Ultrafast GHz-Range Swept-Tuned Spectrum Analyzer with 20 ns Temporal Resolution Based on a Spin-Torque Nano-Oscillator with a Uniformly Magnetized "Free" Layer.

The advantage of an ultrafast frequency-tunability of spin-torque nano-oscillators (STNOs) that have a large (>100 MHz) relaxation frequency of amplitude fluctuations is exploited to realize ultrafast wide-band time-resolved spectral analysis at nanosecond time scale with a frequency resolution limited only by the "bandwidth" theorem. The demonstration is performed with an STNO generating in the 9 GHz frequency range and comprised of a perpendicular polarizer and a perpendicularly and uniformly magnetized "free" layer. It is shown that such a uniform-state STNO-based spectrum analyzer can efficiently perform spectral analysis of frequency-agile signals with rapidly varying frequency components.

Control of the Bose-Einstein Condensation of Magnons by the Spin Hall Effect.

Previously, it has been shown that rapid cooling of yttrium-iron-garnet-platinum nanostructures, preheated by an electric current sent through the Pt layer, leads to overpopulation of a magnon gas and to subsequent formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect (SHE), which creates a spin-polarized current in the Pt layer, can inject or annihilate magnons depending on the electric current and applied field orientations. Here we demonstrate that the injection or annihilation of magnons via the SHE can prevent or promote the formation of a rapid cooling-induced magnon BEC. Depending on the current polarity, a change in the BEC threshold of -8% and +6% was detected. These findings demonstrate a new method to control macroscopic quantum states, paving the way for their application in spintronic devices.

Ultrafast Sweep-Tuned Spectrum Analyzer with Temporal Resolution Based on a Spin-Torque Nano-Oscillator.

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.

Bose-Einstein condensation of quasiparticles by rapid cooling.

The fundamental phenomenon of Bose-Einstein condensation has been observed in different systems of real particles and quasiparticles. The condensation of real particles is achieved through a major reduction in temperature, while for quasiparticles, a mechanism of external injection of bosons by irradiation is required. Here, we present a new and universal approach to enable Bose-Einstein condensation of quasiparticles and to corroborate it experimentally by using magnons as the Bose-particle model system. The critical point to this approach is the introduction of a disequilibrium of magnons with the phonon bath. After heating to an elevated temperature, a sudden decrease in the temperature of the phonons, which is approximately instant on the time scales of the magnon system, results in a large excess of incoherent magnons. The consequent spectral redistribution of these magnons triggers the Bose-Einstein condensation.

Emission and propagation of 1D and 2D spin waves with nanoscale wavelengths in anisotropic spin textures.

Spin waves offer intriguing perspectives for computing and signal processing, because their damping can be lower than the ohmic losses in conventional complementary metal-oxide-semiconductor (CMOS) circuits. Magnetic domain walls show considerable potential as magnonic waveguides for on-chip control of the spatial extent and propagation of spin waves. However, low-loss guidance of spin waves with nanoscale wavelengths and around angled tracks remains to be shown. Here, we demonstrate spin wave control using natural anisotropic features of magnetic order in an interlayer exchange-coupled ferromagnetic bilayer. We employ scanning transmission X-ray microscopy to image the generation of spin waves and their propagation across distances exceeding multiples of the wavelength. Spin waves propagate in extended planar geometries as well as along straight or curved one-dimensional domain walls. We observe wavelengths between 1 µm and 150 nm, with excitation frequencies ranging from 250 MHz to 3 GHz. Our results show routes towards the practical implementation of magnonic waveguides in the form of domain walls in future spin wave logic and computational circuits.

Ultra-fast artificial neuron: generation of picosecond-duration spikes in a current-driven antiferromagnetic auto-oscillator.

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.

Reconfigurable nanoscale spin-wave directional coupler.

Spin waves, and their quanta magnons, are prospective data carriers in future signal processing systems because Gilbert damping associated with the spin-wave propagation can be made substantially lower than the Joule heat losses in electronic devices. Although individual spin-wave signal processing devices have been successfully developed, the challenging contemporary problem is the formation of two-dimensional planar integrated spin-wave circuits. Using both micromagnetic modeling and analytical theory, we present an effective solution of this problem based on the dipolar interaction between two laterally adjacent nanoscale spin-wave waveguides. The developed device based on this principle can work as a multifunctional and dynamically reconfigurable signal directional coupler performing the functions of a waveguide crossing element, tunable power splitter, frequency separator, or multiplexer. The proposed design of a spin-wave directional coupler can be used both in digital logic circuits intended for spin-wave computing and in analog microwave signal processing devices.

Interface-Induced Phenomena in Magnetism.

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Antiferromagnetic THz-frequency Josephson-like Oscillator Driven by Spin Current.

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 108 A/cm2 to 109 A/cm2. The THz-frequency signal from the AFM with the amplitude exceeding 1 V/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.

Parametric Resonance of Magnetization Excited by Electric Field.

Manipulation of magnetization by electric field is a central goal of spintronics because it enables energy-efficient operation of spin-based devices. Spin wave devices are promising candidates for low-power information processing, but a method for energy-efficient excitation of short-wavelength spin waves has been lacking. Here we show that spin waves in nanoscale magnetic tunnel junctions can be generated via parametric resonance induced by electric field. Parametric excitation of magnetization is a versatile method of short-wavelength spin wave generation, and thus, our results pave the way toward energy-efficient nanomagnonic devices.

Magnetic vortex cores as tunable spin-wave emitters.

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.

Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures: Hybridization of Flexure Gyromodes with Spin Waves.

Three-dimensional linear spin-wave eigenmodes of a vortex-state Permalloy disk are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The simulations confirm that the increase of the disk thickness leads to the appearance of additional exchange-dominated so-called gyrotropic flexure modes having nodes along the disk thickness, and eigenfrequencies that decrease when the thickness is increased. We observe the formation of a gap in the mode spectrum caused by the hybridization of the first flexure mode with one of the azimuthal spin-wave modes of the disk. A qualitative change of the transverse profile of this azimuthal mode is found, demonstrating that in a thick vortex-state disk the influence of the "transverse" and the "azimuthal" coordinates cannot be separated. The three-dimensional character of the eigenmodes is essential to explain the recently observed asymmetries in an experimentally obtained phase diagram of vortex-core reversal in relatively thick Permalloy disks.

Excitation of propagating spin waves in ferromagnetic nanowires by microwave voltage-controlled magnetic anisotropy.

The voltage-controlled magnetic anisotropy (VCMA) effect, which manifests itself as variation of anisotropy of a thin layer of a conductive ferromagnet on a dielectric substrate under the influence of an external electric voltage, can be used for the development of novel information storage and signal processing devices with low power consumption. Here it is demonstrated by micromagnetic simulations that the application of a microwave voltage to a nanosized VCMA gate in an ultrathin ferromagnetic nanowire results in the parametric excitation of a propagating spin wave, which could serve as a carrier of information. The frequency of the excited spin wave is twice smaller than the frequency of the applied voltage while its amplitude is limited by 2 mechanisms: (i) the so-called "phase mechanism" described by the Zakharov-L'vov-Starobinets "S-theory" and (ii) the saturation mechanism associated with the nonlinear frequency shift of the excited spin wave. The developed extension of the "S-theory", which takes into account the second limitation mechanism, allowed us to estimate theoretically the efficiency of the parametric excitation of spin waves by the VCMA effect.

Reduction of phase noise in nanowire spin orbit torque oscillators.

Spin torque oscillators (STOs) are compact, tunable sources of microwave radiation that serve as a test bed for studies of nonlinear magnetization dynamics at the nanometer length scale. The spin torque in an STO can be created by spin-orbit interaction, but low spectral purity of the microwave signals generated by spin orbit torque oscillators hinders practical applications of these magnetic nanodevices. Here we demonstrate a method for decreasing the phase noise of spin orbit torque oscillators based on Pt/Ni80Fe20 nanowires. We experimentally demonstrate that tapering of the nanowire, which serves as the STO active region, significantly decreases the spectral linewidth of the generated signal. We explain the observed linewidth narrowing in the framework of the Ginzburg-Landau auto-oscillator model. The model reveals that spatial non-uniformity of the spin current density in the tapered nanowire geometry hinders the excitation of higher order spin-wave modes, thus stabilizing the single-mode generation regime. This non-uniformity also generates a restoring force acting on the excited self-oscillatory mode, which reduces thermal fluctuations of the mode spatial position along the wire. Both these effects improve the STO spectral purity.

Bose-Einstein condensation in an ultra-hot gas of pumped magnons.

Bose-Einstein condensation of quasi-particles such as excitons, polaritons, magnons and photons is a fascinating quantum mechanical phenomenon. Unlike the Bose-Einstein condensation of real particles (like atoms), these processes do not require low temperatures, since the high densities of low-energy quasi-particles needed for the condensate to form can be produced via external pumping. Here we demonstrate that such a pumping can create remarkably high effective temperatures in a narrow spectral region of the lowest energy states in a magnon gas, resulting in strikingly unexpected transitional dynamics of Bose-Einstein magnon condensate: the density of the condensate increases immediately after the external magnon flow is switched off and initially decreases if it is switched on again. This behaviour finds explanation in a nonlinear 'evaporative supercooling' mechanism that couples the low-energy magnons overheated by pumping with all the other thermal magnons, removing the excess heat, and allowing Bose-Einstein condensate formation.

Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback.

For auto-oscillators of different nature (e.g. active cells in a human heart under the action of a pacemaker, neurons in brain, spin-torque nano-oscillators, micro and nano-mechanical oscillators, or generating Josephson junctions) a critically important property is their ability to synchronize with each other. The synchronization properties of an auto oscillator are directly related to its sensitivity to external signals. Here we demonstrate that a non-isochronous (having generation frequency dependent on the amplitude) auto-oscillator with delayed feedback can have an extremely high sensitivity to external signals and unusually large width of the phase-locking band near the boundary of the stable auto-oscillation regime. This property could be used for the development of synchronized arrays of non-isochronous auto-oscillators in physics and engineering, and, for instance, might bring a better fundamental understanding of ways to control a heart arrythmia in medicine.

Magnetic nano-oscillator driven by pure spin current.

With the advent of pure-spin-current sources, spin-based electronic (spintronic) devices no longer require electrical charge transfer, opening new possibilities for both conducting and insulating spintronic systems. Pure spin currents have been used to suppress noise caused by thermal fluctuations in magnetic nanodevices, amplify propagating magnetization waves, and to reduce the dynamic damping in magnetic films. However, generation of coherent auto-oscillations by pure spin currents has not been achieved so far. Here we demonstrate the generation of single-mode coherent auto-oscillations in a device that combines local injection of a pure spin current with enhanced spin-wave radiation losses. Counterintuitively, radiation losses enable excitation of auto-oscillation, suppressing the nonlinear processes that prevent auto-oscillation by redistributing the energy between different modes. Our devices exhibit auto-oscillations at moderate current densities, at a microwave frequency tunable over a wide range. These findings suggest a new route for the implementation of nanoscale microwave sources for next-generation integrated electronics.

Nano-structured magnetic metamaterial with enhanced nonlinear properties.

Nano-structuring can significantly modify the properties of materials. We demonstrate that size-dependent modification of the spin-wave spectra in magnetic nano-particles can affect not only linear, but also nonlinear magnetic response. The discretization of the spectrum removes the frequency degeneracy between the main excitation mode of a nano-particle and the higher spin-wave modes, having the lowest magnetic damping, and reduces the strength of multi-magnon relaxation processes. This reduction of magnon-magnon relaxation for the main excitation mode leads to a dramatic increase of its lifetime and amplitude, resulting in the intensification of all the nonlinear processes involving this mode. We demonstrate this experimentally on a two-dimensional array of permalloy nano-dots for the example of parametric generation of a sub-harmonic of an external microwave signal. The characteristic lifetime of this sub-harmonic is increased by two orders of magnitude compared to the case of a continuous magnetic film, where magnon-magnon relaxation limits the lifetime.

Control of spin waves in a thin film ferromagnetic insulator through interfacial spin scattering.

Control of spin waves in a ferrite thin film via interfacial spin scattering was demonstrated. The experiments used a 4.6 µm-thick yttrium iron garnet (YIG) film strip with a 20-nm thick Pt capping layer. A dc current pulse was applied to the Pt layer and produced a spin current across the Pt thickness. As the spin current scatters off the YIG surface, it can either amplify or attenuate spin-wave pulses that travel in the YIG strip, depending on the current or field configuration. The spin scattering also affects the saturation behavior of high-power spin waves.