Persistent magnetic coherence in magnets.

When excited, the magnetization in a magnet precesses around the field in an anticlockwise manner on a timescale governed by viscous magnetization damping, after which any information carried by the initial actuation seems to be lost. This damping appears to be a fundamental bottleneck for the use of magnets in information processing. However, here we demonstrate the recall of the magnetization-precession phase after times that exceed the damping timescale by two orders of magnitude using dedicated two-colour microwave pump-probe experiments for a Y3Fe5O12 microstructured film. Time-resolved magnetization state tomography confirms the persistent magnetic coherence by revealing a double-exponential decay of magnetization correlation. We attribute persistent magnetic coherence to a feedback effect, that is, coherent coupling of the uniform precession with long-lived excitations at the minima of the spin-wave dispersion relation. Our finding liberates magnetic systems from the strong damping in nanostructures that has limited their use in coherent information storage and processing.

Stimulated Amplification of Propagating Spin Waves.

Spin-wave amplification techniques are key to the realization of magnon-based computing concepts. We introduce a novel mechanism to amplify spin waves in magnonic nanostructures. Using the technique of rapid cooling, we create a nonequilibrium state in excess of high-energy magnons and demonstrate the stimulated amplification of an externally seeded, propagating spin wave. Using an extended kinetic model, we qualitatively show that the amplification is mediated by an effective energy flux of high energy magnons into the low energy propagating mode, driven by a nonequilibrium magnon distribution.

The 2021 Magnonics Roadmap.

Magnonics is a budding research field in nanomagnetism and nanoscience that addresses the use of spin waves (magnons) to transmit, store, and process information. The rapid advancements of this field during last one decade in terms of upsurge in research papers, review articles, citations, proposals of devices as well as introduction of new sub-topics prompted us to present the first roadmap on magnonics. This is a collection of 22 sections written by leading experts in this field who review and discuss the current status besides presenting their vision of future perspectives. Today, the principal challenges in applied magnonics are the excitation of sub-100 nm wavelength magnons, their manipulation on the nanoscale and the creation of sub-micrometre devices using low-Gilbert damping magnetic materials and its interconnections to standard electronics. To this end, magnonics offers lower energy consumption, easier integrability and compatibility with CMOS structure, reprogrammability, shorter wavelength, smaller device features, anisotropic properties, negative group velocity, non-reciprocity and efficient tunability by various external stimuli to name a few. Hence, despite being a young research field, magnonics has come a long way since its early inception. This roadmap asserts a milestone for future emerging research directions in magnonics, and hopefully, it will inspire a series of exciting new articles on the same topic in the coming years.

Room temperature and low-field resonant enhancement of spin Seebeck effect in partially compensated magnets.

Resonant enhancement of spin Seebeck effect (SSE) due to phonons was recently discovered in Y[Formula: see text]Fe[Formula: see text]O[Formula: see text] (YIG). This effect is explained by hybridization between the magnon and phonon dispersions. However, this effect was observed at low temperatures and high magnetic fields, limiting the scope for applications. Here we report observation of phonon-resonant enhancement of SSE at room temperature and low magnetic field. We observe in Lu[Formula: see text]BiFe[Formula: see text]GaO[Formula: see text] an enhancement 700% greater than that in a YIG film and at very low magnetic fields around 10[Formula: see text] T, almost one order of magnitude lower than that of YIG. The result can be explained by the change in the magnon dispersion induced by magnetic compensation due to the presence of non-magnetic ion substitutions. Our study provides a way to tune the magnon response in a crystal by chemical doping, with potential applications for spintronic devices.

Backscattering Immunity of Dipole-Exchange Magnetostatic Surface Spin Waves.

The existence of backscattering-immune spin-wave modes is demonstrated in magnetic thin films of nanoscale thickness. Our results reveal that chiral magnetostatic surface waves (CMSSWs), which propagate perpendicular to the magnetization direction in an in-plane magnetized thin film, are robust against backscattering from surface defects. CMSSWs are protected against various types of surface inhomogeneities and defects as long as their frequency lies inside the gap of the volume modes. Our explanation is independent of the topology of the modes and predicts that this robustness is a consequence of symmetry breaking of the dynamic magnetic fields of CMSSWs due to the off-diagonal part of the dipolar interaction tensor, which is present both for long- (dipole-dominated) and short-wavelength (exchange-dominated) spin waves. Micromagnetic simulations confirm the robust character of the CMSSWs. Our results open a new direction in designing highly efficient magnonic logic elements and devices employing CMSSWs in nanoscale thin films.

Phase-to-intensity conversion of magnonic spin currents and application to the design of a majority gate.

Magnonic spin currents in the form of spin waves and their quanta, magnons, are a promising candidate for a new generation of wave-based logic devices beyond CMOS, where information is encoded in the phase of travelling spin-wave packets. The direct readout of this phase on a chip is of vital importance to couple magnonic circuits to conventional CMOS electronics. Here, we present the conversion of the spin-wave phase into a spin-wave intensity by local non-adiabatic parallel pumping in a microstructure. This conversion takes place within the spin-wave system itself and the resulting spin-wave intensity can be conveniently transformed into a DC voltage. We also demonstrate how the phase-to-intensity conversion can be used to extract the majority information from an all-magnonic majority gate. This conversion method promises a convenient readout of the magnon phase in future magnon-based devices.

Splitting of standing spin-wave modes in circular submicron ferromagnetic dot under axial symmetry violation.

The spin wave dynamics in patterned magnetic nanostructures is under intensive study during the last two decades. On the one hand, this interest is generated by new physics that can be explored in such structures. On the other hand, with the development of nanolithography, patterned nanoelements and their arrays can be used in many practical applications (magnetic recording systems both as media and read-write heads, magnetic random access memory, and spin-torque oscillators just to name a few). In the present work the evolution of spin wave spectra of an array of non-interacting Permalloy submicron circular dots for the case of magnetic field deviation from the normal to the array plane have been studied by ferromagnetic resonance technique. It is shown that such symmetry violation leads to a splitting of spin-wave modes, and that the number of the split peaks depends on the mode number. A quantitative description of the observed spectra is given using a perturbation theory for small angles of field inclination from the symmetry direction. The obtained results give possibility to predict transformation of spin wave spectra depending on direction of the external magnetic field that can be important for spintronic and nanomagnetic applications.

Non-Gilbert-damping Mechanism in a Ferromagnetic Heusler Compound Probed by Nonlinear Spin Dynamics.

The nonlinear decay of propagating spin waves in the low-Gilbert-damping Heusler film Co_{2}Mn_{0.6}Fe_{0.4}Si is reported. Here, two initial magnons with frequency f_{0} scatter into two secondary magnons with frequencies f_{1} and f_{2}. The most remarkable observation is that f_{1} stays fixed if f_{0} is changed. This indicates, that the f_{1} magnon mode has the lowest instability threshold, which, however, cannot be understood if only Gilbert damping is present. We show that the observed behavior is caused by interaction of the magnon modes f_{1} and f_{2} with the thermal magnon bath. This evidences a significant contribution of the intrinsic magnon-magnon scattering mechanisms to the magnetic damping in high-quality Heusler compounds.

Realization of a spin-wave multiplexer.

Recent developments in the field of spin dynamics--like the interaction of charge and heat currents with magnons, the quasi-particles of spin waves--opens the perspective for novel information processing concepts and potential applications purely based on magnons without the need of charge transport. The challenges related to the realization of advanced concepts are the spin-wave transport in two-dimensional structures and the transfer of existing demonstrators to the micro- or even nanoscale. Here we present the experimental realization of a microstructured spin-wave multiplexer as a fundamental building block of a magnon-based logic. Our concept relies on the generation of local Oersted fields to control the magnetization configuration as well as the spin-wave dispersion relation to steer the spin-wave propagation in a Y-shaped structure. Thus, the present work illustrates unique features of magnonic transport as well as their possible utilization for potential technical applications.

Explosive electromagnetic radiation by the relaxation of a multimode magnon system.

Microwave emission from a parametrically pumped ferrimagnetic film of yttrium iron garnet was studied versus the magnon density evolution, which was detected by Brillouin light scattering spectroscopy. It has been found that the shutdown of external microwave pumping leads to an unexpected effect: The conventional monotonic decrease of the population of parametrically injected magnons is accompanied by an explosive behavior of electromagnetic radiation at the magnon frequency. The developed theory shows that this explosion is caused by a nonlinear energy transfer from parametrically driven short-wavelength dipolar-exchange magnons to a long-wavelength dipolar magnon mode effectively coupled to an electromagnetic wave.

Unidirectional spin-wave heat conveyer.

When energy is introduced into a region of matter, it heats up and the local temperature increases. This energy spontaneously diffuses away from the heated region. In general, heat should flow from warmer to cooler regions and it is not possible to externally change the direction of heat conduction. Here we show a magnetically controllable heat flow caused by a spin-wave current. The direction of the flow can be switched by applying a magnetic field. When microwave energy is applied to a region of ferrimagnetic Y3Fe5O12, an end of the magnet far from this region is found to be heated in a controlled manner and a negative temperature gradient towards it is formed. This is due to unidirectional energy transfer by the excitation of spin-wave modes without time-reversal symmetry and to the conversion of spin waves into heat. When a Y3Fe5O12 film with low damping coefficients is used, spin waves are observed to emit heat at the sample end up to 10 mm away from the excitation source. The magnetically controlled remote heating we observe is directly applicable to the fabrication of a heat-flow controller.

Nonlinear emission of spin-wave caustics from an edge mode of a microstructured Co2Mn(0:6)Fe(0:4)Si waveguide.

Magnetic Heusler materials with very low Gilbert damping are expected to show novel magnonic transport phenomena. We report nonlinear generation of higher harmonics leading to the emission of caustic spin-wave beams in a low-damping microstructured Co(2)Mn(0.6)Fe(0.4)Si Heusler waveguide. The source for the higher harmonic generation is a localized edge mode formed by the strongly inhomogeneous field distribution at the edges of the spin-wave waveguide. The radiation characteristics of the propagating caustic waves observed at twice and three times the excitation frequency are described by an analytical calculation based on the anisotropic dispersion of spin waves in a magnetic thin film.

Direct measurement of magnon temperature: new insight into magnon-phonon coupling in magnetic insulators.

We present spatially resolved measurements of the magnon temperature in a magnetic insulator subject to a thermal gradient. Our data reveal an unexpectedly close correspondence between the spatial dependencies of the exchange magnon and phonon temperatures. These results indicate that if--as is currently thought--the transverse spin Seebeck effect is caused by a temperature difference between the magnon and phonon baths, it must be the case that the magnon temperature is spectrally nonuniform and that the effect is driven by the sparsely populated dipolar region of the magnon spectrum.

Storage-recovery phenomenon in magnonic crystal.

The phenomenon of coherent wave trapping and restoration is demonstrated experimentally in a magnonic crystal. Unlike the conventional scheme used in photonics, the trapping occurs not due to the deceleration of the incident wave when it enters the periodic structure but due to excitation of the quasinormal modes of the artificial crystal. This excitation occurs at the group velocity minima of the decelerated wave in narrow frequency regions near the edges of the band gaps of the crystal. The restoration of the traveling wave is implemented by means of phase-sensitive parametric amplification of the stored mode.

Oscillatory energy exchange between waves coupled by a dynamic artificial crystal.

We describe a general mechanism of controllable energy exchange between waves propagating in a dynamic artificial crystal. We show that if a spatial periodicity is temporarily imposed on the transmission properties of a wave-carrying medium while a wave is inside, this wave is coupled to a secondary counterpropagating wave and energy oscillates between the two. The oscillation frequency is determined by the width of the spectral band gap created by the periodicity and the frequency difference between the coupled waves. The effect is demonstrated with spin waves in a dynamic magnonic crystal.

Long-range spin Seebeck effect and acoustic spin pumping.

Imagine that a metallic wire is attached to a part of a large insulator, which itself exhibits no magnetization. It seems impossible for electrons in the wire to register where the wire is positioned on the insulator. Here we found that, using a Ni81Fe19/Pt bilayer wire on an insulating sapphire plate, electrons in the wire recognize their position on the sapphire. Under a temperature gradient in the sapphire, surprisingly, the voltage generated in the Pt layer is shown to reflect the wire position, although the wire is isolated both electrically and magnetically. This non-local voltage is due to the coupling of spins and phonons: the only possible carrier of information in this system. We demonstrate this coupling by directly injecting sound waves, which realizes the acoustic spin pumping. Our finding provides a persuasive answer to the long-range nature of the spin Seebeck effect, and it opens the door to 'acoustic spintronics' in which sound waves are exploited for constructing spin-based devices.

Optical detection of spin transport in nonmagnetic metals.

We determine the dynamic magnetization induced in nonmagnetic metal wedges composed of silver, copper, and platinum by means of Brillouin light scattering microscopy. The magnetization is transferred from a ferromagnetic Ni80Fe20 layer to the metal wedge via the spin pumping effect. The spin pumping efficiency can be controlled by adding an insulating interlayer between the magnetic and nonmagnetic layer. By comparing the experimental results to a dynamical macroscopic spin-transport model we determine the transverse relaxation time of the pumped spin current which is much smaller than the longitudinal relaxation time.

Spin pumping by parametrically excited exchange magnons.

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

Radiation of caustic beams from a collapsing bullet.

We show both theoretically and experimentally that a collapsing (2+1)-dimensional wave packet in a medium with cubic nonlinearity and a two-dimensional dispersion of an order higher than parabolic irradiates untrapped dispersive waves. The studies are performed for a spin-wave bullet propagating in an in-plane magnetized ferrimagnetic film. An induced uniaxial anisotropy in such a medium leads to the formation of narrow spin-wave caustic beams whose angles to the bullet's propagation direction are modified by the motion of the source.

Nondiffractive subwavelength wave beams in a medium with externally controlled anisotropy.

We predict and experimentally demonstrate that in a medium with externally induced anisotropy, a wave source of a sufficiently small size can excite practically nondiffractive wave beams with stable subwavelength transverse aperture. The direction of beam propagation is controlled by rotating the induced anisotropy axis. Nondiffractive wave beam propagation, reflection, and scattering, as well as beam steering have been directly observed by optically probing dipolar spin waves in yttrium iron garnet films, where the uniaxial anisotropy was created by an in-plane bias magnetic field.