Direct observation of the transition from spin waves to the magnon Bose condensate.

Bose-Einstein condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. The transition from the semiclassical paradigm of spin waves to the magnon Bose-Einstein condensed state (mBEC) was obtained experimentally with increasing magnon density. We used the Faraday rotation effect to study the spatial distribution of the magnon density and phase far from their excitation region. A coherent magnetization precession was observed throughout the sample, which indicates the formation of a magnon BEC. It is shown that this result under experimental conditions goes beyond the applicability of the Landau-Lifshitz-Gilbert semiclassical theory.

Optical registration of a coherent magnon state outside of the excitation region.

Magnons have demonstrated enormous potential for the next generation of information technology and quantum computing. In particular, the coherent state of magnons resulting from their Bose-Einstein condensation (mBEC) is of great interest. Typically, mBEC is formed in the magnon excitation region. Here we demonstrate for the first time by optical methods the permanent existence of mBEC at large distances from the magnon excitation region. The homogeneity of the mBEC phase is also demonstrated. The experiments were carried out on films of yttrium iron garnet magnetized perpendicular to the surface and at room temperature. We use the method described in this article to develop coherent magnonics and quantum logic devices.

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.

Normal-Mode Splitting in the Coupled System of Hybridized Nuclear Magnons and Microwave Photons.

In the weak ferromagnetic MnCO_{3} system, a low-frequency collective spin excitation (magnon) is the hybridized oscillation of nuclear and electron spins coupled through the hyperfine interaction. By using a split-ring resonator, we performed transmission spectroscopy measurements of the MnCO_{3} system and observed avoided crossing between the hybridized nuclear magnon mode and the resonator mode in the NMR-frequency range. The splitting strength is quite large due to the large spin density of ^{55}Mn, and the cooperativity value C=0.2 (the magnon-photon coupling parameter) is close to the conditions of strong coupling. The results reveal a new class of spin systems, in which the coupling between nuclear spins and photons is mediated by electron spins via the hyperfine interaction.

Self-trapping of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box confinement.

Long-lived coherent spin precession of (3)He-B at low temperatures around 0.2T(c) is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.

High-Tc spin superfluidity in antiferromagnets.

We report the observation of the unusual behavior of induction decay signals in antiferromagnetic monocrystals with Suhl-Nakamura interactions. The signals show the formation of the Bose-Einstein condensation (BEC) of magnons and the existence of spin supercurrent, in complete analogy with the spin superfluidity in the superfluid (3)He and the atomic BEC of quantum gases. In the experiments described here, the temperature of the magnon BEC is a thousand times larger than in the superfluid (3)He. It opens a possibility to apply the spin supercurrent for various magnetic spintronics applications.

Micromagnetic modeling of magnon coherent states in a nonuniform magnetic field.

Quantum magnonics is an emerging research field, with great potential for applications in a magnon based quantum technologies, including quantum computing, processing and encoding information. Magnon correlation and quantum entanglement are the main concepts in many quantum technologies under development. Of particular interest is the magnon Bose condensation. The emerging current question is the applicability of quasi-classical Landau-Lifshitz-Gilbert equations to describe the coherent state of magnons. We performed micromagnetic modeling of the magnetization dynamics at a high angle of deviation in an inhomogeneous magnetic field. We have obtained solutions that are well coincided with the properties of experimentally observed magnon BEC states. This result will be needed for the calculation the properties of magnetic devices on the basis of quantum magnonics.

Quantum paradigm of the foldover magnetic resonance.

The explosive development of quantum magnonics requires the consideration of several previously known effects from a new angle. In particular, taking into account the quantum behavior of magnons is essential at high excitations of the magnetic system, under the conditions of the so-called phenomenon of "foldover" (bi-stable) magnetic resonance. Previously, this effect was considered in the quasi-classical macrospin approximation. However, at large angles of magnetization precession, the magnon density exceeds the critical value for the formation of a magnon Bose condensate (mBEC). Naturally, this purely quantum phenomenon does not exist in the classical approximation. In addition, mBEC leads to superfluid transfer of magnetization, which suppresses the macroinhomogeneity of the samples. The experiments presented in the article show that quantum phenomena well describes the experimental results of nonlinear magnetic resonance in yttrium iron garnet. Thus, we remove the questions that arose earlier when considering this effect without taking into account quantum phenomena. This discovery paves the way for many quantum applications of supermagnonics, such as the magnetic Josephson effect, long-range spin transport, Q-bits, quantum logic, magnetic sensors, and others.

Direct observation of the specific heat of Majorana quasiparticles in superfluid3He-B.

The existence of Majorana quasiparticles was predicted in the edge state in topological insulators, especially in the p-wave superfluid medium [Formula: see text]He-B. Due to its purity and coherent quantum state, [Formula: see text]He-B is an ideal platform for searching for Majorana fermions in condensed matter systems. In the limit of extremely low temperatures, the density of Bogolyubov quasiparticles and the heat capacity of [Formula: see text]He-B decrease exponentially. In this article, we present the first observation of the deviation of its heat capacity from exponential dependence in the limit of record low cooling. We found an additional heat capacity that more than doubled the heat capacity of bulk [Formula: see text]He-B and changes as T[Formula: see text]. The additional heat capacity is in good agreement with the predicted heat capacity of 2D gas of Majorana. This observation is a direct proof of the existence of Majorana quasiparticles in [Formula: see text]He-B.

3D-XY critical behavior of CsMnF3 from static and dynamic thermal properties.

Static and dynamic critical behavior of the easy-plane antiferromagnet CsMnF3 have been studied by means of a high-resolution ac photopyroelectric calorimeter. Thermal diffusivity, thermal conductivity and specific heat have been carefully measured in the near vicinity of the antiferromagnetic to paramagnetic transition (51.1 K). Specific heat and thermal diffusivity show singularities at the Néel temperature while thermal conductivity does not. Both the static and dynamic critical parameters agree with the standard 3D-XY universality class (α = -0.014, A⁺/A⁻ = 1.06): for specific heat α = -0.016, A⁺/A⁻ = 1.09 and for thermal diffusivity b = -0.010, U⁺/U⁻ = 1.09. As the dynamic critical behavior of thermal diffusivity has not yet been theoretically established for the 3D-XY universality class, an approximate equation relating static and dynamic critical parameters has been obtained for it, leading to b ≈ α and A⁺/A⁻ ≈ U⁺/U⁻ by studying the asymptotic behavior of the functions. This equation has also been experimentally verified for another XY antiferromagnet (SmMnO3). As an easy-plane antiferromagnet with a hexagonal structure, CsMnF3 could have been expected to comply with the 3D-XY chiral class (α = +0.34, A⁺/A⁻ = 0.36) (as is the case of CsMnBr3), but the experimental results rule out that possibility. This is attributed to the presence of a small in-plane anisotropy of the spins in CsMnF3, which breaks the chiral degeneracy of the 120° spin structure.

In-situ comprehensive calibration of a tri-port nano-electro-mechanical device.

We report on experiments performed in vacuum and at cryogenic temperatures on a tri-port nano-electro-mechanical (NEMS) device. One port is a very nonlinear capacitive actuation, while the two others implement the magnetomotive scheme with a linear input force port and a (quasi-linear) output velocity port. We present an experimental method enabling a full characterization of the nanomechanical device harmonic response: the nonlinear capacitance function C(x) is derived, and the normal parameters k and m (spring constant and mass) of the mode under study are measured through a careful definition of the motion (in meters) and of the applied forces (in Newtons). These results are obtained with a series of purely electric measurements performed without disconnecting/reconnecting the device, and rely only on known dc properties of the circuit, making use of a thermometric property of the oscillator itself: we use the Young modulus of the coating metal as a thermometer, and the resistivity for Joule heating. The setup requires only three connecting lines without any particular matching, enabling the preservation of a high impedance NEMS environment even at MHz frequencies. The experimental data are fit to a detailed electrical and thermal model of the NEMS device, demonstrating a complete understanding of its dynamics. These methods are quite general and can be adapted (as a whole, or in parts) to a large variety of electromechanical devices.

Coherent precession of magnetization in the superfluid 3He A-phase.

We report the first observation of coherent precession of magnetization in superfluid 3He A-like phase (CP-A) in aerogel. The coherent precession in bulk 3He A-phase is unstable due to the positive feedback of spin supercurrent to the gradient of phase of precession. It was predicted that the homogeneous precession will be stable if the orbital momentum of the 3He A-phase can be oriented along the magnetic field. We have succeeded to prepare this configuration by emerging 3He in uniaxially deformed anisotropic aerogel. The dissipation rate of coherent precession states in aerogel is much larger than that in bulk 3He B-phase. We propose a mechanism of this dissipation.

Strong orientational effect of stretched aerogel on the (3)He order parameter.

Deformation of aerogel strongly modifies the orientation of the order parameter of superfluid (3)He confined in aerogel. We used a radial squeezing of aerogel to keep the orbital angular momentum of the (3)He Cooper pairs in the plane perpendicular to the magnetic field. We did not find strong evidence for a polar phase, with a nodal line along the equator of the Fermi surface, predicted to occur at large radial squeezing. Instead we observed (3)He-A with a clear experimental evidence of the destruction of the long-range order by random anisotropy-the Larkin-Imry-Ma effect. In (3)He-B we observed and identified new modes of NMR, which are impossible to obtain in bulk (3)He-B. One of these modes is characterized by a repulsive interaction between magnons, which is suitable for the magnon Bose-Einstein condensation.

Magnon condensation into a Q ball in 3He-B.

The theoretical prediction of Q balls in relativistic quantum fields is realized here experimentally in superfluid 3He-B. The condensed-matter analogs of relativistic Q balls are responsible for an extremely long-lived signal of magnetic induction observed in NMR at the lowest temperatures. This Q ball is another representative of a state with phase coherent precession of nuclear spins in 3He-B, similar to the well-known homogeneously precessing domain, which we interpret as Bose-Einstein condensation of spin waves--magnons. At large charge Q, the effect of self-localization is observed. In the language of relativistic quantum fields it is caused by interaction between the charged and neutral fields, where the neutral field provides the potential for the charged one. In the process of self-localization the charged field modifies locally the neutral field so that the potential well is formed in which the charge Q is condensed.

Probing "cosmological" defects in superfluid 3He-B with a vibrating-wire resonator.

We report on the observation of an anomalously high damping measured by a vibrating-wire resonator (VWR) immersed into superfluid at ultralow temperatures. The observed dissipation is orders of magnitude above that corresponding to friction with the dilute normal fraction and superfluid vortices. A clear pinning behavior is also observed, as well as a strong magnetic field dependence. Our analysis points to the interaction of the VWR with a planar topological defect, analogue to cosmological vacua defects, as proposed by Salomaa and Volovik.

Pinning of texture and vortices of the rotating B-like phase of superfluid 3He confined in a 98% aerogel.

We have investigated pinning effects on texture and vortices of the B-like phase of superfluid (3)He in a rotating aerogel up to +/-2pi rad/s by cw-NMR. We observed deformation of the NMR spectra in rotation, due to counterflow between the superflow and the normal flow. The average intensity of the counterflow was calculated from the change of NMR spectra. The rotation dependence of the counterflow intensity is similar to the magnetization curve of hard type II superconductors or the counterflow response of (4)He-II in packed powders. This counterflow behavior is in qualitative agreement with a model that vortices are pinned unless the counterflow exceeds a critical velocity v(c). The temperature independence of v(c) suggests that v(c) is associated with the expansion of primordial vortices.