Bose-Einstein Condensation Of Magnons Research Articles

Magnon Bose–Einstein condensates: From time crystals and quantum chromodynamics to vortex sensing and cosmology

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.

Local temperature control of magnon frequency and direction of supercurrents in a magnon Bose–Einstein condensate

The creation of temperature variations in magnetization, and hence in the frequencies of the magnon spectrum in laser-heated regions of magnetic films, is an important method for studying Bose–Einstein condensation of magnons, magnon supercurrents, Bogoliubov waves, and similar phenomena. In our study, we demonstrate analytically, numerically, and experimentally that, in addition to the magnetization variations, it is necessary to consider the connected variations of the demagnetizing field. In the case of a heat-induced local minimum of the saturation magnetization, the combination of these two effects results in a local increase in the minimum frequency value of the magnon dispersion at which the Bose–Einstein condensate emerges. As a result, a magnon supercurrent directed away from the hot region is formed.

Field-induced Bose–Einstein condensation in zigzag spin chain KGaCu(PO4)2

Single crystals of GaKCu(PO4)2 were synthesized using the hydrothermal method, and subsequent measurements of specific heat, magnetic susceptibility, and high-field magnetization were performed. A broad peak is observed in the magnetic susceptibility and specific heat curves, with the maximum values appearing at about 11.5 K and 5.29 K, respectively. The highest maximum peak value of susceptibility is observed when the magnetic field is applied along the c-axis, followed by the a-axis, b-axis, and polycrystalline samples. These indicate that the system exhibits one-dimensional magnetism and the magnetic easy axis is the c axis. The magnetization at 2 K reveals the occurrence of a field-induced Bose–Einstein condensation (BEC) phase within the magnetic field range of approximately 8−12 T. High-field magnetization up to 40 T indicates that the compound reaches magnetization saturation as the field exceeds H s = 12 T. Through systematic measurements, a field-temperature (H−T) phase diagram was constructed, and dome-like phase boundaries were observed. The findings suggest that GaKCu(PO4)2 is a spin gap system and a promising candidate for studying BEC of magnons due to its phase transition boundary occurring at low magnetic fields.

Field-induced bound-state condensation and spin-nematic phase in SrCu2(BO3)2 revealed by neutron scattering up to 25.9 T

In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu2(BO3)2, no clear magnon BEC could be observed, pointing to an alternative mechanism, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu2(BO3)2 up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu2(BO3)2 is best understood as a condensate of bosonic Cooper pairs.

Transition to a Magnon Bose–Einstein Condensate

Parameters of the transition from classical dynamics of spin waves to the formation of a coherent magnon Bose–Einstein condensate have been obtained experimentally for the first time. The studies are performed on an yttrium iron garnet film beyond the radio frequency excitation region; thus, the coherent state of magnons is an eigenstate rather than a state induced by an external radio frequency field. The critical magnon density at the formation of the Bose–Einstein condensate is in good agreement with a theoretically predicted value. The transition is obtained at room temperature, which is possible owing to a small mass of magnons and their high density.

Bose-Einstein condensation of magnons in quantum magnets with spin-orbit coupling in a Zeeman field

We study the response of a quantum magnet with spin-orbit coupling (SOC) to a Zeeman field by constructing effective actions and performing renormalization group (RG) analysis. There are several novel classes of quantum phase transitions at a low ${h}_{c1}$ and an upper critical field ${h}_{c2}$ driven by magnon condensations at commensurate (C) or incommensurate (IC) momenta $0<{k}_{0}<\ensuremath{\pi}$. The intermediate IC-skyrmion crystal (IC-SkX) phase is controlled by a line of fixed points in the RG flows labeled by ${k}_{0}$. We derive the relations between the quantum spin and the order parameters of the effective actions which determine the spin-orbital structures of the IC-SkX phase. We also analyze the operator contents near ${h}_{c1}$ and ${h}_{c2}$ which determine the exotic excitation spectra inside the IC-SkX. The intrinsic differences between the magnon condensations at the C and IC momenta are explored. The two critical fields ${h}_{c1}<{h}_{c2}$ and the intermediate IC-SkX phase could be a generic feature to any quantum magnets with SOC in a Zeeman field. Experimental implications to some materials or cold atom systems with SOC in a Zeeman field are presented.

Spin reorientation in easy-plane kagome ferromagnet Li9Cr3(P2O7)3(PO4)2

We report the successful growth and characterization of Li9Cr3(P2O7)3(PO4)2 single crystal, and investigate its magnetic properties under external magnetic fields via magnetization and heat capacity measurements. Our study reveals that Li9Cr3(P2O7)3(PO4)2 is an easy-plane kagome ferromagnet with S = 3/2, as evidenced by the Curie–Weiss temperature of 6 K which implies a ferromagnetic exchange coupling in the material. Under zero magnetic field, Li9Cr3(P2O7)3(PO4)2 undergoes a magnetic transition at T C = 2.7 K from a paramagnetic state to a ferromagnetically ordered state with the magnetic moment lying in the kagome plane. By applying a c-axis directional magnetic field to rotate the spin alignment from the kagome plane to the c-axis, we observe a reduction in the magnetic transition temperature as the field is increased. We construct a magnetic phase diagram as a function of temperature and magnetic field applied parallel to the c-axis of Li9Cr3(P2O7)3(PO4)2 and find that the phase boundary is linear over a certain temperature range. Regarding that theoretically, the field-induced phase transition of the spin reorientation in the easy-plane ferromagnet can be viewed as the ferromagnetic magnon Bose–Einstein condensation (BEC), the phase boundary scaling of field-induced (B ∥ c) magnetic transition in Li9Cr3(P2O7)3(PO4)2 can be described as the quasi-2D magnon BEC, which has been observed in other ferromagnetic materials such as K2CuF4.

Conductivity Enhancement in a Diffusive Fermi Liquid due to Bose-Einstein Condensation of Magnons.

We theoretically study the conductivity of a disordered 2D metal when it is coupled to ferromagnetic magnons with a quadratic spectrum and a gap Δ. In the diffusive limit, a combination of disorder and magnon-mediated electron interaction leads to a sharp metallic correction to the Drude conductivity as the magnons approach criticality, i.e., Δ→0. The correction is nonsingular and is distinctively weaker than, for example, the log-squared correction obtained when disordered electrons couple to diffusive spin fluctuations near a Hertz-Millis transition. The possibility of verifying this prediction in an S=1/2 easy-plane ferromagnetic insulator K_{2}CuF_{4} under an external magnetic field is proposed. Our results show that the onset of a magnon Bose-Einstein condensation in an insulator can be detected via electrical transport measurements on the proximate metal.

Confinement of Bose–Einstein magnon condensates in adjustable complex magnetization landscapes

Coherent wave states such as Bose–Einstein condensates (BECs), which spontaneously form in an overpopulated magnon gas even at room temperature, have considerable potential for wave-based computing and information processing at microwave frequencies. The ability to control the transport properties of magnon BECs plays an essential role in their practical use. Here, we demonstrate the spatiotemporal control of the BEC density distribution through the excitation of magnon supercurrents in an inhomogeneously magnetized yttrium iron garnet film. The BEC is created by microwave parametric pumping and probed by Brillouin light scattering spectroscopy. The desired magnetization profile is prepared by heating the film with optical patterns projected onto its surface using a phase-based wavefront modulation technique. Specifically, we observe a pronounced spatially localized magnon accumulation caused by magnon supercurrents flowing toward each other originating in two heated regions. This accumulation effect increases the BEC lifetime due to the constant influx of condensed magnons into the confinement region. The shown approach to manipulate coherent waves provides an opportunity to extend the lifetime of freely evolving magnon BECs, create dynamic magnon textures, and study the interaction of magnon condensates formed in different regions of the sample.

Classical analog of qubit logic based on a magnon Bose–Einstein condensate

Advances in quantum computing and telecommunications stimulate the search for classical systems allowing partial implementation of a similar functionality under less stringent environmental conditions. Here, we present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose–Einstein condensate (BEC) formed at opposite wavevectors in a room-temperature yttrium-iron-garnet ferrimagnetic film. Employing micromagnetic numerical simulations, we show the use of wavelength-selective parametric pumping to controllably initialize and manipulate the two-component BEC. Next, by modeling the interaction of this BEC with a pulse- and radio-frequency-driven dynamic magnonic crystal we translate the concept of Rabi-oscillations into the wavevector domain and demonstrate how to manipulate the magnon-BEC system regarding the polar and azimuthal angles in the Bloch sphere representation. We hope that our study provides a significant stimulus on the boundary between qubit functionality and classical systems of interacting BECs, which use a subset of qubit-based algorithms.

Magic-angle magnonic nanocavity in a magnetic moiré superlattice

Moir\'e superlattices have recently been extensively studied in both electronic and photonic systems, e.g., magic-angle bilayer graphene showing superconductivity and twisted bilayer photonic crystals leading to magic-angle lasers. However, the moir\'e physics is barely studied in the field of magnonics, i.e., in using spin waves for information processing. In this work, we report magnon flat-band formation in twisted bilayer magnonic crystals at the optimal ``magic angle'' and interlayer exchange coupling combination using micromagnetic simulations. At the flat-band frequency, magnons undergo a strong two-dimensional confinement with a lateral scale of about 185 nm. The magic-angle magnonic nanocavity occurs at the $AB$ stacking region of a moir\'e unit cell, unlike its photonic counterpart which is at the $AA$ region, due to the exchange-induced magnon spin torque. The magnon flat band originates from band structure reformation induced by interlayer magnon-magnon coupling. Our results enable efficient accumulation of magnon intensity in a confined region that is key for potential applications such as magnon Bose-Einstein condensation and even magnon lasing.

Magnon condensation in dimerized antiferromagnets with spin-orbit coupling

Bose-Einstein condensation (BEC) of triplet excitations triggered by a magnetic field, sometimes called magnon BEC, in dimerized antiferromagnets gives rise to a long-range antiferromagnetic order in the plane perpendicular to the applied magnetic field. To explore the effects of spin-orbit coupling on magnon condensation, we study a spin model on a distorted honeycomb lattice with dimerized Heisenberg exchange ($J$ terms) and uniform off-diagonal exchange ($\Gamma'$ terms) interactions. Via variational Monte Carlo calculations and spin-wave theory, we find that an out-of-plane magnetic field can induce different types of long-range magnetic orders, no matter if the ground state is a non-magnetic dimerized state or an ordered N\'{e}el state. Furthermore, the critical properties of field-driven phase transitions in the presence of spin-orbit couplings, as illustrated from spin-wave spectrum and interpreted by effective field theory, can be different from the conventional magnon BEC. Our study is helpful to understand the rich phases of spin-orbit coupled antiferromagnets induced by magnetic fields.

Magneto-optical imaging of coherent spin dynamics in ferrites.

The explosive development of quantum magnonics is associated with the possibility of its use as macroscopic quantum systems. In particular, they can find an application for quantum computing processors and other devices. The recently discovered phenomenon of magnon Bose-Einstein condensation and coherent precession of magnetization can be used for these purposes. Our letter describes a method for the optical observation of the coherently precessing magnetization in conditions when the concentration of magnons reaches the value necessary for their quantum condensation. The investigations were conducted in the out-of-plane magnetized yttrium iron garnet films. The required magnon density was achieved by magnetic resonance technique. The magneto-optical imaging method provides such important parameters of the coherent spin dynamics as the amplitude and phase distributed all over the sample. It should become an indispensable read-out tool for the upcoming quantum technologies based on the magnon Bose-Einstein condensation.

Dzyaloshinskii-Moriya anisotropy effect on field-induced magnon condensation in the kagome antiferromagnet α−Cu3.26Mg0.74(OH)6Br2

We performed a comprehensive electron spin resonance, magnetization and heat capacity study on the field-induced magnetic phase transitions in the kagome antiferromagnet $\alpha-Cu_3Mg(OH)_6Br_2$. With the successful preparation of single crystals, we mapped out the magnetic phase diagrams under the $c$-axis and $ab$-plane directional magnetic fields $B$. For $B\|c$, the three-dimensional (3D) magnon Bose-Einstein condensation (BEC) is evidenced by the power law scaling of the transition temperature, $T_c\propto (B_c-B)^{2/3}$. For $B\|ab$, the transition from the canted antiferromagetic (CAFM) state to the fully polarized (FP) state is a crossover rather than phase transition, and the characteristic temperature has a significant deviation from the 3D BEC scaling. The different behaviors of the field-induced magnetic transitions for $B\|c$ and $B\|ab$ could result from the Dzyaloshinkii-Moriya (DM) interaction with the DM vector along the $c$-axis, which preserves the $c$-axis directional spin rotation symmetry and breaks the spin rotation symmetry when $B\|ab$. The 3D magnon BEC scaling for $B\|c$ is immune to the off-stoichiometric disorder in our sample $\alpha-Cu_{3.26}Mg_{0.74}(OH)_6Br_2$. Our findings have the potential to shed light on the investigations of the magnetic anisotropy and disorder effects on the field-induced magnon BEC in the quantum antiferromagnet.

Control of the Bose-Einstein Condensation of Magnons by the Spin Hall Effect

Previously, it has been shown that rapid cooling of yttrium-iron-garnet-platinum nanostructures, preheated by an electric current sent through the Pt layer, leads to overpopulation of a magnon gas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnons depending on the electric current and applied field orientations. Here we demonstrate that the injection or annihilation of magnons via the SHE can prevent or promote the formation of a rapid cooling-induced magnon BEC. Depending on the current polarity, a change in the BEC threshold of -8% and +6% was detected. These findings demonstrate a new method to control macroscopic quantum states, paving the way for their application in spintronic devices.

Experimental observation of Josephson oscillations in a room-temperature Bose-Einstein magnon condensate

The alternating current (ac) Josephson effect in a time-independent spatially inhomogeneous setting is manifested by the occurrence of Josephson oscillations---periodic macroscopic phase-induced collective motions of the quantum condensate. So far, this phenomenon was observed at cryogenic temperatures in superconductors, in superfluid helium, and in Bose-Einstein condensates (BECs) of trapped atoms. Here, we report on the discovery of the ac Josephson effect in a magnon BEC carried by a room-temperature ferrimagnetic film. The BEC is formed in a parametrically populated magnon gas in the spatial vicinity of a magnetic trench created by a dc electric current. The appearance of the Josephson effect is manifested by oscillations of the magnon BEC density in the trench, caused by a coherent phase shift between this BEC and the BEC in the nearby regions. Our findings advance the physics of room-temperature macroscopic quantum phenomena and will allow for their application for data processing in magnon spintronics devices.

Stabilization of a nonlinear magnonic bullet coexisting with a Bose-Einstein condensate in a rapidly cooled magnonic system driven by spin-orbit torque

We have recently shown that injection of magnons into a magnetic dielectric via the spin-orbit torque (SOT) effect in the adjacent layer of a heavy metal subjected to the action of short (0.1 $\mu$s) current pulses allows for control of a magnon Bose-Einstein Condensate (BEC). Here, the BEC was formed in the process of rapid cooling (RC), when the electric current heating the sample is abruptly terminated. In the present study, we show that the application of a longer (1.0 $\mu$s) electric current pulse triggers the formation of a nonlinear localized magnonic bullet below the linear magnon spectrum. After pulse termination, the magnon BEC, as before, is formed at the bottom of the linear spectrum, but the nonlinear bullet continues to exist, stabilized for additional 30 ns by the same process of RC-induced magnon condensation. Our results suggest that a stimulated condensation of excess magnons to all highly populated magnonic states occurs.

Optomagnonic Josephson effect in antiferromagnets

Combining advanced technologies of optics and antiferromagnetic spintronics, we present a method to realize ultrafast spin transport. The optical Barnett effect provokes quasiequilibrium Bose-Einstein condensates (BECs) of magnons associated with the fully spin-polarized state in insulating antiferromagnets (AFs). This optomagnonic Barnett effect enables us to exploit coherent magnons of high frequency over the conventional ones of (sub-) terahertz associated with the N\'eel magnetic order. We show that the macroscopic coherence of those optical magnon BECs induces a spin current across the junction interface of weakly coupled two insulating AFs, and this optomagnonic Josephson effect realizes ultrafast spin transport. The period of the optomagnonic Josephson oscillation is much shorter than the conventional one of the order of picoseconds. Thus we propose a way to realize ultrafast spin transport in AFs by means of the macroscopic coherence of optical magnon BECs.

Vortex-mediated relaxation of magnon BEC into light Higgs quasiparticles

A magnon Bose-Einstein condensate in superfluid $^3$He is a fine instrument for studying the surrounding macroscopic quantum system. At zero temperature, the BEC is subject to a few, distinct forms of decay into other collective excitations, owing to momentum and energy conservation in a quantum vacuum. We study the vortex-Higgs mechanism: the vortices relax the requirement for momentum conservation, allowing the optical magnons of the BEC to transform into light Higgs quasiparticles. This observation expands the spectrum of possible interactions between magnetic quasiparticles in $^3$He-B, opens pathways for hunting down elusive phenomena such as the Kelvin wave cascade or bound Majorana fermions, and lays groundwork for building magnon-based quantum devices.

Two Phases Inside the Bose Condensation Dome of Yb_{2}Si_{2}O_{7}.

Recent experimental data on Bose-Einstein condensation of magnons in the spin-gap compound Yb_{2}Si_{2}O_{7} revealed an asymmetric Bose-Einstein condensation dome [G. Hester et al., Phys. Rev. Lett. 123, 027201 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.027201]. We examine modifications to the Heisenberg model on a breathing honeycomb lattice, showing that this physics can be explained by competing anisotropic perturbations. We employ a gamut of analytical and numerical techniques to show that the anisotropy yields a field driven phase transition from a state with broken Ising symmetry to a phase that breaks no symmetries and crosses over to the polarized limit.