Condensation Of Magnons Research Articles

Magnon Supercurrent and the Phase Slippage in an Yttrium Iron Garnet Film

Exactly forty years ago, the spin superfluidity and Bose–Einstein condensation of magnons in superfluid antiferromagnetic 3He-B were discovered. In this work, the existence of spin superfluidity and phase slippage in an yttrium iron garnet film at room temperature is demonstrated using the optical Faraday effect. The s-patial distribution of the phase and amplitude of the spin precession under the conditions of magnon Bose‒Einstein condensation are studied by varying the pump phase difference between two strip lines exciting magnons.

Bose-Einstein condensation of magnons under coherent pumping by light

Bose-Einstein condensation of magnons under coherent pumping by light

Nonequilibrium Criticality at the Onset of Time-Crystalline Order.

We explore the phase transitions at the onset of time-crystalline order in O(N) models driven out of equilibrium. The spontaneous breaking of time translation symmetry and its Goldstone mode are captured by an effective description with O(N)×SO(2) symmetry, where the emergent external SO(2) results from a transmutation of the internal symmetry of time translations. Using the renormalization group and the ε=4-d expansion in a leading two-loop analysis, we identify a new nonequilibrium universality class. Strikingly, it controls the long-distance physics no matter how small the microscopic breaking of equilibrium conditions is. The O(N=2)×SO(2) symmetry group is realized for magnon condensation in pumped yttrium iron garnet films and in exciton-polariton systems with a polarization degree of freedom.

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.

Amplitude representation of Landau–Lifshitz equation and its application to ferromagnetic films

In this article we develop a systematic approach to the solution of the Landau-Lifshitz equation in terms of the magnon wave function ψr and apply it to physical phenomena in a thin ferromagnetic film. In this article we represent the modern state of art for the properties of ferromagnetic films and the pumping-induced Bose–Einstein condensation of magnons in them at room temperature. It can be considered as a review on basic principles and the recent advances in the field.

Correlation-Enhanced Interaction of a Bose-Einstein Condensate with Parametric Magnon Pairs and Virtual Magnons.

Nonlinear interactions are crucial in science and engineering. Here, we investigate wave interactions in a highly nonlinear magnetic system driven by parametric pumping leading to Bose-Einstein condensation of spin-wave quanta-magnons. Using Brillouin light scattering spectroscopy in yttrium-iron garnet films, we found and identified a set of nonlinear processes resulting in off-resonant spin-wave excitations-virtual magnons. In particular, we discovered a dynamically strong, correlation-enhanced four-wave interaction process of the magnon condensate with pairs of parametric magnons having opposite wave vectors and fully correlated phases.

Antiferromagnetic magnon spintronic based on nonreciprocal and nondegenerated ultra-fast spin-waves in the canted antiferromagnet α-Fe2O3.

Spin-waves in antiferromagnets hold the prospects for the development of faster, less power-hungry electronics and promising physics based on spin superfluids and coherent magnon condensates. For both these perspectives, addressing electrically coherent antiferromagnetic spin-waves is of importance, a prerequisite that has been so far elusive, because, unlike ferromagnets, antiferromagnets couple weakly to radiofrequency fields. Here, we demonstrate the detection of ultra-fast nonreciprocal spin-waves in the dipolar exchange regime of a canted antiferromagnet using both inductive and spintronic transducers. Using time-of-flight spin-wave spectroscopy on hematite (α-Fe2O3), we find that the magnon wave packets can propagate as fast as 20 kilometers/second for reciprocal bulk spin-wave modes and up to 6 kilometers/second for surface spin-waves propagating parallel to the antiferromagnetic Néel vector. We lastly achieve efficient electrical detection of nonreciprocal spin-wave transport using nonlocal inverse spin-Hall effects. The electrical detection of coherent nonreciprocal antiferromagnetic spin-waves paves the way for the development of antiferromagnetic and altermagnet-based magnonic devices.

State space geometry of the spin-1 antiferromagnetic Heisenberg chain

We study the phase diagram of the spin-1 antiferromagnetic Heisenberg chain with uniaxial anisotropy and applied magnetic field in terms of the genuine multipartite entanglement as witnessed by the mean quantum Fisher information density. By considering the manifold generated by the staggered magnetization operator, we connect the state space curvature in the vicinity of the ground state of the Heisenberg chain to the genuine multipartite entanglement. Our analysis demonstrates that the quantum critical points and symmetry protected topological (SPT) phase exhibit large state space curvature, while the separable phases are completely flat, offering insight into the physical interpretation of state space curvature. We further show that the entanglement in the SPT phase is enhanced by the presence of uniaxial anisotropy and undiminished in the presence of uniform magnetic fields. The magnon condensate phase induced by large fields is shown to emanate from the Gaussian critical point and exhibits massive multipartite entanglement over a robust region of the parameter space.

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.

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.

High-Angular Momentum Excitations in Collinear Antiferromagnet FePS3.

We report on magneto-optical studies of the quasi-two-dimensional van der Waals antiferromagnet FePS3. Our measurements reveal an excitation that closely resembles the antiferromagnetic resonance mode typical of easy-axis antiferromagnets; nevertheless, it displays an unusual, four-times larger Zeeman splitting in an applied magnetic field. We identify this excitation with an |Sz| = 4 multipolar magnon─a single-ion 4-magnon bound state─that corresponds to a full reversal of a single magnetic moment of the Fe2+ ion. We argue that condensation of multipolar magnons in large-spin materials with a strong magnetic anisotropy can produce new exotic states.

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.

Filtering and Imaging of Frequency-Degenerate Spin Waves Using Nanopositioning of a Single-Spin Sensor.

Nitrogen-vacancy (NV) magnetometry is a new technique for imaging spin waves in magnetic materials. It detects spin waves by their microwave magnetic stray fields, which decay evanescently on the scale of the spin-wavelength. Here, we use nanoscale control of a single-NV sensor as a wavelength filter to characterize frequency-degenerate spin waves excited by a microstrip in a thin-film magnetic insulator. With the NV probe in contact with the magnet, we observe an incoherent mixture of thermal and microwave-driven spin waves. By retracting the tip, we progressively suppress the small-wavelength modes until a single coherent mode emerges from the mixture. In-contact scans at low drive power surprisingly show occupation of the entire isofrequency contour of the two-dimensional spin-wave dispersion despite our one-dimensional microstrip geometry. Our distance-tunable filter sheds light on the spin-wave band occupation under microwave excitation and opens opportunities for imaging magnon condensates and other coherent spin-wave modes.

Thermal squeezing and nonlinear spectral shift of magnons in antiferromagnetic insulators

We investigate the effect of magnon–magnon interactions on the dispersion and polarization of magnon modes in collinear antiferromagnetic (AF) insulators at finite temperatures. In two-sublattice AF systems with uniaxial easy-axis and biaxial easy-plane magneto-crystalline anisotropies, we implement a self-consistent Hartree–Fock mean-field approximation to explore the nonlinear thermal interactions. The resulting nonlinear magnon interactions separate into two-magnon intra- and interband scattering processes. Furthermore, we compute the temperature dependence of the magnon bandgap and AF resonance modes due to nonlinear magnon interactions for square and hexagonal lattices. In addition, we study the effect of magnon interactions on the polarization of magnon modes. We find that although the noninteracting eigenmodes in the uniaxial easy-axis case are circularly polarized, but in the presence of nonlinear thermal interactions the U(1) symmetry of the magnon Hamiltonian is broken. The attractive nonlinear interactions squeeze the low energy magnon modes and make them elliptical. In the biaxial easy-plane case, on the other hand, the bare eigenmodes of low energy magnons are elliptically polarized but thermal nonlinear interactions squeeze them further. Direct measurements of the predicted temperature-dependent AF resonance modes and their polarization can be used as a tool to probe the nonlinear interactions. Our findings establish a framework for exploring the effect of thermal magnon interactions in technologically important magnetic systems, such as magnetic stability of recently discovered two-dimensional magnetic materials, coherent transport of magnons, Bose–Einstein condensation of magnons, and magnonic topological insulators.

Accumulation of magnetoelastic bosons in yttrium iron garnet: Kinetic theory and wave-vector-resolved Brillouin light scattering

We derive and solve quantum kinetic equations describing the accumulation of magnetoelastic bosons in an overpopulated magnon gas realized in a thin film of the magnetic insulator yttrium iron garnet. We show that in the presence of a magnon condensate, there is a non-equilibrium steady state in which incoherent magnetoelastic bosons accumulate in a narrow region in momentum space for energies slightly below the bottom of the magnon spectrum. The results of our calculations agree quite well with Brillouin light scattering measurements of the stationary non-equilibrium state of magnons and magnetoelastic bosons in yttrium iron garnet.

Antiferromagnetism and magnetic frustration in the metalorganic compounds MCl2 -4SC( NH2)2, M = (Mn,Fe)

We report magnetic and specific heat measurements at low temperatures ($>100$ mK) and high magnetic fields (up to 9 T) for the metalorganic compounds ${\mathrm{MnCl}}_{2}\text{\ensuremath{-}}4\mathrm{SC}{({\mathrm{NH}}_{2})}_{2}$ (DTM) and ${\mathrm{FeCl}}_{2}\text{\ensuremath{-}}4\mathrm{SC}{({\mathrm{NH}}_{2})}_{2}$ (DTF). Fits to the experimental data from the Curie-Weiss law and mean-field theory indicate the antiferromagnetic nature of both compounds. For temperatures down to $T=0.56$ K the compound DTM exhibits two successive transitions, which may be associated with different magnetic orderings. In this system the external magnetic field is a tuning parameter that allows us to access such magnetic phases separated by distinct quantum critical points. No indication of magnetic ordering is found in DTF down to 100 mK, making this compound a candidate for a strongly frustrated material with frustration parameter $f=|{\ensuremath{\theta}}_{\mathrm{CW}}|/{T}_{N}>100$. Finally, we discuss the absence of Bose-Einstein condensation of magnons and the possibility of a spin-orbital liquid state in DTF.

Stability of Spin-Wave Solitons in Bose-Einstein Condensates of Magnons: A Possible Application in Ferromagnetic Films.

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.

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.

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.