Nonreciprocity, the defining characteristic of isolators, circulators, and a wealth of other applications in radio/microwave communications technologies, is generally difficult to achieve as most physical systems incorporate symmetries that prevent the effect. In particular, acoustic waves are an important medium for information transport, but they are inherently symmetric in time. In this work, we report giant nonreciprocity in the transmission of surface acoustic waves (SAWs) on lithium niobate substrate coated with ferromagnet/insulator/ferromagnet (FeGaB/Al2O3/FeGaB) multilayer structure. We exploit this structure with a unique asymmetric band diagram and expand on magnetoelastic coupling theory to show how the magnetic bands couple with acoustic waves only in a single direction. We measure 48.4-dB (power ratio of 1:69,200) isolation that outperforms current state-of-the-art microwave isolator devices in a previously unidentified acoustic wave system that facilitates unprecedented size, weight, and power reduction. In addition, these results offer a promising platform to study nonreciprocal SAW devices.

An analog microwave signal correlator, based on parametric pumping of a spin wave by an rf magnetic field, is demonstrated. The binary codes to be correlated modulate the two microwave signals input to the device to, respectively, excite the spin wave and rf field at twice the carrier frequency of the spin wave. The magnetic field parametrically pumps the spin wave, generating a counter-propagating idler spin wave, the modulation of which is the cross-correlation of the binary codes. In the experimental device implemented, correlation of codes up to 16 chips in length at a spin wave carrier frequency of 1.2 GHz is demonstrated. The code length is limited by the time available for the parametric interaction as well as the signal bandwidth of the device. Process gain, which quantifies the performance of the correlator in recognizing a given code and rejecting interfering codes, is determined for shorter codes and found to be close to the theoretical maximum for each length. The correlator efficiency, with a bilinearity coefficient of -79 dBm, is poor. However, there remains significant scope for optimization of the experimental device so that correlation of longer codes with improved efficiency will be possible.

It is shown theoretically that in a layered heterostructure comprising piezoelectric, dielectric antiferromagnetic crystal, and heavy metal (PZ/AFM/HM), it is possible to control the anisotropy of the AFM layer by applying a dc voltage across the PZ layer. In particular, we show that by varying the dc voltage across the heterostructure and/or the dc current in the HM, it is possible to vary the frequency of the antiferromagnetic resonance of the AFM in a passive (subcritical) regime and, also, to reduce the threshold of the current-induced terahertz-frequency generation. Our analysis also shows that, unfortunately, the voltage-induced reduction of the generation threshold leads to the proportional reduction of the amplitude of the terahertz-frequency signal generated in the active (supercritical) regime. The general results are illustrated by a calculation of the characteristics of experimentally realizable PZT-5H/NiO/Pt.

A theory of magnetization dynamics in ferrimagnetic materials with antiparallel aligned spin sublattices under the action of spin-transfer torques (STTs) is developed. In contrast with antiferromagnets, the magnetic sublattices in ferrimagnets are formed by different magnetic ions, which results in a symmetry breaking in the dynamic equations for Néel’s vector. We demonstrate that this symmetry breaking becomes crucially essential for the THz signal extraction in ferrimagnetic spin-torque oscillators. As an example, we consider magnetization dynamics in GdFeCo layers in spin Hall and nanocontact spin-torque oscillator geometries. We demonstrate that (i) the application of spin current leads to a conical precession of Néel’s vector with sub-THz frequencies, (ii) in the spin Hall geometry, the conical precession leads to sub-THz oscillations of the Hall voltage, and (iii) in the nanocontact geometry the Néel’s vector precession leads to sub-THz oscillations of the magnetoresistance.

The strong strain-mediated magnetoelectric (ME) coupling found in thin-film ME heterostructures has attracted an ever-increasing interest and enables realization of a great number of integrated multiferroic devices, such as magnetometers, mechanical antennas, RF tunable inductors and filters. This paper first reviews the thin-film characterization techniques for both piezoelectric and magnetostrictive thin films, which are crucial in determining the strength of the ME coupling. After that, the most recent progress on various integrated multiferroic devices based on thin-film ME heterostructures are presented. In particular, rapid development of thin-film ME magnetometers has been seen over the past few years. These ultra-sensitive magnetometers exhibit extremely low limit of detection ($\mathrm{sub-pT/Hz}^{1/2}$) for low-frequency AC magnetic fields, making them potential candidates for applications of medical diagnostics. Other devices reviewed in this paper include acoustically actuated nanomechanical ME antennas with miniaturized size by 1–2 orders compared to the conventional antenna; integrated RF tunable inductors with a wide operation frequency range; integrated RF tunable bandpass filter with dual H- and E-field tunability. All these integrated multiferroic devices are compact, lightweight, power-efficient, and potentially integrable with current complementary metal oxide semiconductor (CMOS) technology, showing great promise for applications in future biomedical, wireless communication, and reconfigurable electronic systems.

A theory of parametric interaction between spin waves localized in a waveguide and traveling elastic waves is developed for ferromagnetic thin films. The presented theoretical formalism takes into account an arbitrary spatial distribution of the displacement field in the acoustic waves and an arbitrary magnetization in spin waves. Using the theory, we examine interaction of forward-volume spin waves (FVSW) localized in a narrow waveguide and Rayleigh surface acoustic waves traveling in a substrate underneath the waveguide. We show that, in contrast to classical electromagnetic pumping, the symmetry of the magnetoelastic interaction allows for the generation of first-order parametric instabilities in spin waves with circular precession, such as FVSW. At the same time the localization of spin waves modifies the momentum conservation law for the parametric process to include the transfer of momentum to the waveguide, which allows for a frequency separation of the interacting counterpropagating spin waves. The frequency separation enables amplification of a localized spin wave without generation of a traveling idler wave, which results in a greater amplification efficiency.

We demonstrate analytically and numerically, that a thin film of an antiferromagnetic (AFM) material, having biaxial magnetic anisotropy and being driven by an external spin-transfer torque signal, can be used for the generation of ultra-short “Dirac-delta-like” spikes. The duration of the generated spikes is several picoseconds for typical AFM materials and is determined by the inplane magnetic anisotropy and the effective damping of the AFM material. The generated output signal can consist of a single spike or a discrete group of spikes (“bursting”), which depends on the repetition (clock) rate, amplitude, and shape of the external control signal. The spike generation occurs only when the amplitude of the control signal exceeds a certain threshold, similar to the action of a biological neuron in response to an external stimulus. The “threshold” behavior of the proposed AFM spike generator makes possible its application not only in the traditional microwave signal processing but also in the future neuromorphic signal processing circuits working at clock frequencies of tens of gigahertz.

It has been shown previously that spin-Hall oscillators based on current-driven bi-layered film structures containing an antiferromagnet (AFM) and a normal metal can generate ultra-short (∼2 ps) “spike-like” pulses in response to an external current stimulus of a sufficient amplitude, thus operating as ultra-fast artificial “neurons.” Here, we report the results of numerical simulations demonstrating that a single AFM “neuron” can perform the logic functions of or, and, majority, or q-gates, while a circuit consisting of a small number $n<5$ of AFM “neurons” can function as a full-adder or as a dynamic memory loop with variable clock frequency. The clock frequencies of such AFM-based logic devices could reach tens of GHz, which make them promising as base elements of future ultra-fast high-efficiency neuromorphic computing.

Surface acoustic waves (SAWs) propagating in a piezoelectric substrate covered with a thin ferromagnetic–heavy-metal bilayer are found to exhibit a substantial degree of nonreciprocity, i.e., the frequencies of these waves are nondegenerate with respect to the inversion of the SAW propagation direction. The simultaneous action of the magnetoelastic interaction in the ferromagnetic layer and the interfacial Dzyaloshinskii-Moriya interaction in the ferromagnetic–heavy-metal interface results in the openings of magnetoelastic band gaps in the SAW spectrum, and the frequency position of these band gaps is different for opposite SAW propagation directions. The band-gap widths and the frequency separation between them can be controlled by a proper selection of the magnetization angle and the thickness of the ferromagnetic layer. Using numerical simulations, we demonstrate that the isolation between SAWs propagating in opposite directions in such a system can exceed the direct SAW propagation losses by more than 1 order of magnitude.

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.

The development of compact and tunable room temperature sources of coherent THz-frequency signals would open a way for numerous new applications. The existing approaches to THz-frequency generation based on superconductor Josephson junctions (JJ), free electron lasers, and quantum cascades require cryogenic temperatures or/and complex setups, preventing the miniaturization and wide use of these devices. We demonstrate theoretically that a bi-layer of a heavy metal (Pt) and a bi-axial antiferromagnetic (AFM) dielectric (NiO) can be a source of a coherent THz signal. A spin-current flowing from a DC-current-driven Pt layer and polarized along the hard AFM anisotropy axis excites a non-uniform in time precession of magnetizations sublattices in the AFM, due to the presence of a weak easy-plane AFM anisotropy. The frequency of the AFM oscillations varies in the range of 0.1–2.0 THz with the driving current in the Pt layer from $10^8 \text{A}/\text{cm}^2$ to $10^9 \text{A}/\text{cm}^2$. The THz-frequency signal from the AFM with the amplitude exceeding $1 \text{V}/\text{cm}$ is picked up by the inverse spin-Hall effect in Pt. The operation of a room-temperature AFM THz-frequency oscillator is similar to that of a cryogenic JJ oscillator, with the energy of the easy-plane magnetic anisotropy playing the role of the Josephson energy.

A general theory of collective spin-wave edge modes in semi-infinite and finite periodic arrays of magnetic nanodots having uniform dynamic magnetization (macrospin approximation) is developed. The theory is formulated using a formalism of multivectors of magnetization dynamics, which allows one to study edge modes in arrays having arbitrarily complex primitive cells and lattice structure. The developed formalism can describe spin-wave edge modes localized both at the physical edges of the array and at the internal “domain walls” separating the array regions existing in different static magnetization states. Using a perturbation theory, in the framework of the developed formalism, it is possible to calculate damping of the edge modes and to describe their excitation by external variable magnetic fields. The theory is illustrated on the following practically important examples: (i) calculation of the FMR absorption in a finite nanodot array having the shape of a right triangle; (ii) calculation of the spectra of nonreciprocal spin-wave edge modes, including the modes at the physical edges of an array and modes at the domain walls inside the array; and (iii) study of the influence of the domain wall modes on the FMR spectrum of an array existing in a nonideal chessboard antiferromagnetic ground state.

It is demonstrated theoretically that a thin layer of an anisotropic antiferromagnetic (AFM) insulator can effectively conduct spin current through the excitation of a pair of evanescent AFM spin wave modes. The spin current flowing through the AFM is not conserved due to the interaction between the excited AFM modes and the AFM lattice and, depending on the excitation conditions, can be either attenuated or enhanced. When the phase difference between the excited evanescent modes is close to $\pi/2$, there is an optimum AFM thickness for which the output spin current reaches a maximum, which can significantly exceed the magnitude of the input spin current. The spin current transfer through the AFM depends on the ambient temperature and increases substantially when temperature approaches the Néel temperature of the AFM layer.

We develop a theoretical formalism for the description of the interaction of microwave photons with a thin (compared to the photon wavelength) magnetic metasurface comprised of dipolarly interacting nanoscale magnetic elements. We derive a scattering matrix describing the processes of photon transmission and reflection at the metasurface boundary. As an example of the use of the developed formalism, we demonstrate that the introduction of a magnetic metasurface inside a microstrip electromagnetic waveguide quantitatively changes the dispersion relation of the fundamental waveguide mode, opening a nonpropagation frequency band gap in the waveguide spectrum. The frequency position and the width of the band gap are dependent on the waveguide thickness and can be controlled dynamically by switching the magnetic ground state of the metasurface. For sufficiently thin waveguides, the position of the band gap is shifted from the resonance absorption frequency of the metasurface. In such a case, the magnetic metasurface inside a waveguide works as an efficient reflector, as the energy absorption in the metasurface is small, and most of the electromagnetic energy inside the nonpropagation band gap is reflected.

A design of a magnonic phase shifter operating without an external bias magnetic field is proposed. The phase shifter uses a localized collective spin wave mode propagating along a domain wall “waveguide” in a dipolarly-coupled magnetic dot array with a chessboard antiferromagnetic (CAFM) ground state. It is demonstrated numerically that the remagnetization of a single magnetic dot adjacent to the domain wall waveguide introduces a controllable phase shift in the propagating spin wave mode without significant change to the mode amplitude. It is also demonstrated that a logic XOR gate can be realized in the same system.

Recent results in magnonics – a topical and rapidly developing branch of spintronics and magnetoelectronics – are presented. The paper describes measurement techniques and theoretical approaches used to explore physical processes associated with the spin-wave propagation in complex nano- and micro-dimensional magnetic structures. The results of the application of magnetic structures in signal processing and transmission systems are discussed. In particular, results on spin wave propagation in distributed magnetic periodic structures, lumped systems, coupled waveguide structures, and controllable magnonic structures are considered. Specific examples of circuitry based on magnonic structures are discussed, and possibilities for further developing this circuitry are explored.

Approximate electrodynamic boundary conditions are derived for an array of dipolarly coupled magnetic elements. It is assumed that the elements’ thickness is small compared to the wavelength of an electromagnetic wave in a free space. The boundary conditions relate electric and magnetic fields existing at the top and bottom sides of the array through the averaged uniform dynamic magnetization of the array. This dynamic magnetization is determined by the collective dynamic eigen-excitations (spin wave modes) of the array and is found using the external magnetic susceptibility tensor. The problem of oblique scattering of a plane electromagnetic wave on the array is considered to illustrate the use of the derived boundary conditions.

Spin waves propagation in 1D magnonic crystals is investigated theoretically. Mathematical model based on plane wave expansion method is applied to different types of magnonic crystals, namely bi-component magnonic crystal with symmetric/asymmetric boundaries and ferromagnetic film with periodically corrugated top surface. It is shown that edge modes in magnonic crystals may exhibit nonreciprocal behaviour at much lower frequencies than in homogeneous films.

The frequency spectrum of spin-wave edge modes localized near the boundaries of a finite array of dipolarly coupled magnetic nanopillars is calculated theoretically. Two mechanisms of edge mode formation are revealed: inhomogeneity of the internal static magnetic field existing near the array boundaries and time-reversal symmetry breaking of the dipole-dipole interaction. The latter mechanism is analogous to the formation mechanism of a surface Damon-Eschbach mode in continuous in-plane magnetized magnetic films and is responsible for the nonreciprocity of edge modes in finite-width nanopillar arrays. The number of edge modes in nanopillar arrays depends on the spatial profile of the internal static magnetic field near the array boundaries and several edge modes are formed if a substantial field inhomogeneity extends over several rows of nanopillars.

We show theoretically that in elastic layered structures containing an upper layer of smoothly varied thickness and a substrate of a highly dispersive metametarial it is possible to significantly enhance spatial frequency separation of surface acoustic waves. Theory of Love surface acoustic waves propagation in waveguides with varied thickness, taking into account mutual modes coupling, is built. Appropriate structure of metamatererial with resonant frequency dependence of material parameters, making frequency separation effective, is provided. Efficiency of spatial frequency separation and modes coupling is calculated for various metamaterial parameters and wave frequencies.

It is predicted that in 2D magnonic crystals the edge rotational magnons of forward volume magnetostatic spin waves can exist. Under certain conditions, locally bounded magnons may appear within the crystal consisting of the ferromagnetic matrix and periodically inserted magnetic/non-magnetic inclusions. It is also shown that interplay of different resonances in 2D magnonic crystal may provide conditions for spin wave modes existence with negative group velocity.

The nonreciprocal properties of spin waves in metallized one-dimensional bi-component magnonic crystal composed of two materials with different magnetizations are investigated numerically. Nonreciprocity leads to the appearance of indirect magnonic band gaps for magnonic crystals with both low and high magnetization contrast. Specific features of the nonreciprocity in low contrast magnonic crystals lead to the appearance of several magnonic band gaps located within the first Brillouin zone for waves propagating along the metallized surface. Analysis of the spatial distribution of dynamic magnetization amplitudes explains the mechanism of dispersion band formation and hybridization between magnonic bands in magnonic crystals with metallization.

The Doppler effect in doubly double negative acoustic media is theoretically investigated. The radiation spectra of a source moving relative to a medium are calculated with the help of the method of the Green’s functions. It is shown that several Doppler modes can be generated by a monochromatic source owing to the strong dependence of the wave number on frequency. The dependence of the width of the opacity band on the velocity of the relative motion of the source and medium is analyzed.

Acoustic wave propagation in a composite of water with embedded double-layered silicone resin/silver rods is considered. Approximate values of effective dynamical constitutive parameters are obtained. Frequency ranges of simultaneous negative constitutive parameters are found. Localized surface states on the interface between metamaterial and “normal” material are found. The Doppler effect in metamaterial is considered. The presence of anomalous modes is shown.

Elastic wave propagation along the structure of hollow cylinders in a linear isotropic medium is investigated. The multipole method for modeling elastic waves propagation in such structures is formulated and implemented. Using the multipole method, dispersion dependencies of the structures (microstructured fibers) containing 3, 6, and 7 hollow cylinders are calculated. Comparison with wave dispersion properties along one cylinder is made. Also, an approximate physical model based on an equivalent coaxial waveguide and multipole method is proposed. Exploiting this model, wave dispersion of the wave propagating along a structure with 18 hollow cylinders is calculated. Validation of the model is also proposed.

Two ways of modeling of elastic wave propagation in microstructured acoustic fiber are considered. First one is the calculation of band gap parameters by FEM for phononic crystal forming cross section of fiber. Second one is immediate calculation of dispersion characteristics of elastic fiber containing hole cylindric chanels. For fiber made of fused β quarz numerical results are proposed. For the first type full forbidden gap obtained and for second two different types of modes was found.

Propagation of elastic waves in a system of cylindrical channels embedded in a homogeneous isotropic elastic medium (a phononic crystal) is investigated. A multipole method is proposed for simulation of wave propagation in such structures. The dispersion characteristics of wave propagation in systems consisting of three, six, and seven cylindrical channels are calculated. The results are compared to the data corresponding to wave propagation along a single channel. The computational efficiency of the method and its applicability to simulation of the propagation of elastic waves in large phononic crystals are assessed.