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A single resonance-type spin-torque microwave diode (STMD) can be used as a quadratic detector to determine the frequency $f$ of an external microwave signal when the power $P_{\rm rf}$ of this signal is known. However, unless the signal's frequency $f$ exactly coincides with the detector's resonance frequency $f_{\rm res}$ , there exists a finite frequency determination error $\Delta f$ . In this letter, we show theoretically and experimentally that if a pair of independent STMDs with different resonance frequencies connected in parallel is used for the signal frequency determination, knowledge of the signal power is not necessary, and the frequency determination error can be substantially reduced to $\Delta f \approx $ 30 MHz at the frequency of $f \approx $ 5.0 GHz.

It is well-known that a spin-transfer torque caused by a dc electric current can excite in a two-dimensional ferromagnetic film exchange-dominated magnetic solitons, often called “spin-wave bullets”, under the condition of a negative nonlinear shift of spin wave frequency. In this work, we demonstrate that in a quasi-one-dimensional (1D) case, e.g., in a nanowire spin-Hall oscillator, it is possible to excite a stable dissipative magnetic soliton, which is dominated by the dipole-dipole interaction. This dissipative magnetic soliton can be described in the framework of a 1D Ginzburg-Landau auto-oscillator model, and has the shape similar to that of the exchange-dominated spin wave bullet, but with a different spatial localization law. The influence of the dipolar interaction makes possible the stabilization of a dissipative soliton in a relatively large (micron-sized) active area of the oscillator, which is in a sharp contrast with the two-dimensional case, where the excitation of a stable spin-wave bullet was observed only in relatively small active areas having typical sizes of the order of 100 nm. The characteristics and possible applications of these dipole-dominated spin wave bullets are discussed.

We demonstrate that a spin-torque nano-oscillator (STNO) rapidly sweep-tuned by a bias voltage can be used to perform an ultrafast time-resolved spectral analysis of frequency-manipulated microwave signals. The critical reduction in the time of the spectral analysis comes from the naturally small-time constants of a nanosized STNO (1-100 ns). The demonstration is performed on a vortex-state STNO generating in a frequency range around 300 MHz, when frequency down-conversion and matched filtering is used for signal processing. It is shown that this STNO-based spectrum analyzer can perform analysis of frequency-agile signals, having multiple rapidly changing frequency components with temporal resolution in a μs time scale and frequency resolution limited only by the "bandwidth" theorem. Our calculations show that using uniform magnetization state STNOs it would be possible to increase the operating frequency of a spectrum analyzer to tens of GHz.

We have recently shown that injection of magnons into a magnetic dielectric via the spin-orbit torque (SOT) effect in the adjacent layer of a heavy metal subjected to the action of short (0.1 $\mu$s) current pulses allows for control of a magnon Bose-Einstein Condensate (BEC). Here, the BEC was formed in the process of rapid cooling (RC), when the electric current heating the sample is abruptly terminated. In the present study, we show that the application of a longer (1.0 $\mu$s) electric current pulse triggers the formation of a nonlinear localized magnonic bullet below the linear magnon spectrum. After pulse termination, the magnon BEC, as before, is formed at the bottom of the linear spectrum, but the nonlinear bullet continues to exist, stabilized for additional 30 ns by the same process of RC-induced magnon condensation. Our results suggest that a stimulated condensation of excess magnons to all highly populated magnonic states occurs.

Second sound is a quantum mechanical effect manifesting itself as a wave-like (in contrast with diffusion) heat transfer, or energy propagation, in a gas of quasi-particles. So far, this phenomenon has been observed only in an equilibrium gas of phonons existing in liquid/solid helium, or in dielectric crystals (Bi, NaF) at low temperatures. Here, we report observation of a room-temperature magnonic second sound, or a wave-like transport of both energy and spin angular momentum, in a quasi-equilibrium gas of magnons undergoing Bose-Einstein condensation (BEC) in a ferrite film. Due to the contact of the magnon gas with pumping photons and phonons, dispersion of the magnonic second sound differ qualitatively from the phononic case, as there is no diffusion regime, and the second sound velocity remains finite at low wavenumbers. Formation of BEC in the gas of magnons modifies the second sound properties by creating an additional channel of energy relaxation.

Spin waves offer intriguing novel perspectives for computing and signal processing, since their damping can be lower than the Ohmic losses in conventional CMOS circuits. For controlling the spatial extent and propagation of spin waves on the actual chip, magnetic domain walls show considerable potential as magnonic waveguides. However, low-loss guidance of spin waves with nanoscale wavelengths, in particular around angled tracks, remains to be shown. Here we experimentally demonstrate that such advanced control of propagating spin waves can be obtained using natural features of magnetic order in an interlayer exchange-coupled, anisotropic ferromagnetic bilayer. Using Scanning Transmission X-Ray Microscopy, we image generation of spin waves and their propagation across distances exceeding multiple times the wavelength, in extended planar geometries as well as along one-dimensional domain walls, which can be straight and curved. The observed range of wavelengths is between 1 {\mu}m and 150 nm, at corresponding excitation frequencies from 250 MHz to 3 GHz. Our results show routes towards practical implementation of magnonic waveguides employing domain walls in future spin wave logic and computational circuits.

A theory of an electrically controlled terahertz-frequency auto-oscillator is developed here within the framework of the antiferromagnetic sigma model. The structure is based on a trilayer heterostructure: a piezoelectric ceramic, NiO-based antiferromagnet (AFM), and a heavy metal. The authors demonstrate that the frequency of the AFM resonance of the layered structure in a passive subcritical regime can be controlled by the external electric field applied to the piezoelectric, by choosing a proper piezoelectric material, and by the magnitude of the electric current flowing in the heavy metal.

A frequency-tunable low-phase-noise magnetoacoustic resonator is developed on the base of a parallel-plate straight-edge bilayer consisting of an yttrium-iron-garnet (YIG) layer grown on a substrate of a gallium gadolinium garnet (GGG). When a YIG-GGG sample forms an ideal parallel plate, it supports a series of high-quality-factor acoustic modes standing along the plate thickness. Due to the magnetostriction of the YIG layer the ferromagnetic resonance (FMR) mode of the YIG layer can strongly interact with the acoustic thickness modes of the YIG-GGG structure, when the modes' frequencies match. A particular acoustic thickness mode used for the resonance excitations of the hybrid magnetoacoustic oscillations in a YIG-GGG bilayer is chosen by the YIG-layer FMR frequency, which can be tuned by the variation of the external bias magnetic field. A composite scheme of a magnetoacoustic oscillator, which includes a FMR-based resonance preselector, is developed to guarantee satisfaction of the Barkhausen criteria for a single-acoustic-mode oscillation regime. The developed low-phase-noise composite magnetoacoustic oscillator can be tuned from 0.84 to 1 GHz with an increment of about 4.773 MHz (frequency distance between the adjacent acoustic thickness modes in a YIG-GGG parallel plate), and demonstrates the phase noise of $\ensuremath{-}116$ dBc/Hz at the offset frequency of 10 kHz.

The discovery of interfacial Dzyaloshinskii-Moriya interaction (DMI) enables development of novel ultra-compact non-reciprocal devices for microwave signal processing. Such devices are based on control of spin waves and magneto-elastic waves by electric field and addition of ultra-thin layers of heavy metals to the devices. Here we discuss recent advances in the development of such systems, which can be used for implementation of on-chip non-reciprocal microwave devices.

A spin current - a flow of spin angular momentum - can be carried either by spin polarised free electrons or by magnons, the quanta of a moving collective oscillation of localised electron spins - a spin wave. Traditionally, it was assumed, that a spin wave in a magnetic film with spin-sink-free surfaces can transfer energy and angular momentum only along its propagation direction. In this work, using Brillouin light scattering spectroscopy in combination with a theory of dipole-exchange spin-wave spectra, we show that in obliquely magnetized free magnetic films the in-plane propagation of spin waves is accompanied by a transverse spin current along the film normal without any corresponding transverse transport of energy.

The transmission and reflection of a spin wave at an internal boundary created by the local variation of anisotropy (or a bias magnetic field) are studied taking into account not only the changes in the wave amplitude, but also the changes in the wave polarization. It is shown that the account of the changes in the spin-wave polarization before and after the boundary leads to (i) increase of the spin-wave amplitude reflection coefficient, (ii) appearance of an additional phase shift $\mathrm{\ensuremath{\Delta}}\ensuremath{\phi}\ensuremath{\ne}0,\ensuremath{\pi}$ in both transmitted and reflected waves, and (iii) creation of additional evanescent waves in the vicinity of the boundary. It is also shown that even when significant changes in the transmitted wave polarization take place at the boundary, a spin wave could pass a finite-width boundary without reflection, if a certain resonance condition is satisfied. The effect of the polarization change at an internal boundary is especially pronounced for the exchange-dominated spin waves, while in the case of the dipole-dominated spin waves, this effect can vanish completely for certain configurations of the static magnetization.

A concept of an electrically tunable resonance detector of THz-frequency signals based on antiferromagnetic/heavy metal (AFM/HM) hetero-structure is proposed. The conversion of a THz-frequency input signal into DC voltage is done using the inverse spin Hall effect in an (AFM/HM) bilayer. An additional bias DC current in the HM layer can be used to vary the effective anisotropy of the AFM, and, therefore, to tune the AFMR frequency. The proposed AFM/HM hetero-structure works as a resonance-type quadratic detector which can be tuned by the bias current in the range of at least 10 percent of the AFMR frequency and our estimations show that the sensitivity of this detector could be comparable to that of modern detectors based on the Schottky, Gunn or graphene-based diodes.

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/$\mathrm{Ni}\mathrm{O}$/$\mathrm{Pt}$.

We demonstrate theoretically that in a spintronic diode (SD), having a free magnetic layer with perpendicular magnetic anisotropy of the first and second order and no external bias magnetic field, the out-of-plane regime of magnetization precession can be excited by sufficiently large (exceeding a certain threshold) RF signals with the frequencies, Comment: 6 pages, 3 figures. Submitted to the Appl. Phys. Lett

We use vector Hamiltonian formalism (VHF) to study theoretically three-magnon parametric interaction (or three-wave splitting) in a magnetic disk existing in a magnetic vortex ground state. The three-wave splitting in a disk is found to obey two selection rules: (i) conservation of the total azimuthal number of the resultant spin-wave modes, and (ii) inequality for the radial numbers of interacting modes, if the mode directly excited by the driving field is radially symmetric (i.e. if the azimuthal number of the directly excited mode is $m = 0$). The selection rule (ii), however, is relaxed in the "small" magnetic disks, due to the influence of the vortex core. We also found, that the efficiency of the three-wave interaction of the directly excited mode strongly depends on the azimuthal and radial mode numbers of the resultant modes, that becomes determinative in the case when several splitting channels (several pairs of resultant modes) simultaneously approximately satisfy the resonance condition for the splitting. The good agreement of the VHF analytic calculations with the experiment and micromagnetic simulations proves the capability of the VHF formalism to predict the actual splitting channels and the magnitudes of the driving field thresholds for the three-wave splitting., Comment: 10 pages, 4 figures

In this review, we consider theoretical and experimental results related to the properties of two-dimensional spin-wave (SW) solitons, so-called SW bullets and SW droplets. Such nonlinear self-localized SW modes possess very interesting physical properties, and could have practical applications in modern and future magnonics and spintronics. The experimental and theoretical results presented in this review have undeniably proven the existence of SW bullets in magnetic films and confined magnetic nanostructures (magnetic nanocontacts), and have elucidated the essential distinctions between the properties of the one-dimensional nonlinear SW solitons, two-dimensional nonlinear SW bullets and linear spin wave packets, as well as the possibility of self-generation, parametrical excitation, and phase-conjugation of the SW bullets, similar to the case of the conventional linear spin waves. Also, in this review we presented experimental results demonstrating the nucleation, dynamics, and annihilation of two-dimensional strongly nonlinear SW “droplets” in spin-torque-driven magnetic nanocontacts. The properties of these exotic nonlinear objects are analyzed using recently developed theoretical models and illustrated by micromagnetic numerical simulations.

We propose a novel type of terahertz-frequency (TF) signal source based on an antiferromagnetic tunnel junction (ATJ), where the generated ac signal is extracted through the variations of the tunneling anisotropic magnetoresistance (TAMR) of an ATJ. The signal source comprises a layered structure consisting of a current-driven platinum (Pt) layer and a layer of an antiferromagnet (AFM) separated by an MgO spacer from an additional Pt electrode. A dc electric current flowing in the first Pt layer due to the spin Hall effect creates a perpendicular spin current that, being injected in the AFM layer, tilts the magnetizations of the AFM sublattices and, therefore, causes TF rotation of these magnetizations in a large internal exchange magnetic field of the AFM. This rotation, through the TAMR effect, causes the TF variation of the total resistance of the layered structure. We evaluate the output power and efficiency of the above-described Pt/AFM/MgO/Pt TF signal source, and demonstrate that optimization of the source's geometrical parameters allows one to obtain the output power exceeding 1 $\mu$ W at the frequency of 0.5 THz with the efficiency not smaller than 1%. Although the efficiency of the TAMR method of the TF signal extraction is reduced with the increase of the generation frequency, we believe that this method could be used for the generation of signals with frequencies of up to 10 THz due to its relative simplicity and convenience.

A method to perform spectrum analysis on low power signals between 0.1 and 10 THz is proposed. It utilizes a nanoscale antiferromagnetic tunnel junction (ATJ) that produces an oscillating tunneling anisotropic magnetoresistance, whose frequency is dependent on the magnitude of an evanescent spin current. It is first shown that the ATJ oscillation frequency can be tuned linearly with time. Then, it is shown that the ATJ output is highly dependent on matching conditions that are highly dependent on the dimensions of the dielectric tunneling barrier. Spectrum analysis can be performed by using an appropriately designed ATJ, whose frequency is driven to increase linearly with time, a low pass filter, and a matched filter. This method of THz spectrum analysis, if realized in experiment, will allow miniaturized electronics to rapidly analyze low power signals with a simple algorithm. It is also found by simulation and analytical theory that for an ATJ with a 0.09 $\mu$m$^2$ footprint, spectrum analysis can be performed over a 0.25 THz bandwidth in just 25 ns on signals that are at the Johnson-Nyquist thermal noise floor., Comment: 10 pages, 5 figures, submitted to the Journal of Applied Physics

One of the major challenges in surface acoustic wave (SAW) technology, which is widely used in modern signal processing, is the absence of wave nonreciprocity (one-way propagation). To tackle this problem, the authors propose an approach based on magnetoelastic coupling of SAWs to spin waves possessing a suitable spectrum. This approach allows the creation of nonreciprocal SAW devices with almost no limitations on the working-frequency band (in contrast to the severe band limitations of traditional approaches), to realize the full potential of magnetoelastically induced SAW nonreciprocity. These results could become a breakthrough step toward nonreciprocal SAW signal processing.

We report a ferromagnetic resonance study of an electrically insulating magnetic bi-layer consisting of two yttrium iron garnet (YIG) films epitaxially grown on both sides of a non-magnetic gadolinium gallium garnet (GGG) slab. We show that standing transverse sound waves couple the coherent magnetization dynamics of the two YIG films half millimeter apart through the magnetoelastic interaction, periodically modulating the microwave absorption as a function of frequency. Constructive and destructive interferences between the dynamics of the two YIG layers is observed. This long range coherent coupling by phononic angular momentum currents through non-magnetic dielectric waveguide brings new functionalities to insulator hybrid spin circuits and devices.

A Hamiltonian formalism is applied for the investigation of nonlinear spin wave dynamics under the influence of antisymmetric magnetic interactions. In the framework of this formalism we account not only for symmetric magnetic interactions (exchange, dipole-dipole, magnetocrystalline anisotropy), but also for antisymmetric interactions, such as Dzyaloshinskii-Moriya exchange interaction. The account of antisymmetric exchange, in general, could lead to the appearance of an additive nonreciprocal term in the spin wave dispersion law. We present the generalization of the linear transformation for the diagonalization of quadratic part of the Hamiltonian (so-called ``third Holstein-Primakoff transformation'') for the antisymmetric case, which allowed us to obtain generalized expressions for the coefficients of the nonlinear three- and four-magnon interactions. As an example, nonlinear spin wave interactions in ultrathin ferromagnetic nanowires and films subjected to interfacial Dzyaloshinskii-Moriya interaction (IDMI) are considered. It was found that three-magnon interaction coefficients in the ``Damon-Eshbach'' geometry are nonzero only in the case of the noncollinear interacting spin waves, and vanish in the case of the collinear spin waves. It was also found that the nonlinear spin wave frequency shift caused by the four-magnon interaction is nonreciprocal, and has the sign opposite to that of the nonreciprocal term in linear spin wave dispersion, so that the IDMI-induced nonreciprocity of the spin wave spectrum decreases with the increase of the spin wave amplitude.

Spin waves propagating in nanoscale ferromagnetic waveguides are considered promising for a new generation of digital and analog magnonic signal-processing devices, where the signal is encoded in a spin wave's amplitude or phase, or both. Stable, error-free operation of spin-wave devices requires well-defined spin-wave phase, which can be disrupted by technological imperfections or thermal noise, leading to the accumulation of phase errors in a magnonic circuit. The authors demonstrate that such phase errors can be corrected by the application of parametric pumping, via voltage-controlled magnetic anisotropy, to local gates placed in the spin wave's path.

Time-resolved scanning transmission x-ray microscopy (TR-STXM) has been used for the direct imaging of spin wave dynamics in thin film yttrium iron garnet (YIG) with spatial resolution in the sub 100 nm range. Application of this x-ray transmission technique to single crystalline garnet films was achieved by extracting a lamella (13x5x0.185 $\mathrm{\mu m^3}$) of liquid phase epitaxy grown YIG thin film out of a gadolinium gallium garnet substrate. Spin waves in the sample were measured along the Damon-Eshbach and backward volume directions of propagation at gigahertz frequencies and with wavelengths in a range between 100~nm and 10~$\mathrm{\mu}$m. The results were compared to theoretical models. Here, the widely used approximate dispersion equation for dipole-exchange spin waves proved to be insufficient for describing the observed Damon-Eshbach type modes. For achieving an accurate description, we made use of the full analytical theory taking mode-hybridization effects into account.

The realization of THz sources is a fundamental aspect for a wide range of applications. Over different approaches, compact THz oscillators can be realized taking advantage of dynamics in antiferromagnetic (AFMs) thin films driven by spin-Hall effect. Here we perform a systematic study of these THz oscillators within a full micromagnetic solver based on the numerical solution of two coupled Landau-Lifshitz-Gilbert-Slonczewski equations, for the case of ultra-thin films, i.e. when the N\'eel temperature of an AFM is substantially reduced. We have found two different dynamical modes depending on the strength of the Dzyaloshinskii-Moriya interaction (DMI). At low DMI, a large amplitude precession is excited where both the magnetizations of the sublattices are in a uniform state and rotate in the same direction. At large enough DMI, the ground state of the AFM becomes non-uniform and the antiferromagnetic dynamics is characterized by ultrafast domain wall motion., Comment: manuscript 15 pages 7 figures - supplemental material 3 pages 2 figures

In the emerging field of magnonics, spin waves are foreseen as signal carriers for future spintronic information processing and communication devices, owing to both the very low power losses and a high device miniaturisation potential predicted for short-wavelength spin waves. Yet, the efficient excitation and controlled propagation of nanoscale spin waves remains a severe challenge. Here, we report the observation of high-amplitude, ultrashort dipole-exchange spin waves (down to 80 nm wavelength at 10 GHz frequency) in a ferromagnetic single layer system, coherently excited by the driven dynamics of a spin vortex core. We used time-resolved x-ray microscopy to directly image such propagating spin waves and their excitation over a wide range of frequencies. By further analysis, we found that these waves exhibit a heterosymmetric mode profile, involving regions with anti-Larmor precession sense and purely linear magnetic oscillation. In particular, this mode profile consists of dynamic vortices with laterally alternating helicity, leading to a partial magnetic flux closure over the film thickness, which is explained by a strong and unexpected mode hybridisation. This spin-wave phenomenon observed is a general effect inherent to the dynamics of sufficiently thick ferromagnetic single layer films, independent of the specific excitation method employed.

A broadband spintronic diode would be important for electromagnetic energy harvesting, with the advantages of nanoscale size and low output resistance. This study gives experimental proof of broadband microwave detection in a magnetic tunnel junction, with a spintronic diode providing sufficient dc voltage to supply a low-power nanodevice. Such diodes also work as rectifiers below 1 nW, outperforming traditional Schottky diodes. These results point to spintronic diodes as building blocks in self-powered systems such as implantable biomedical devices, wireless sensors, and portable electronics, plus ultralow-power detectors for aerospace applications and the ``Internet of Things''.

The use of spin waves as information carriers in spintronic devices can substantially reduce energy losses by eliminating the ohmic heating associated with electron transport. Yet, the excitation of short-wavelength spin waves in nanoscale magnetic systems remains a significant challenge. Here, we propose a method for their coherent generation in a heterostructure composed of antiferromagnetically coupled magnetic layers. The driven dynamics of naturally formed nanosized stacked pairs of magnetic vortex cores is used to achieve this aim. The resulting spin-wave propagation is directly imaged by time-resolved scanning transmission X-ray microscopy. We show that the dipole-exchange spin waves excited in this system have a linear, non-reciprocal dispersion and that their wavelength can be tuned by changing the driving frequency.

NiFe-Cu-Co trilayer nano-contact spin-torque oscillators (NC-STOs) fabricated on an yttrium-iron garnet (YIG) film were studied in two different modes. In passive mode, i.e. without any NC-STO auto-oscillations, a microwave current through the nano-contact can excite spin waves (SW) in the YIG film, and, vice versa, antenna generated SWs in the YIG film can be detected by the nano-contact. In active mode, i.e., in the presence of auto-oscillations, significant changes appear in the NC-STO spectrum when its frequency approaches that of the SWs excited in the YIG. These results demonstrate strong coupling between NC-STOs and SWs in YIG and open new possibilities of 1) pure spin-current generation in YIG by NC-STOs; 2) mutual locking of a number of NC-STOs through SWs in YIG; and 3) improvement of NC-STO spectra through SW feedback in YIG. QC 20160531

It is demonstrated both analytically and numerically that a layered structure consisting of a layer of a bi-anisotropic antiferromagnet (AFM) and an adjacent layer of a heavy metal driven by a DC current is a perspective system for use in novel THz-frequency signal generators. It is also demonstrated, that the same AFMlPt bilayer can be used for the generation of ultra-short “Dirac-delta-like” spikes. The spike generation occurs only when the amplitude of the driving current exceeds a certain threshold, similar to the action of a biological neuron in response to an external stimulus. The “threshold” neuron-like behavior of the proposed AFM spike generator makes possible its application in neuromorphic signal processing circuits working at clock frequencies of tens of gigahertz.

A general perturbation theory for the description of weak damping of linear spin-wave modes in magnetic nanostructures is developed. This perturbative approach allows one to account for the usual uniform Gilbert damping, as well as for the spatially nonuniform (coordinate-dependent) and nonlocal (magnetization-texture-dependent) Gilbert-like dissipation mechanisms. Using the derived general expression, it is possible to calculate the damping rate of a particular spin-wave mode if the frequency and the spatial profile of this mode, along with the relevant parameters of a magnetic material, are known. The examples demonstrating the applications of the developed general formalism include (i) generalization of the damping rate of a spin-wave mode propagating in a magnetic sample for the case of a nonuniform static magnetization or/and bias magnetic field, (ii) calculation of a damping rate of a gyrotropic mode in a vortex-state magnetic nanodot, (iii) evaluation of the spin diffusion influence on the damping rate of spin-wave modes in a conducting ferromagnet, and (iv) calculation of damping rates of spin-wave modes in a ferromagnetic film in the presence of a spin pumping into an adjacent nonmagnetic metal layer. The developed formalism is especially useful in micromagnetic simulations, as it allows one to calculate damping rates of spin-wave modes based on the numerical solution of a conservative eigenmode problem.

One of the most fascinating topics in current quantum physics are hybridised systems, in which different quantum resonators are strongly coupled. Prominent examples are circular resonators with high quality factors that allow the coupling of optical whispering gallery modes to microwave cavities or magnon resonances in optomagnonics. Whispering gallery modes play a special role in this endeavour because of their high quality factor and strong localisation, which ultimately increases the overlap of the wavefunctions of quantum particles in hybridised systems. The hybridisation with magnons, the collective quantum excitations of the electron spins in a magnetically ordered material, is of particular interest because magnons can take over two functionalities: due to their collective nature they are robust and can serve as a quantum memory and, moreover, they can act as a wavelength converter between microwave and THz photons. However, the observation of whispering gallery magnons has not yet been achieved due to the lack of efficient excitation schemes for magnons with large wave vectors in a circular geometry. To tackle this problem, we studied nonlinear 3-magnon scattering as a means to generate whispering gallery magnons. This Letter discusses the basics of this nonlinear mechanism in a confined, circular geometry from experimental and theoretical point of view.

A spintronic method of ultra-fast broadband microwave spectrum analysis is proposed. It uses a rapidly tuned spin torque nano-oscillator (STNO), and does not require injection locking. This method treats an STNO generating a microwave signal as an element with an oscillating resistance. When an external signal is applied to this "resistor" for analysis, it is mixed with the signal generated by the STNO. The resulting mixed voltage contains the "sum" and "difference" frequencies, and the latter produces a DC component when the external frequency matches the frequency generated by the STNO. The mixed voltage is processed using a low pass filter to exclude the "sum" frequency components, and a matched filter to exclude the dependence of the resultant DC voltage on the phase difference between the two signals. It is found analytically and by numerical simulation, that the proposed spectrum analyzer has a frequency resolution at a theoretical limit in a real-time scanning bandwidth of 10~GHz, and a frequency scanning rate above 1~GHz/ns, while remaining sensitive to signal power as low as the Johnson-Nyquist thermal noise floor., 5 pages, 4 figures

The design of modern circulators and isolators relies on nonreciprocal (discriminating forward and backward wave vectors, breaking time-reversal symmetry) electromagnetic waves in magnetic materials. Creating such devices that are small enough for portable electronics (think mobile phones) remains challenging. The authors show theoretically the nonreciprocal propagation of surface acoustic waves in multilayers with simultaneous magnetoelastic and Dzyaloshinskii-Moriya interactions. Despite both interactions being relatively weak, their interplay creates up to 45 dB of isolation for counterpropagating waves, making these multilayers promising for miniaturized rf isolators.

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.

In the last decades, the research in spintronics has mainly concentrated on ferromagnetic materials, which respond to the different kinds of spintransfer torques with gigahertz-frequency dynamics [1]–[3]. A jump to higher-frequency devices, working in the range of terahertz, is promised by the use of antiferromagnets (AFM) [4]–[6]. AFM materials will, probably, be in the research spotlight in the near future. In order to study their behavior, however, a new theoretical approach is needed, which, for instance, has to account for the strong internal exchange field in AFMs, for the absence of macroscopic magnetization, and possibility to operate without an external bias field. When it comes to modeling, AFMs are generally studied by considering the magnetizations M 1 and M 2 of the two sublattices. Dynamics of M 1 and M 2 is ruled by two coupled Landau-Lifshitz-Gilbert equations [6]. In this work, we model micromagnetically an antiferromagnetic spin-Hall oscillator (ASHO). This device consists of an AFM layer coupled to a layer of a heavy metal, as sketched in Fig. 1, where a coordinate system $x-y-z$is also shown. The AFM layer is square-shaped, with dimensions 40×40 nm 2, whereas the dimension along $z$, namely its thickness $d$, varies from 1 to 5 nm. The heavy metal is designed with 4 terminals that can be used to apply a charge current, and/or to read the device resistance [7]. According to the well-known spin-Hall effect, when a current is applied (in our case in the plane $x- y$), it creates a spin polarization in the heavy metal. The consequent spin current, flowing along the $z$direction, creates a spin accumulation at the interface with the AFM, and, therefore, a torque on the AFM. The direction of the spin-Hall polarization p is perpendicular to the plane of the charge and spin currents, namely, if the charge current is applied along the axis $x$and the spin current is along the axis $z$, the spin polarization is along the axis $y[{2 ,7}]$. The spin-Hall-driven torque, therefore, acts on the magnetizations M 1 and M 2 of the two AFM sublattices in the same direction, thus allowing dynamics with a non-zero net magnetization. We investigate this dynamics, solving the equations of motion for the two sublattices by means of a custom-developed micromagnetic code. The following parameters are used in our simulations: saturation magnetization $M_{S}=350 \mathrm {x}10 ^{3}\mathrm {A} /\mathrm {m}$, spinHall angle $\theta _{SH}=0.10$. The exchange constant $A$is a variable parameter in our simulations, and assumes the values of 0.5, 1.0 and $1.5\mathrm {x} 10 ^{11}\mathrm {J} /\text{m}$. Similarly, the Gilbert damping constant $\alpha $is set equal to 0.01, 0.05 and 0.1. The AFM is assumed to have the in-plane anisotropy along the $x$direction, the corresponding constant is $K_{u}= 10 ^{5}\mathrm {J}/ \mathrm {m}^{3}$, and simulations start from the equilibrium AFM configuration of M 1 and M 2 along the easy axis, shown in Fig. 1. Last, but not least, the current is applied differently at the terminals, in order to modify the direction of the spin-Hall polarization with respect to the easy axis $x$. We consider three cases: (i) current at the terminals A-A' along $x$direction (p along $y$), (ii) current at the terminals B-B' along $- y$direction (p along $x$axis), and (iii) current at both A-A' and B-B' with equal intensity (p is directed 45° w.r.t. to x and y axes). By means of this configuration, it is, therefore, possible to manage the direction of the spin-Hall polarization with respect to the AFM easy axis, simply by tuning the two currents at the two couples of terminals. The above described systematic study has provided important data on the behavior of an AFM under the action of the spinHall effect. Dynamics of magnetization is excited above a certain threshold current. However, the same dynamics is turned off at the lower values of the driving current, highlighting a clear hysteretic behavior of the excitation. The values of the threshold currents and the width of the hysteresis region depend on different parameters. For instance, the threshold current increases with the increase of the AFM thickness, or the damping, or the exchange constant. When the polarization is moved from the axis $y$to the AFM easy axis, the threshold current slightly increases, and to get the excitation of dynamics we need to include a small thermal field. Above the threshold, the magnetizations of the two AFM sublattices show a precession around the spin-polarization direction, as shown in the inset of Fig. 2. The net magnetization is, mainly, given by the sum of the components of M 1 and M 2 along the spin polarization p, whereas the other two components give almost zero contribution when the sum of M 1 and M 2 is evaluated. The frequency of the net magnetization dynamics shows a blue-shift with the increase of the applied current (see the example in Fig. 2). The values of the generated frequency are from hundreds of GHz up to several THz, as expected. The hysteretic excitation, the blue-shift of the frequency, the order of threshold current, and of output frequencies confirm the predictions of the previous analytical studies [6], and confirm the validity of our numerical approach.

Recent advances in the spintronic design and fabrication techniques have led to the development of spin torque diodes having a perpendicular magnetic anisotropy (STD-PMA) in their free layer. Such STD-PMAs can act as energy harvesters of ambient microwave radiation [1], and when driven with a dc bias current, can operate as microwave generators [2]. The analytical formalism [3] has shown that STD-PMAs have a number of interesting properties. In particular: (i) in the presence of an external microwave current they can produce a rectified dc voltage that is linearly proportional to the external microwave frequency, and independent of the input power; (ii) the STD-PMA can perform a signal rectification without an independent power supply, drawing power entirely from the input signal; (iii) in contrast with the traditional spin torque diodes, the STD-PMA do not require an external bias magnetic field, and therefore can be easily integrated with CMOS and other microelectronic systems; (iv) the power threshold of operation of STD-PMA is rather low (several nanowatts), and thus, they can be used in applications where non-spintronic (e.g. Schottky-diode-based) devices fail; (v) above a particular threshold frequency, the STD-PMA does not produce a dc voltage, thus acting as a natural lowpass filter. Here, we propose a novel application for an STD-PMA: this device can perform passive demodulation for low-power frequency-modulated (FM) signals. To demonstrate this effect we performed a numerical simulation for an STD-PMA under the action of an external FM signal. The magnetization dynamics of the STD-PMA free layer, which performs the signal demodulation, was modeled using the Landau-Lifshift-Gilbert-Slonczewski equation in a macrospin approximation. We chose the following typical parameters of the system. We used a 1.65 nm-thick circular free layer having a radius of 50 nm, and made of Co 20 Fe 60 B 20 . With this configuration, the effective field of the 1st order PMA was 1162 mT, and the field of the 2nd order PMA was 63 mT. The Gilbert damping parameter was 0.02, the spin-polarization efficiency was chosen to be 0.6, and the pinned layer of the STD-PMA was assumed to have the in-plane magnetization. With these parameters, the static magnetization of the free layer had an equilibrium out-of-plane angle of 45 degrees, a resistance of ≈ 800 Ω, and a tunneling magneto-resistance (TMR) of 112.5%. The two figures below demonstrate the numerically modeled STD-PMA performing both digital and analog FM demodulation. Fig. 1 shows the passive demodulation of a signal encoded with frequency shift keying (FSK). A short digital data sequence with a data rate of 2.5 MB is shown in Fig. 1(a), with voltages varying between a high and low state, and Fig. 1(b) shows this data encoded in the frequency of a signal, where $f_{in} =40$ MHz is representing the “low” state and $f_{in} =60$ MHz is representing the “high” state. The FSK signal has two powers, starting initially at 14 nW (−48dBm), increasing to 25 nW (−45 dBm), then again decreasing to 14 nW. When the FSK signal is incident on the simulated STD-PMA, it produces a dc voltage as shown in Fig 1(c). For the “low” state, the STD-PMA produces $V_{out} = 400 ~\mu \mathrm {V}$, and in the “high” state the STD-PMA produces $V_{out} = 600 ~\mu \mathrm {V}$. Note, that the voltage $V_{out}$ is only dependent on the input frequency, and is independent of the input power. It is also important to emphasize, that despite the low power levels of this signal, the STD-PMA is powered entirely by the external signal, and that the magnetic anisotropy allows its operation in the absence of a bias magnetic field. The FM demodulation of an analog signal using an STD-PMA is demonstrated in Fig. 2. An analog signal with frequencies scanning a 5 MHz bandwidth (Fig. 2(a)) is FM modulated by a 50 MHz carrier signal. The power spectral density (PSD) of the signal after a single-sideband FM modulation is shown in Fig. 2(b), with a bandwidth in the 50–60 MHz frequency range. The curve presented in Fig. 2(c) shows that the STD-PMA output dc voltage faithfully reproduces the shape of the input analog signal. In summary, a spin torque diode with perpendicular magnetic anisotropy can act as a reliable FM demodulator that does not require any power and/or any bias magnetic field. The basis of its operation is the linear relationship between the input frequency and the STD dc voltage output. Our numerical simulation has shown that an STD-PMA can demodulate both a digital signal encoded by FSK, and an analog signal with a single-sideband FM modulation. We believe, that STD-PMAs will be useful in power-critical applications, which has growing relevance for autonomous devices and internet of things (IOT) applications.

Spintronic nano-oscillators [1], [2]are now considered as promising nanoscale AC signal sources for the future energy-efficient electronics. However, nowadays such sources mainly utilize ferromagnetic materials (FM), and, therefore, their operation frequencies are limited to the interval of 1–50 GHz [1], [2], which is not sufficiently high for many practical applications. To substantially increase the frequency of the spintronic AC signal sources one could use antiferromagnets (AFMs), where characteristic operation frequencies, typically, lie in the terahertz range (0.1–10 THz) [3]–[5]. The theoretically proposed AFM-based nano-oscillators can operate in the absence of a bias dc magnetic field, and can be driven by a dc electric current [6]–[8]. However, the problem of a practical development of AFM-based AC signal generators, and, in particular, the problem of a power extraction from such AFM generators, has not been solved yet. In [7]an AFM-based spin Hall oscillator (SHO), where the power of the generated AC signal is extracted through the inverse spin-Hall effect (ISHE), has been proposed. The other power extraction mechanism, based on the reception of the magneto-dipolar radiation from a current-driven canted AFM attached to the high-Q resonator has been analyzed in [8]. Both these methods of the THz-frequency signal extraction have some disadvantages: for an SHO utilizing ISHE the AFM material must be bi-anisotopic with a weak perpendicular anisotropy [7], while in the case of a canted AFM embedded in a resonator, the device has a large size $( \sim 10 \mu \mathrm {m})$defined by the wavelength of the generated signal [8]. In this paper we consider an alternative mechanism of the THz-frequency signal extraction from an AFM-based SHO, where the signal power is collected through the AC variation of the tunneling anisotropic magnetoresistance (TAMR) in an AFM tunnel junction (ATJ), the electrical switching of which has been experimentally observed in the recent works [9], [10]. We consider an AFM SHO based on an IrMn/Pt bilayer structure, where the driving dc current $I_{drive}$flowing in the Pt layer forces a flow of a spin current $I_{SH}$into the AFM layer. This spin current excites the rotation of magnetizations of the IrMn AFM sublattices through the spin-Hall effect (SHE) [5], which gives rise to the AC variations of the TAMR [10]. Thus the junction resistance changes in time as $R(t) \quad = R_{0} + \Delta {R} \sin(\omega{t})$(Fig. 1). At the same time, the simultaneously supplied bias dc current $I_{dc}$, traversing the junction cross-section, results in the generation of the AC voltage of the magnitude $U_{ac} \quad = I_{dc} \Delta {R}$across the whole structure. Thus, when such a dc biased ATJ is connected through a bias tee to a load, having the resistance of $R_{L} \quad = 50 \Omega $, the AC voltage generated in the ATJ excites an AC current in the load, allows one to extract an AC power $P_{L}$of the excited signal from the load. Our theoretical model of the proposed AC source based on an ATJ is very simple. We consider an ATJ as a circuit consisting of an AC voltage source (generating AC voltage of the magnitude $U_{ac})$with the internal resistance $R_{0}$shunted by a capacitor of the capacitance $C$. This equivalent circuit is connected through an ideal bias tee to a resistive load of the resistance $R_{L}$. Using Kirchhoff's laws, we found the following expressions for the powers: $P_{dc} \quad = \quad I_{dc}^{2}R_{0}$is the dc power injected in the ATJ, $P_{L} \quad = ( R_{L} U_{ac}^{2})/ [ 2 ( R_{L} \quad + R_{0})^{2} \quad + \quad R_{L}^{2}\beta ^{2})]$is the power emitted in the load, where $\beta \quad = \omega R_{0}C$. Then, the efficiency of the AC power extraction can be estimated as $\zeta \quad = \quad P_{L}/ P_{dc}$. The frequency dependences of the $P_{L}$and $\zeta $, calculated for a junction having experimental parameters (resistance-area product, tunnel magneto-resistance ratio, etc.) taken from [10], are shown in Fig. 2. They demonstrate that both these characteristics are decreasing with the increase of the generated frequency. The calculations also demonstrated, that the output power $P_{L}$, injected into the load in the frequency range 0.1 – 1 THz, is comparable to, or may even exceed, the power extracted via ISHE and magneto-dipole emission mechanism, while the efficiency of the power extraction mechanism via AC TAMR variations is about 1%, which may be sufficient for some practical applications. Also, it should be noted, that a substantial advantage of the proposed AFM-based AC signal source with signal extraction through TAMR lies in the simplicity and reliability of its experimental realization at micro- and nano-scale. In conclusion, we proposed a method of the AC signal extraction from an ATJ-based SHO based on TAMR, which can be easily experimentally realized at micro- and nano-scale, and can provide an output AC power of the order of $P_{L} \sim 10 \mu \mathrm {W}$and an efficiency of about 1%.

International audience; We report a study on spin conductance in ultra-thin films of Yttrium Iron Garnet (YIG), where spin transport is provided by propagating spin waves, that are generated and detected by direct and inverse spin Hall effects in two Pt wires deposited on top. While at low current the spin conductance is dominated by transport of thermal magnons, at high current, the spin conductance is dominated by low-damping non-equilibrium magnons thermalized near the spectral bottom by magnon-magnon interaction, with consequent a sensitivity to the applied magnetic field and a longer decay length. This picture is supported by microfocus Brillouin Light Scattering spectroscopy.