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Magnon Supercurrent in a Magnon Bose-Einstein Condensate subject to a Thermal Gradient

Per Axel Clausen, B. Hillebrands

Published Mar 2, 2015• 1 citation
OpenAlex

Abstract

We report evidence for the existence of a supercurrent of magnons in a magnon Bose-Einstein condensate (BEC) prepared in a room temperature yttrium-iron-garnet (YIG) magnetic film. The magnon BEC is formed in a parametrically populated magnon gas, and its temporal evolution is studied by time-resolved Brillouin light scattering (BLS) spectroscopy in the area of the BLS laser focus. It has been found that local laser heating in the center of the condensate decreases the density of the magnon BEC in the steady-state pump regime and it enhances the temporal decrease of the freely evolving magnon condensate after the termination of the pumping pulse, but it does not alter the relaxation dynamics of the gaseous magnon phase. This phenomenon is understood as the appearance of a magnon supercurrent within the condensate due to a temperature-gradient induced phase gradient in the condensate. Bose-Einstein condensation [1] can be achieved either by decreasing the temperature of a boson gas [2] or by increasing its density. The latter method is especially applicable to g ases of weakly interacting quasi-particles such as excitons [3] , polaritons [4, 5], photons [6], and magnons [7, 8]. When a spin system is pumped, and when the injected magnons thermalize through scattering processes conserving both their number and the total energy, a Bose-Einstein condensate (BEC) may be formed at the lowest energy state of the energy-momentum spectrum even at room temperature conditions of the magnetic film carrying the magnons [8, 9]. As the condensed magnon phase is localized in the global energy minimum, its group velocity is exactly zero and no energy transport can be associated with the magnon BEC. The situation can change, when a magnon supercurrent driven by a gradient in the phase of the wavefunction of a magnon condensate can be excited. Such a phase gradient can be induced by, e.g., a potential gradient or a temperature gradient. However, the dynamics of magnon condensates in such a gradient is still terra incognita. Here we provide experimental insight into the evolution of a magnon BEC in a thermal gradient generated by local laser heating. We show that such a heating influences both the steady-state characteristics and the transitional behavior of the magno n BEC, which can be understood using the concept of a magnon supercurrent. We study the temporal evolution of a magnon BEC in a single-crystal yttrium iron garnet (YIG, Y3Fe5O12) film by

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We report evidence for the existence of a supercurrent of magnons in a magnon Bose-Einstein condensate (BEC) prepared in a room temperature yttrium-iron-garnet (YIG) magnetic film. The magnon BEC is formed in a parametrically populated magnon gas, and its temporal evolution is studied by time-resolved Brillouin light scattering (BLS) spectroscopy in the area of the BLS laser focus. It has been found that local laser heating in the center of the condensate decreases the density of the magnon BEC in the steady-state pump regime and it enhances the temporal decrease of the freely evolving magnon condensate after the termination of the pumping pulse, but it does not alter the relaxation dynamics of the gaseous magnon phase. This phenomenon is understood as the appearance of a magnon supercurrent within the condensate due to a temperature-gradient induced phase gradient in the condensate. Bose-Einstein condensation [1] can be achieved either by decreasing the temperature of a boson gas [2] or by increasing its density. The latter method is especially applicable to g ases of weakly interacting quasi-particles such as excitons [3] , polaritons [4, 5], photons [6], and magnons [7, 8]. When a spin system is pumped, and when the injected magnons thermalize through scattering processes conserving both their number and the total energy, a Bose-Einstein condensate (BEC) may be formed at the lowest energy state of the energy-momentum spectrum even at room temperature conditions of the magnetic film carrying the magnons [8, 9]. As the condensed magnon phase is localized in the global energy minimum, its group velocity is exactly zero and no energy transport can be associated with the magnon BEC. The situation can change, when a magnon supercurrent driven by a gradient in the phase of the wavefunction of a magnon condensate can be excited. Such a phase gradient can be induced by, e.g., a potential gradient or a temperature gradient. However, the dynamics of magnon condensates in such a gradient is still terra incognita. Here we provide experimental insight into the evolution of a magnon BEC in a thermal gradient generated by local laser heating. We show that such a heating influences both the steady-state characteristics and the transitional behavior of the magno n BEC, which can be understood using the concept of a magnon supercurrent. We study the temporal evolution of a magnon BEC in a single-crystal yttrium iron garnet (YIG, Y3Fe5O12) film by
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.
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.
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 Bose-Einstein condensation (BEC) of magnons created by a strong pumping in ferromagnetic thin films of yttrium iron garnet used as systems of finite size is considered analytically. Such a peculiarity, typical for this magnetic material, as the presence of a minimum in the spectrum of spin waves at a finite value of the wave vector is taken into account. The definition of high-temperature BEC is introduced and its characteristics are discussed. A role of boundary conditions for spin variables is analyzed, and it is shown that in the case of free spins on the boundary the magnon lattice can form in the system. The factors responsible for its appearance are discussed