Direct observation of the transition from spin waves to the magnon Bose condensate.

Bose-Einstein condensation occurs at an appropriate density of bosonic particles, depending on their mass and temperature. The transition from the semiclassical paradigm of spin waves to the magnon Bose-Einstein condensed state (mBEC) was obtained experimentally with increasing magnon density. We used the Faraday rotation effect to study the spatial distribution of the magnon density and phase far from their excitation region. A coherent magnetization precession was observed throughout the sample, which indicates the formation of a magnon BEC. It is shown that this result under experimental conditions goes beyond the applicability of the Landau-Lifshitz-Gilbert semiclassical theory.

Topological Faraday Effect for Optical Vortices in Magnetic Films.

Here we experimentally demonstrate the topological Faraday effect-the polarization rotation caused by the orbital angular momentum of light. It is found that the Faraday effect of the optical vortex beam passing through a transparent magnetic dielectric film differs from the Faraday effect for a plane wave. The additional contribution to the Faraday rotation depends linearly on the topological charge and radial number of the beam. The effect is explained in terms of the optical spin-orbit interaction. These findings underline the importance of using the optical vortex beams for studies of magnetically ordered materials.

Optical registration of a coherent magnon state outside of the excitation region.

Magnons have demonstrated enormous potential for the next generation of information technology and quantum computing. In particular, the coherent state of magnons resulting from their Bose-Einstein condensation (mBEC) is of great interest. Typically, mBEC is formed in the magnon excitation region. Here we demonstrate for the first time by optical methods the permanent existence of mBEC at large distances from the magnon excitation region. The homogeneity of the mBEC phase is also demonstrated. The experiments were carried out on films of yttrium iron garnet magnetized perpendicular to the surface and at room temperature. We use the method described in this article to develop coherent magnonics and quantum logic devices.

Accumulation and control of spin waves in magnonic dielectric microresonators by a comb of ultrashort laser pulses.

Spin waves in magnetic microresonators are at the core of modern magnonics. Here we demonstrate a new method of tunable excitation of different spin wave modes in magnetic microdisks by using a train of laser pulses coming at a repetition rate higher than the decay rate of spin precession. The microdisks are etched in a transparent bismuth iron garnet film and the light pulses influence the spins nonthermally through the inverse Faraday effect. The high repetition rate of the laser stimulus of 10 GHz establishes an interplay between the spin wave resonances in the frequency and momentum domains. As a result, scanning of the focused laser spot near the disk boarder changes interference pattern of the magnons and leads to a resonant dependence of the spin wave amplitude on the external magnetic field. Apart from that, we achieved a switching between volume and surface spin waves by a small variation of the external magnetic field.

Magneto-optical imaging of coherent spin dynamics in ferrites.

The explosive development of quantum magnonics is associated with the possibility of its use as macroscopic quantum systems. In particular, they can find an application for quantum computing processors and other devices. The recently discovered phenomenon of magnon Bose-Einstein condensation and coherent precession of magnetization can be used for these purposes. Our letter describes a method for the optical observation of the coherently precessing magnetization in conditions when the concentration of magnons reaches the value necessary for their quantum condensation. The investigations were conducted in the out-of-plane magnetized yttrium iron garnet films. The required magnon density was achieved by magnetic resonance technique. The magneto-optical imaging method provides such important parameters of the coherent spin dynamics as the amplitude and phase distributed all over the sample. It should become an indispensable read-out tool for the upcoming quantum technologies based on the magnon Bose-Einstein condensation.

Quantum paradigm of the foldover magnetic resonance.

The explosive development of quantum magnonics requires the consideration of several previously known effects from a new angle. In particular, taking into account the quantum behavior of magnons is essential at high excitations of the magnetic system, under the conditions of the so-called phenomenon of "foldover" (bi-stable) magnetic resonance. Previously, this effect was considered in the quasi-classical macrospin approximation. However, at large angles of magnetization precession, the magnon density exceeds the critical value for the formation of a magnon Bose condensate (mBEC). Naturally, this purely quantum phenomenon does not exist in the classical approximation. In addition, mBEC leads to superfluid transfer of magnetization, which suppresses the macroinhomogeneity of the samples. The experiments presented in the article show that quantum phenomena well describes the experimental results of nonlinear magnetic resonance in yttrium iron garnet. Thus, we remove the questions that arose earlier when considering this effect without taking into account quantum phenomena. This discovery paves the way for many quantum applications of supermagnonics, such as the magnetic Josephson effect, long-range spin transport, Q-bits, quantum logic, magnetic sensors, and others.

Nanophotonic structures with optical surface modes for tunable spin current generation.

We propose a novel type of photonic-crystal (PC)-based nanostructures for efficient and tunable optically-induced spin current generation via the spin Seebeck and inverse spin Hall effects. It has been experimentally demonstrated that optical surface modes localized at the PC surface covered by ferromagnetic layer and materials with giant spin-orbit coupling (SOC) notably increase the efficiency of the optically-induced spin current generation, and provides its tunability by modifying the light wavelength or angle of incidence. Up to 100% of the incident light power can be transferred to heat within the SOC layer and, therefore, to the spin current. Importantly, the high efficiency becomes accessible even for ultra-thin SOC layers. Moreover, the surface patterning of the PC-based spintronic nanostructure allows for the local generation of spin currents at the pattern scales rather than the diameter of the laser beam.

Layer-selective magnetization switching in the chirped photonic crystal with GdFeCo.

Here we propose a magnetophotonic structure for the layer-selective magnetization switching with femtosecond laser pulses of different wavelengths. It is based on a chirped magnetophotonic crystal (MPC) containing magnetic GdFeCo and nonmagnetic dielectric layers. At each operating wavelength the laser pulses heat up to necessary level only one GdFeCo layer that leads to its magnetization reversal without any impact on the magnetization of the other layers. Moreover, magneto-optical reading of the MPC magnetization state is discussed. Lateral dimensions of the considered MPC can be made small enough to operate as a unit cell for data storage.

Bound states in the continuum enable modulation of light intensity in the Faraday configuration.

We demonstrate a novel, to the best of our knowledge, magneto-optical effect that reveals itself in light intensity modulation without polarization rotation in the Faraday configuration. We design a photonic crystal with a magnetized optical cavity that supports bound states in the continuum (BICs), since it simultaneously provides the extended state (continuum) for TM polarization, and the bound (localized) state in the form of a cavity mode for TE-polarized light. Magnetization of the photonic crystal in the Faraday configuration results in efficient polarization conversion and trapping of the acquired TE components of the TM incident light inside the magnetized optical cavity. As a result, a BIC manifests itself as a significant magneto-optical modulation of transmitted light intensity, while its polarization is preserved. Therefore, the proposed structure is promising for magnetic control of light in various applications.

Plasmonic layer-selective all-optical switching of magnetization with nanometer resolution.

All-optical magnetization reversal with femtosecond laser pulses facilitates the fastest and least dissipative magnetic recording, but writing magnetic bits with spatial resolution better than the wavelength of light has so far been seen as a major challenge. Here, we demonstrate that a single femtosecond laser pulse of wavelength 800 nm can be used to toggle the magnetization exclusively within one of two 10-nm thick magnetic nanolayers, separated by just 80 nm, without affecting the other one. The choice of the addressed layer is enabled by the excitation of a plasmon-polariton at a targeted interface of the nanostructure, and realized merely by rotating the polarization-axis of the linearly-polarized ultrashort optical pulse by 90°. Our results unveil a robust tool that can be deployed to reliably switch magnetization in targeted nanolayers of heterostructures, and paves the way to increasing the storage density of opto-magnetic recording by a factor of at least 2.

Optically pumped Floquet states of magnetization in ferromagnets.

Floquet states have been the subject of great research interest since Zel'dovich's pioneering work on the quasienergy of a quantum system influenced by a temporally periodic action. Nowadays, periodic modulation of the system Hamiltonian is achieved mostly by microwaves, leading to novel exciting phenomena in condensed matter physics. On the other hand, nonthermal optical control of magnetization at picosecond time scales is currently a highly appealing research topic for potential applications in magnetic data storage. Here we combine these two concepts to theoretically investigate Floquet states in the system of exchange-coupled spins in a ferromagnet. Periodic perturbation of the magnetization of an iron-garnet film by circularly polarized femtosecond laser pulses is shown to establish the magnetization dynamics behaving like Floquet states. An external magnetic field allows tuning of the Floquet states, leading to pronounced increase in the precession amplitude by one order of magnitude at the center of the Brillouin zone, i.e., when the precession frequency is a multiple of the laser pulse repetition rate. Floquet states might potentially allow for parametric generation of magnetic oscillations. The observed phenomena expand the capabilities of coherent ultrafast optical control of magnetization and pave the way for their application in quantum computation or data processing.

Generation of spin waves by a train of fs-laser pulses: a novel approach for tuning magnon wavelength.

Currently spin waves are considered for computation and data processing as an alternative to charge currents. Generation of spin waves by ultrashort laser pulses provides several important advances with respect to conventional approaches using microwaves. In particular, focused laser spot works as a point source for spin waves and allows for directional control of spin waves and switching between their different types. For further progress in this direction it is important to manipulate with the spectrum of the optically generated spin waves. Here we tackle this problem by launching spin waves by a sequence of femtosecond laser pulses with pulse interval much shorter than the relaxation time of the magnetization oscillations. This leads to the cumulative phenomenon and allows us to generate magnons in a specific narrow range of wavenumbers. The wavelength of spin waves can be tuned from 15 µm to hundreds of microns by sweeping the external magnetic field by only 10 Oe or by slight variation of the pulse repetition rate. Our findings expand the capabilities of the optical spin pump-probe technique and provide a new method for the spin wave generation and control.

Optical excitation of spin waves in epitaxial iron garnet films: MSSW vs BVMSW.

In most of the previous studies of the spin wave optical generation in magnetic dielectrics, the backward volume spin waves were excited. Here we modified the parameters of the circularly polarized optical pump beams emitted by femtosecond laser to reveal surface spin waves in bismuth iron garnet thin film. Beams that are larger than 10 µm in diameter generate both surface and volume spin waves with only one spectral peak near the ferromagnetic resonance. On the contrary, narrower beams excite predominantly surface spin waves of higher frequency, providing an additional peak in the spin wave spectrum. Thus different interference patterns of the magnetization dynamics are achievable. This may significantly broaden the capabilities of spin wave based devices.

Surface plasmons in nanowires with toroidal magnetic structure.

We consider the problem of the influence of a toroidal magnetization on a cylindrical surface plasmon polariton (SPP) propagating along a nanowire of a circular cross section. It follows from the dispersion equations that the SPP wavenumber linearly depends on the toroidal moment and the effect of magneto-optical nonreciprocity appears. The numerical solution of the dispersion equations demonstrates that the corresponding splitting of the SPP dispersion curves for two opposite directions of the toroidal moment is increased by an order of magnitude with respect to the planar case. The largest values of this splitting are observed for systems with relatively low optical losses, as is demonstrated by calculations for SPPs in a gold cylinder surrounded by rare-earth bismuth iron garnet.

Plasmon-mediated magneto-optical transparency.

Magnetic field control of light is among the most intriguing methods for modulation of light intensity and polarization on sub-nanosecond timescales. The implementation in nanostructured hybrid materials provides a remarkable increase of magneto-optical effects. However, so far only the enhancement of already known effects has been demonstrated in such materials. Here we postulate a novel magneto-optical phenomenon that originates solely from suitably designed nanostructured metal-dielectric material, the so-called magneto-plasmonic crystal. In this material, an incident light excites coupled plasmonic oscillations and a waveguide mode. An in-plane magnetic field allows excitation of an orthogonally polarized waveguide mode that modifies optical spectrum of the magneto-plasmonic crystal and increases its transparency. The experimentally achieved light intensity modulation reaches 24%. As the effect can potentially exceed 100%, it may have great importance for applied nanophotonics. Further, the effect allows manipulating and exciting waveguide modes by a magnetic field and light of proper polarization.

Enhanced magneto-optical effects in magnetoplasmonic crystals.

Plasmonics allows light to be localized on length scales much shorter than its wavelength, which makes it possible to integrate photonics and electronics on the nanoscale. Magneto-optical materials are appealing for applications in plasmonics because they open up the possibility of using external magnetic fields in plasmonic devices. Here, we fabricate a new magneto-optical material, a magnetoplasmonic crystal, that consists of a nanostructured noble-metal film on top of a ferromagnetic dielectric, and we demonstrate an enhanced Kerr effect with this material. Such magnetoplasmonic crystals could have applications in telecommunications, magnetic field sensing and all-optical magnetic data storage.

On surface plasmon polariton wavepacket dynamics in metal-dielectric heterostructures.

The WKB equations for the dynamics of the surface plasmon polariton (SPP) wavepacket are studied. The dispersion law for the SPP in a metal-dielectric heterostructure with varying thickness of a dielectric grating is rigorously calculated and investigated using the scattering matrix method. Two channels of the SPP wavepacket optical losses related to the absorption in a metal and to the SPP leakage are analyzed. It is shown that change of the dielectric layer thickness acts on the SPP as an external force leading to evolution of its quasimomentum and to the wavepacket reversal or even to optical Bloch oscillations (BO). Properties of these phenomena are investigated and discussed. Typical values of the BO amplitude are about tens of microns and the period is around tens or hundreds of femtoseconds.

Giant magneto-optical orientational effect in plasmonic heterostructures.

Magneto-optical (MO) properties of perforated heterostructures consisting of a thin metallic film perforated with a periodic array of subwavelength slits and a smooth magnetic dielectric are investigated. Rigorous modeling revealed a magnetization-even MO effect determined by the relative change in the intensity of the transmitted or reflected light when the sample is magnetized in-plane perpendicularly to the slits. The effect takes its maximum value when the p-polarized incident light excites quasi-waveguided eigenmodes in the magnetic layer with the phase velocity close to the one of the TE mode in the nongyrotropic planar waveguide.

Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems.

We predict theoretically a significant enhancement of the magneto-optical Faraday and Kerr effects in the bilayer systems of a metallic film perforated with subwavelength hole arrays and a uniform dielectric film magnetized perpendicular to its plane. Calculations, based on a rigorous coupled-wave analysis of Maxwell's equations, demonstrate that in such structures the Faraday effect spectrum has several resonance peaks in the near-infrared range, some of them coinciding with transmittance peaks, providing simultaneous large Faraday rotation enhanced by an order of magnitude and high transmittance of about 35%.