Bose-Einstein Condensation Of Magnons Research Articles

Ferroelectricity by Bose-Einstein condensation in a quantum magnet.

The Bose–Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. Surprising properties, such as superfluidity, vortex quantization or Josephson effect, appear owing to the macroscopic quantum coherence, which spontaneously develops in Bose–Einstein condensates. Realization of Bose–Einstein condensation is not restricted in fluids like liquid helium, a superconducting phase of paired electrons in a metal and laser-cooled dilute alkali atoms. Bosonic quasi-particles like exciton-polariton and magnon in solids-state systems can also undergo Bose–Einstein condensation in certain conditions. Here, we report that the quantum coherence in Bose–Einstein condensate of the magnon quasi particles yields spontaneous electric polarization in the quantum magnet TlCuCl3, leading to remarkable magnetoelectric effect. Very soft ferroelectricity is realized as a consequence of the O(2) symmetry breaking by magnon Bose–Einstein condensation. The finding of this ferroelectricity will open a new window to explore multi-functionality of quantum magnets.

Low-temperature heat transport of spin-gapped quantum magnets

This article reviews low-temperature heat transport studies of spin-gapped quantum magnets in the last few decades. Quantum magnets with small spins and low dimensionality exhibit a variety of novel phenomena. Among them, some systems are char-acteristic of having quantum-mechanism spin gap in their magnetic excitation spectra, including spin-Peierls systems, S = 1 Haldane chains, S = 1/2 spin ladders, and spin dimmers. In some particular spin-gapped systems, the XY-type antiferromagnetic state induced by magnetic field that closes the spin gap can be described as a magnon Bose-Einstein condensation (BEC). Heat transport is effective in probing the magnetic excitations and magnetic phase transitions, and has been extensively studied for the spin-gapped systems. A large and ballistic spin thermal conductivity was observed in the two-leg Heisenberg S = 1/2 ladder compounds. The characteristic of magnetic thermal transport of the Haldane chain systems is quite controversial on both the theoretical and experimental results. For the spin-Peierls system, the spin excitations can also act as heat carriers. In spin-dimer compounds, the magnetic excitations mainly play a role of scattering phonons. The magnetic excitations in the magnon BEC systems displayed dual roles, carrying heat or scattering phonons, in different materials.

Supercurrent in a room-temperature Bose–Einstein magnon condensate

We report evidence for the existence of a supercurrent of magnons in a magnon Bose-Einstein condensate prepared in a room temperature yttrium-iron-garnet magnetic film and subject to a thermal gradient. The magnon condensate is formed in a parametrically populated magnon gas, and its temporal evolution is studied by time-, frequency- and wavector-resolved Brillouin light scattering spectroscopy. It has been found that local heating in the focal point of a probing laser beam enhances the temporal decrease in the density 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- and, consequently, magnetisation-gradient induced phase gradient in the condensate wave function.

Magneto-optical and magnetic properties in a Co/Pd multilayered thin film

The paper describes investigation of ferromagnetism at low temperatures. We explored the magneto-optical properties, influenced by photon–magnon interactions, of a ferromagnetic Co/Pd multilayered thin film below and above the magnon Bose–Einstein Condensation (BEC) temperature. Analyses of SQUID and MOKE low temperature experimental results reveal a noticeable phase transition in both magnetic and magneto-optical properties of the material at the BEC temperature.

Growth and magnetic properties of MnCl2–4SC(NH2)2 single crystals

NiCl2–4SC(NH2)2 (DTN) is a famous one-dimensional antiferromagnet with magnon Bose–Einstein condensation. In this work, single crystals of MnCl2–4SC(NH2)2 (DTM) with size up to (8–10)×(8–10)×(3–5)mm3 are grown by using the slow evaporation method with optimized conditions. The single crystals are characterized by measurements of X-ray diffraction, magnetic susceptibility, and specific heat. It is found that although DTM has a similar crystal structure to DTN, it shows a paramagnetic behavior. The reason for no spin exchange among Mn2+ ions can be understood in terms of the negligible overlap of the Mn2+-3d orbital and the neighboring Cl−-3p orbital.

Magnon BEC Versus Atomic BEC

The Bose–Einstein condensation (BEC) corresponds to the formation of a collective quantum state in which macroscopic number of particles is governed by a single wave function. The magnon BEC, the coherent state of a macroscopic number of magnons, manifests itself by coherent precession of magnetization even in an inhomogeneous magnetic field. The magnon BEC has many similarities with the atomic BEC. But it shows a great variety of properties in different magnetic materials. Here we will classify the different types of magnonic BECs.

High-Resolution Magneto-Optical Kerr-Effect Spectroscopy of Magnon Bose–Einstein Condensate

Using a novel heterodyne magneto-optical Kerr-effect technique, we have studied the spectral characteristics of a room-temperature magnon Bose–Einstein condensate (BEC) in yttrium-iron-garnet (YIG) films. Thanks to the ultimate frequency resolution of the technique of better than 100 Hz, we were able to directly determine the spectral linewidth of the spontaneously formed condensate of microwave-frequency magons. The value of 1.7 MHz provides direct evidence of high temporal coherence of the magnon condensate, and shows that the condensation phenomenon can be used for implementation of tunable microwave oscillators with a quality factor ${{Q}} = {{f}}/\Delta {{f}}= {3}{\times}{10}^{3}$ . The measured linewidth is close to, but larger than, the lower limit estimated from previous indirect experiments based on the measurements of the condensate lifetime. Additionally, the technique enables a determination of the wavevector of the condensate ${{k}}_{\text{BEC}} = {5}{\times}{10}^{4} {\text{cm}}^{-1}$ , which is in agreement with previous studies.

Anomalous magnetoresistance in nanocrystalline gadolinium at low temperatures

The results of a detailed investigation of electrical resistivity, ρ(T) and transverse magnetoresistance (MR) in nanocrystalline Gd samples with an average grain size d = 12 nm and 18 nm reveal the following. Besides a major contribution to the residual resistivity, ρr(0), arising from the scattering of conduction electrons from grain surfaces/interfaces/boundaries (which increases drastically as the average grain size decreases, as expected), coherent electron–magnon scattering makes a small contribution to ρr(0), which gets progressively suppressed as the applied magnetic field (H) increases in strength. At low temperatures (T ≲ 40 K) and fields (H = 0 and H = 5 kOe), ρH(T) varies as T3/2 with a change in slope at T+ ≃ 16.5 K. As the field increases beyond 5 kOe, the T3/2 variation of ρH(T) at low temperatures (T ≲ 40 K) changes over to the T2 variation and a slight change in the slope dρH/dT2 at T+(H) disappears at H ⩾ 20 kOe. The electron–electron scattering (Fermi liquid) contribution to the T2 term, if present, is completely swamped by the coherent electron–magnon scattering contribution. As a function of temperature, (negative) MR goes through a dip at a temperature Tmin ≃ T+, which increases with H as H2/3. MR at Tmin also increases in magnitude with H and attains a value as large as ∼15% (17%) for d = 12 nm (18 nm) at H = 90 kOe. This value is roughly five times greater than that reported earlier for crystalline Gd at Tmin ≃ 100 K. Unusually large MR results from an anomalous softening of magnon modes at T ≃ Tmin ≈ 20 K. In the light of our previous magnetization and specific heat results, we show that all the above observations, including the H2/3 dependence of Tmin (with Tmin(H) identified as the Bose–Einstein condensation (BEC) transition temperature, TBEC(H)), are the manifestations of the BEC of magnons at temperatures T ⩽ TBEC. Contrasted with crystalline Gd, which behaves as a three-dimensional (3D) pure uniaxial dipolar ferromagnet in the asymptotic critical region, ρH=0(T) of nanocrystalline Gd, in the critical region near the ferromagnetic-paramagnetic phase transition, is better described by the model proposed for a 3D random uniaxial dipolar ferromagnet.

Bose-Einstein condensation in antiferromagnets at low temperatures

The Bose-Einstein condensation (BEC) was predicted by Einstein in 1925 and this effect is characterized by the formation of a collective quantum state, when macroscopic number of particles is governed by a single wave function. The BEC of magnons was discovered experimentally in superfluid phase of 3He. In the present work we report our progress on the BEC of magnons investigations in solid antiferromagnets at low temperatures by magnetic resonance methods. The duration of the FID signal in two samples of easy-plane antiferromagnets CsMnF3 has been studied. Obtained data confirm the formation of magnon BEC in antiferromagnet CsMnF3.

Josephson and persistent spin currents in Bose-Einstein condensates of magnons

Using the Aharonov-Casher (A-C) phase, we present a microscopic theory of the Josephson and persistent spin currents in quasi-equilibrium Bose-Einstein condensates (BECs) of magnons in ferromagnetic insulators. Starting from a microscopic spin model that we map onto a Gross-Pitaevskii Hamiltonian, we derive a two-state model for the Josephson junction between the weakly coupled magnon-BECs. We then show how to obtain the alternating-current (ac) Josephson effect with magnons as well as macroscopic quantum self-trapping in a magnon-BEC. We next propose how to control the direct-current (dc) Josephson effect electrically using the A-C phase, which is the geometric phase acquired by magnons moving in an electric field. Finally, we introduce a magnon-BEC ring and show that persistent magnon-BEC currents flow due to the A-C phase. Focusing on the feature that the persistent magnon-BEC current is a steady flow of magnetic dipoles that produces an electric field, we propose a method to directly measure it experimentally.

Magnon qubit and quantum computing on magnon Bose-Einstein condensates

Recently, great progress has been made in the creation of a solid-state quantum computer using superconducting qubits on Cooper pairs of charged electrons. However, this approach has met limitations due to decoherence effects caused by the strong Coulomb interaction of the superconducting qubit with the environment. Here, we propose the solution of this problem by switching to another Bose-Einstein condensate (BEC), uncharged long-lived magnons, wherein the magnon BEC qubit can be realized due to the magnon blockade isolating a pair of the magnon condensate energy levels in the mesoscopic and nanoscopic ferromagnetic dielectric sample. We demonstrate the single-qubit gates by operating quantum transition between these states in the external microwave field. We also consider implementation of the two-qubit gates by using the interaction between such magnon BEC qubits due to exchange by virtual photons in a microwave cavity. Finally, we discuss the condition for long-lived magnon BEC qubits, a scalable architecture, and promising advantages of the multiqubit quantum computer based on the magnon qubit.

Kinetics of pulse-induced magnon Bose-Einstein condensate

We have analysed the kinetics of Bose-Einstein condensed (BEC) magnons after pulsed excitation in a ferromagnet at room and low temperatures. For this purpose, we have derived the kinetic equations using the nonequilibrium statistical operator method to describe the general form of the interactions in the magnon system. On the basis of this approach, we have analysed the nonlinear properties of the magnon BEC kinetics caused by interactions with magnon reservoir modes and phonons. We have found that formation of a quasi-stationary BEC magnon state is possible not only at room temperature but also at low temperatures, where the magnon-phonon interaction leads to formation of a residual BEC state with magnon population much larger than at room temperature. It was also observed that a moderately strong four-particle part of the magnon-magnon interaction violating the number of magnons is sufficient to facilitate magnon BEC formation. The predicted long-lived magnon BEC state could be promising for realisation of macroscopic qubits.

Bose-Einstein Condensation of Confined Magnons in Nanostructures

A number of diverse kinds of magnetic experiments are shown to lead to the observation of a Bose-Einstein condensation of magnons in some nanostructures, especially in Fe and in Co/Pt. The experiments include 1) the measurement of magnetic aftereffect, 2) measurements of Neel’s fluctuation field, including an estimate of activation volume, 3) the measurement of the energy gap which provides a lower limit on the BEC temperature, 4) using Lagrange multipliers in the quantum thermodynamics of magnons, and 5) the observation of a visible anomaly in the Bloch T3/2 law for the temperature dependence of magnetization of nanostructured ferromagnets.

Magnon Bose-Einstein condensation at inhomogeneous conditions

The Spin Supercurrent and Bose-Einstein condensation of magnons, similar to an atomic BEC, was discovered in superfluid 3He-B, which is characterized by absolute purity. Later this phenomena were observed in a few magnetically ordered materials with different types of impurities. In this article we will review the properties of magnon BEC in a presence of impurities and defects.

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ Q of the charge Q and the energy relaxation time τ E . If τ Q ≫ τ E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid 4He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.

Spin-motive force and orbital-motive force: from magnon Bose-Einstein condensation to chiral Weyl superfluids

Spin-motive geometric force acting on electrons in metallic ferromagnets is extended to spin-motive force in magnon BEC, which is represented by phase-coherent precession of magnetization, and to the orbital-motive force in superfluid 3He-A. In 3He-A there are two contributions to the orbital-motive force. One of them comes from the chiral nature of this liquid. Another one originates from chiral Weyl fermions living in the vicinity of the topologically protected Weyl points, and is related to the phenomenon of chiral anomaly.

Magnon supersolid and anomalous hysteresis in spin dimers on a triangular lattice

We study the magnetic phase diagram and hysteresis behavior of weakly coupled spin dimers on a triangular lattice using the cluster mean-field method with cluster-size scaling. We find that the magnetization curve has plateaus at 1/3 and 2/3 of the total magnetization, in which local singlet and triplet states form a superlattice pattern. Moreover, if increasing (decreasing) the magnetic field from the 1/3 (2/3) plateau, the Bose-Einstein condensation (BEC) of triplons occurs on the superlattice background, leading to the transition into magnon supersolid phase. We also find that the first-order transition between these solid states and the standard magnon BEC state exhibits an anomalous hysteresis upon cycling the magnetic field; the transition can occur only from solid to BEC, and the system cannot return to the initial solid state in the reverse process.

Atomic type magnon Bose-Einstein condensation in antiferromagnet.

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 antiferromagnet CsMnF3. 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.

Bose–Einstein condensation of magnons in ferromagnetic thin films

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.

Spatially non-uniform ground state and quantized vortices in a two-component Bose-Einstein condensate of magnons.

A gas of magnons in magnetic films differs from all other known systems demonstrating Bose-Einstein condensation (BEC), since it possesses two energetically degenerate lowest-energy quantum states with non-zero wave vectors ±kBEC. Therefore, BEC in this system results in a spontaneously formed two-component Bose-Einstein condensate described by a linear combination of two spatially non-uniform wave-functions ∝exp(±ikBECz), while condensates found in other physical systems are characterized by spatially uniform wave-functions. Here we report a study of BEC of magnons with sub-micrometer spatial resolution. We experimentally confirm the existence of the two wave-functions and show that their interference results in a non-uniform ground state of the condensate with the density oscillating in space. Additionally, we observe stable topological defects in the condensate. By comparing the experimental results with predictions of a theoretical model based on the Ginzburg-Landau equation, we identify these defects as quantized vortices.