, form a Bose–Einstein condensate (BEC), where the spins precess with a globally coherent phase. Bose–Einstein condensation of magnons has been reported in a few systems, including superfluid phases of 3He, solid state systems, such as yttrium-iron-garnet films, and cold atomic gases. The superfluid phases of 3He provide a nearly ideal test bench for coherent magnon physics owing to experimentally proven spin superfluidity, the long lifetime of the magnon condensate, and the versatility of the accessible phenomena. We first briefly recap the properties of the different magnon BEC systems, with focus on superfluid 3He. The main body of this review summarizes recent advances in the application of magnon BEC as a laboratory to study basic physical phenomena connecting to diverse areas from particle physics and cosmology to vortex dynamics and new phases of condensed matter. This line of research complements the ongoing efforts to utilize magnon BECs as probes and components for potentially room-temperature quantum devices. In conclusion, we provide a roadmap for future directions in the field of applications of magnon BEC to fundamental research.
The formation of a Bose—Einstein condensate of magnons in a perpendicularly magnetized iron yttrium garnet film under radio-frequency pumping in a stripline has been studied experimentally. The characteristics of the nonlinear magnetic resonance and spatial distribution of the Bose—Einstein condensate of magnons in the gradient of a magnetic field have been analyzed. In these experiments, the system of bosonic magnons behaves in much the same way as the Bose—Einstein condensate of magnons in antiferromagnetic superfluid 3 He-B, which was previously studied in detail. The Bose—Einstein condensate of magnons forms a coherently precessing state having the properties of magnon superfluidity. Its stability is determined by the repulsion potential between excited magnons, which compensates the inhomogeneity of the magnetic field.
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.
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.
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.