Nonlinear interaction of resonator photons with parametric magnon pairs

We condider the process of parametric resonance of magnons in magneto-ordered crystals in a microwave resonator. The nonlinear interaction of the resonator photons with the parametric magnon pairs is analysed theoretically, and the result expressed by the deviation frequencies relative to the pump frequency further demonstrates that the dynamics of resonator modes plays an important role once the pump power exceeds the threshold of parallel pumping.     

Observation of spontaneous coherence in Bose-Einstein condensate of magnons

The room-temperature dynamics of a magnon gas driven by short microwave pumping pulses is studied. An overpopulation of the lowest energy level of the system following the pumping is observed. Using the sensitivity of the Brillouin light scattering technique to the coherence degree of the scattering magnons we demonstrate the spontaneous emergence of coherence of the magnons at the lowest level, if their density exceeds a critical value. This finding is clear proof of the quantum nature of the observed phenomenon and direct evidence of Bose-Einstein condensation of magnons at room temperature.     

Dynamical theory of photon superradiative emission by nanoscale system of Bose-condensed magnons

We have shown the possibility of non-Dicke superradiance for non-ideal magnon Bose-Einstein condensate (BEC) in a broadband frequency bath. Here, it is found that all the stored energy in the system of Bose-condensed magnons can be irradiated into a short pulse with a time delay caused by the strong frequency modulation of magnons due to direct inter-particle interactions in the Bose-condensed state. The last mechanism radically distinguishes this effect from the well-known Dicke superradiance of two-level atomic ensemble where the delay is connected with enhancement of the inter-atomic correlations due to exchange by virtual photons. In our case, the superradiance is the consequence of Bose-condensation in the coherent state where the particles are coupled by direct interaction. We have discussed the conditions for observation of this effect for Bose-condensed magnons in a solid-state sample with a spatial size smaller comparing with the wavelength of the emitted field. In general, we had shown that this kind of superradiance can proceed in samples with ferromagnetic type interaction. As for the antiferromagnetic ones, the effect of magnon superradiance takes place without delay.     

Thermalization of a parametrically driven magnon gas leading to Bose-Einstein condensation

The thermalization of parametrically pumped magnons caused by nonlinear multimagnon scattering processes and leading to the magnon Bose-Einstein condensation is investigated experimentally with high temporal resolution. The threshold pumping power necessary for the thermalization is determined. For pumping powers above this threshold the thermalization time has been found to decrease rapidly with power reaching the value down to 50 ns, which is much smaller than the magnon lifetime.     

Recent progress on optomagnetic coupling and optical manipulation based on cavity-optomagnonics

Recently, the photon–magnon coherent interaction based on the collective spins excitation in ferromagnetic materials has been achieved experimentally. Under the prospect, the magnons are proposed to store and process quantum information. Meanwhile, cavity-optomagnonics which describes the interaction between photons and magnons has been developing rapidly as an interesting topic of the cavity quantum electrodynamics. Here in this short review, we mainly introduce the recent theoretical and experimental progress in the field of optomagnetic coupling and optical manipulation based on cavity-optomagnonics. According to the frequency range of the electromagnetic field, cavity optomagnonics can be divided into microwave cavity optomagnonics and optical cavity optomagnonics, due to the different dynamics of the photon–magnon interaction. As the interaction between the electromagnetic field and the magnetic materials is enhanced in the cavity-optomagnonic system, it provides great significance to explore the nonlinear characteristics and quantum properties for different magnetic systems. More importantly, the electromagnetic response of optomagnonics covers the frequency range from gigahertz to terahertz which provides a broad frequency platform for the multi-mode controlling in quantum systems.     

The <Superscript>55</Superscript>Mn Spin Echo Test of Magnon BEC State in MnCO<Subscript>3</Subscript>

The coherent quantum state of magnons—Bose–Einstein condensate (BEC) has been observed in several types of antiferromagnets. According to the Bose statistics of magnons, BEC appears when the magnon density exceeds the critical density N _BEC and the magnon gas condenses to a quantum liquid. The BEC state is characterized by a coherent precession of the magnetization. In this paper, the first experiments showing the suppression of the spin echo signal by the magnon BEC is presented. These experiments confirm the coherence of magnetic excitations in the BEC state.     

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.     

Supercurrent pumping in Josephson junctions with a half-metallic ferromagnet

A Josephson current through a half-metallic ferromagnet between two conventional superconductors is theoretically studied. The spin dynamics such as magnon excitation plays a crucial role not only for the conversion between spin-singlet and spin-triplet pairs but also for the formation of the composite state of a triplet Cooper pair and magnon, by which the Josephson current flows between the superconductors. We propose the supercurrent pumping driven by the coherent precession of the magnetization by tuning the microwave frequency to the ferromagnetic resonance frequency in a ferromagnetic Josephson junction.     

Effect of photons on the magnon splitting

The self energy of a uniform magnon due to splitting into two magnons of oppositely directed momenta is calculated in the presence of a magnon-photon interaction, and it is found that the magnons and the photons form excitations of mixed character. Thus there is a net correction to the magnon splitting due to an interference.     

Quantum magnonics: The magnon meets the superconducting qubit

The techniques of microwave quantum optics are applied to collective spin excitations in a macroscopic sphere of a ferromagnetic insulator. We demonstrate, in the single-magnon limit, strong coupling between a magnetostatic mode in the sphere and a microwave cavity mode. Moreover, we introduce a superconducting qubit in the cavity and couple the qubit with the magnon excitation via the virtual photon excitation. We observe the magnon–vacuum-induced Rabi splitting. The hybrid quantum system enables generation and characterization of non-classical quantum states of magnons.     

Spin pumping by parametrically excited exchange magnons

We experimentally show that exchange magnons can be detected by using a combination of spin pumping and the inverse spin-Hall effect proving its wavelength integrating capability down to the submicrometer scale. The magnons were injected in a ferrite yttrium iron garnet film by parametric pumping and the inverse spin-Hall effect voltage was detected in an attached Pt layer. The role of the density, wavelength, and spatial localization of the magnons for the spin pumping efficiency is revealed.     

Squeezed States of Magnons and Phonons in a Cavity Magnomechanical System with a Microwave Parametric Amplifier

The cavity magnomechanical system has become a promising platform for preparing macroscopic quantum states. In this work, a scheme for generating the steady-state quadrature squeezing of the magnon and phonon modes in a cavity magnomechanical system is presented. This scheme uses a degenerate microwave parametric amplifier (PA) inside the microwave cavity. It is found that the squeezing of the cavity mode produced by the PA can be transferred to the magnon mode due to the cavity-magnon beamsplitter-like interaction, and the squeezing of the magnon mode can be further transferred to the phonon mode due to the magnon-phonon beamsplitter-like interaction induced by driving the magnon mode with a red-detuned microwave field. The effects of the parametric gain and phase of the PA, the magnon-cavity coupling strength, the power of the magnon drive, and the temperature of the environment on the squeezing of the magnon and phonon modes have been evaluated. The results show that the squeezing of the magnon and phonon modes is robust against the temperature of the environment.     

Magnon scattering by a symmetric atomic well in free standing very thin magnetic films

A theoretical model is presented for the study of the scattering of magnons at an extended symmetric atomic well in very thin magnetic films. The thin film consists of three cubic atomic planes with ordered spins coupled by Heisenberg exchange, and the system is supported on a non-magnetic substrate, and considered otherwise free from magnetic interactions. The coherent transmission and reflection scattering coefficients are derived as elements of a Landauer type scattering matrix. Transmission and reflection scattering cross sections are hence calculated specifically, as a function of the varying local magnetic exchange on the inhomogeneous boundary. Detailed numerical results for the individual incident film magnons, and for the calculated overall magnon conductance, show characteristic transmission properties, with associated Fano resonances, depending on the magnetic boundary conditions and on the magnon incidence.     

Periodic density redistribution of parametrically excited spin waves in an antiferromagnet

A nonuniform distribution of the density of parametrically excited magnons is observed experimentally in an antiferromagnetic CsMnF₃ sample. The nonuniform distribution occurs at a high pumping power when oscillations of the high frequency susceptibility occur. These oscillations were observed earlier and their nature was not clear. It is found that during the increase of the absorbed power on the occurrence of the oscillation, the spin wave condenses near the middle of the sample. The condensation occurs as a result of a nonlinear shift of the magnon spectrum and is similar to self-focusing of light in nonlinear media. The electromagnetic radiation of parametrically excited spin waves is studied. It is found that the periodic redistribution of the density exerts an additional restrictive effect on the amplitude of the parametrically excited magnons.     

Ballistic magnon transport and phonon scattering in the antiferromagnet Nd2CuO4

The thermal conductivity of the antiferromagnet Nd2CuO4 was measured down to 50 mK. Using the spin-flop transition to switch on and off the acoustic Nd magnons, we can reliably separate the magnon and phonon contributions to heat transport. We find that magnons travel ballistically below 0.5 K, with a thermal conductivity growing as T3, from which we extract their velocity. We show that the rate of scattering of acoustic magnons by phonons grows as T3, and the scattering of phonons by magnons peaks at twice the average Nd magnon frequency.     

Magnon excitation by spin injection in thin Fe/Cr/Fe films

The technique of Brillouin light scattering is used to observe strong excitation of magnons in antiferromagnetically coupled trilayers of Fe/Cr/Fe at room temperature. The magnons are driven out of equilibrium by a microwave current applied in the trilayer through point contacts. The magnitude of the scattering intensity is investigated as a function of the magnon wave number and applied magnetic field. Confirming recent theoretical predictions, the observations provide strong evidence of electronic spin injection in the rf driving field.     

Stationary Entanglement between Light and Microwave via Ferromagnetic Magnons

It is shown how to generate stationary entanglement between light and microwave in a hybrid opto-electro-magnonical system which mainly consists of a microwave cavity, a yttrium iron garnet (YIG) sphere, and a nanofiber. The optical modes in nanofiber can evanescently be coupled to whispering gallery modes, that are able to interact with magnon mode via spin–orbit interaction, in YIG sphere, while the microwave cavity photons and magnons are coupled through magnetic dipole interaction simultaneously. Under reasonable parameter regimes, pretty amount of entanglement can be generated, and it also shows persistence against temperature. The present work is expected to provide a new perspective for building more advanced and comprehensive quantum networks along with magnons for fast-developing quantum technologies and for studying the macroscopic quantum phenomena.     

Amplification of non-Cerenkovian magnons by electrons in a laser radiation field

The rate of change of the magnon population due to scattering by conduction electrons in the presence of an electromagnetic wave is calculated. It is found that non-Cerenkovian high-frequency magnons may be amplified over a very narrow band of magnon wavenumbers.     

Magnon edge modes

We present a theory of long wavelength magnons localized at the apex of a semi-infinite, right angle wedge of a simple cubic, Heisenberg ferromagnet, with nearest and next nearest neighbor exchange interactions, formed by the intersection of two [100] surfaces. The finite difference equation of motion for the magnon creation operators is converted into a partial differential equation in the long wavelength limit, which incorporates the boundary conditions on these operators at the faces of the wedge. The modes obtained are wavelike in the direction parallel to the edge of the wedge, and their amplitudes decay exponentially with increasing distance into the wedge from its apex. The energies of these models lie below those of bulk and surface magnons.