We review the development trends in microwave magnetism and superconductivity over the last five decades. The review contains the key results of recent studies related to the promising areas of modern magnetism and applied physics – spintronics, magnonics, magnon caloritronics, physics of magnonic crystals, spin-wave logic, and the development of novel micro- and nano-scale magnetic devices. The main achievements in these fields of physics are summarized and generalized.

The Bose-Einstein condensate of magnons (mBEC) that is formed at room temperature in parametrically pumped magnetic films is doubly degenerate: it is formed simultaneously in two spectral minima corresponding to the lowest-energy magnons propagating in opposite directions along the in-plane bias magnetic field. In this work the interactions of magnons in the mBEC are studied both theoretically and experimentally. It is shown by direct calculation that the magnons residing in each of the degenerate spectral minima of mBEC form a practically ideal magnon gas, as the attractive self-interaction between these magnons is very weak. At the same time, the interaction between the magnons residing in different spectral minima, corresponding to opposite directions of the magnon wave vector, is relatively strong and repulsive, leading to a repulsive total intermagnon interaction. By measuring the spectral characteristics of the mBEC it is shown that with increased magnon density the energy per magnon in the mBECs increases, thus confirming experimentally that the net intermagnon interaction in a doubly degenerate mBEC is repulsive.

We demonstrate experimentally that a sizable chiral charge pumping can be achieved at room temperature in graphene/yttrium iron garnet (YIG) bilayer systems. The effect, which cannot be attributed to the ordinary spin pumping, reveals itself in the creation of a dc electric field/voltage in graphene as a response to the dynamic magnetic excitations (spin waves) in an adjacent out-of-plane magnetized YIG film. We show that the induced voltage changes its sign when the orientation of the static magnetization is reversed, clearly indicating the broken mirror reflection symmetry about the planes normal to the graphene/YIG interface. The strength of effect shows a nonmonotonous dependence on the spin-wave frequency, in agreement with the proposed theoretical model.

We study the control and manipulation of propagating spin waves in yttrium iron garnet films using a local laser-induced heating. We show that, due to the refraction of spin waves in the thermal gradients, the heated region acts as a defocusing lens for Damon-Eshbach spin waves and as a focusing lens for backward volume waves enabling collimation of spin-wave beams in the latter case. In addition to the focusing/defocusing functionality, the local heating allows one to manipulate the propagation direction of the spin-wave beams and to efficiently suppress their diffraction spreading by utilizing caustic effects.

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/Δf = 3×103. 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 kBEC = 5×104 cm-1, which is in agreement with previous studies.

Abstract This chapter discusses the room-temperature kinetics and thermodynamics of the magnon gas in yttrium iron garnet films driven by a parametric microwave pumping. It shows that for high enough pumping powers, the thermalization of the driven gas results in a quasi-equilibrium state described by the Bose–Einstein statistics with a non-zero chemical potential. Further increase of the pumping power causes a Bose–Einstein condensation documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the Brillouin light scattering spectroscopy to the coherence degree of the scattering magnons, the chapter demonstrates the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, which occurs if their density exceeds a critical value.

We study experimentally the spin-current generation in yttrium iron garnet (YIG)/Pt bilayers based on YIG films with different thicknesses. Our results show that for all films with thicknesses exceeding a certain value, the spin current in the YIG/Pt system is enhanced at low frequencies. The cut-off frequencies, at which the enhancement starts, as well as the efficiency of the enhancement were found to increase with increasing film thickness. Good correlation between the cut-off frequency and the frequency at which the three-magnon splitting becomes allowed was observed. These findings prove that the latter process is responsible for the spin-current enhancement.

Since pure spin currents caused by flows of magnons can propagate in insulating spintronic systems over macroscopic distances, this way to transfer angular momentum without the simultaneous transfer of electric charge has recently attracted a great attention. Here, we discuss the two important effects connected with spin current transfer in yttrium iron garnet films. First, we demonstrate that one or several potential barriers created by an inhomogeneous magnetic field on the way of spin current allow its effective control, magnon tunneling being the underlying physical mechanism of the control. Different aspects of the tunneling process such as resonant tunneling and nonlinear tunneling of magnon solitons will be discussed in detail. Second, we show that the nonlinear three-magnon splitting process can be used for amplification of spin current associated with magnons. The amplification results from the fact that angular momentum is generally not conserved in the three-magnon process, which triggers an additional flow of angular momentum from the lattice to the magnetic subsystem.

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.

Spin waves are delocalized excitations of magnetic media that mainly determine their magnetic dynamics and thermodynamics at temperatures far below the critical one. The quantum-mechanical counterparts of spin waves are magnons, which can be considered as a gas of weakly interacting bosonic quasi-particles. Here, we discuss the room-temperature kinetics and thermodynamics of the magnon gas in yttrium iron garnet films driven by parametric microwave pumping. We show that for high enough pumping powers, the thermalization of the driven gas results in a quasi-equilibrium state described by Bose–Einstein statistics with a non-zero chemical potential. Further increases of the pumping power cause a Bose–Einstein condensation documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the Brillouin light scattering spectroscopy to the degree of coherence of the scattering magnons, we confirm the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, occurring if their density exceeds a critical value.

Spin current, that is, the flow of angular momentum without charge transfer, may be used in efficient spintronics devices. One problem is that spin current tends to decrease, owing to spin–orbit interaction. It is now shown that through interaction with spin waves it is possible to reverse this effect and enhance the spin current back. Spin currents—the flow of angular momentum without the simultaneous transfer of electrical charge—play an enabling role in the field of spintronics1,2,3,4,5,6,7,8. Unlike the charge current, the spin current is not a conservative quantity within the conduction carrier system. This is due to the presence of the spin–orbit interaction that couples the spin of the carriers to angular momentum in the lattice. This spin–lattice coupling9 acts also as the source of damping in magnetic materials, where the precessing magnetic moment experiences a torque towards its equilibrium orientation; the excess angular momentum in the magnetic subsystem flows into the lattice. Here we show that this flow can be reversed by the three-magnon splitting process and experimentally achieve the enhancement of the spin current emitted by the interacting spin waves. This mechanism triggers angular momentum transfer from the lattice to the magnetic subsystem and modifies the spin-current emission. The finding illustrates the importance of magnon–magnon interactions for developing spin-current based electronics.

We use both parallel and perpendicular parametric pumping techniques to excite short-wavelength spin waves in an yttrium iron garnet film and study the spin current generation from spin waves excited by these pumping methods with the help of the inverse spin-Hall effect in the adjacent Pt layer. We observed clear spin current generations for these pumping techniques and find that the efficiency is nearly independent of the magnitude and the direction of the wave vectors of excited spin waves. These experimental results are important for future spintronic devices operated by short-wavelength spin waves.

Кинетика и бозе-эйнштейновская конденсация параметрически возбуждённых магнонов при комнатной температуре, Дзяпко О., Демидов В.Е., Демокритов С.О.

We introduce a system of phenomenological equations for Bose-Einstein condensates of magnons in the one-dimensional setting. The nonlinearly coupled equations, written for amplitudes of the right- and left-traveling waves, combine basic features of the Gross-Pitaevskii and complex Ginzburg-Landau models. They include localized source terms to represent the microwave magnon-pumping field. With the source represented by the delta functions, we find analytical solutions for symmetric localized states of the magnon condensates. We also predict the existence of asymmetric states with unequal amplitudes of the two components. Numerical simulations demonstrate that all analytically found solutions are stable. With the delta-function terms replaced by broader sources, the simulations reveal a transition from the single-peak stationary symmetric states to multi-peak ones, generated by the modulational instability of extended nonlinear-wave patterns. In the simulations, symmetric initial conditions always converge to symmetric stationary patterns. On the other hand, asymmetric inputs may generate nonstationary asymmetric localized solutions, in the form of traveling or standing waves. Comparison with experimental results demonstrates that the phenomenological equations provide for a reasonably good model for the description of the spatiotemporal dynamics of magnon condensates.

Bose-Einstein condensation in a gas of magnons pumped by an incoherent pumping source is experimentally studied at room temperature. We demonstrate that the condensation can be achieved in a gas of bosons under conditions of incoherent pumping. The critical transition point is shown to be almost independent of the frequency spectrum of the pumping source and is solely determined by the density of magnons. The electromagnetic power radiated by the magnon condensate is found to scale quadratically with the pumping power. The obtained results are in a good agreement with the theory of Bose-Einstein condensation of quasiequilibrium magnons.

We have studied experimentally the spatial properties and the dynamics of magnon Bose-Einstein condensates created in ferromagnetic films by a parametric pumping with different spatial configurations. Using the specific character of dynamic fields produced by pumping resonators of different shapes, we were able to realize the regime, in which two spatially separated condensates of magnons are formed. Our experiments show that while the separation between the condensates is determined by the size of the resonator, their spatial width can be changed by varying the power of the pumping signal.

Using a novel technique providing simultaneous resolution with respect to the wave vector and frequency of magnons, we observed the formation of a Bose-Einstein condensate documented by the narrowing of the magnon distribution in phase space. Based on the measured width of the distribution we determined the effective correlation length of the condensate, which appears to be anisotropic, reflecting the anisotropy of the magnon dispersion spectrum.

The room-temperature kinetics and thermodynamics of the magnon gas driven by microwave pumping has been investigated by means of the Brillouin light scattering ( BLS) technique. We show that for high enough pumping powers the quantum relaxation of the driven gas results in a quasi-equilibrium state described by the Bose-Einstein statistics with a nonzero chemical potential. Further increase of the pumping power causes a Bose Einstein condensation in the magnon gas documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the BLS to the coherence degree of the scattering magnons, we confirm the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, if their density exceeds a critical value.