Graded-index magnonics

This is the published version. Preprint version and supporting data available at http://hdl.handle.net/10871/17998© 2015 AIP Publishing LLC. The wave solutions of the Landau-Lifshitz equation (spin waves) are characterized by some of the most complex and peculiar dispersion relations among all waves. For example, the spin-wave ("magnonic") dispersion can range from the parabolic law (typical for a quantum-mechanical electron) at short wavelengths to the nonanalytical linear type (typical for light and acoustic phonons) at long wavelengths. Moreover, the long-wavelength magnonic dispersion has a gap and is inherently anisotropic, being naturally negative for a range of relative orientations between the effective field and the spin-wave wave vector. Nonuniformities in the effective field and magnetization configurations enable the guiding and steering of spin waves in a deliberate manner and therefore represent landscapes of graded refractive index (graded magnonic index). By analogy to the fields of graded-index photonics and transformation optics, the studies of spin waves in graded magnonic landscapes can be united under the umbrella of the graded-index magnonics theme and are reviewed here with focus on the challenges and opportunities ahead of this exciting research direction.The research leading to these results has received funding from the Engineering and Physical Sciences Research Council of the United Kingdom under Project Nos. EP/L019876/1, EP/L020696/1, and EP/P505526/1

Generation of Propagating Spin Waves from Edges of Magnetic Nanostructures Pumped by Uniform Microwave Magnetic Field

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.Thin-film patterned magnetic nanostructures are widely employed within perceived magnonic device architectures to guide and/or manipulate spin waves for data processing and communication purposes. Here, using micromagnetic simulations, we explore how the internal magnetic field nonuniformity inherent to patterned magnetic nanostructures can also be exploited to create spin-wave sources. The spin-wave emission is achieved through the resonant excitation of finite-sized regions of increased effective magnetic field formed near the edges of patterned structures. The phenomenon is rather universal and could be used to generate magnetodipole, dipole-exchange, and exchange dominated spin waves. Depending on the frequency of excitation and parameters of the nanostructures, the emitted spin waves may form either highly directional spin-wave caustic beams or more regular plane spin waves.This work was supported by the U.K. Engineering and Physical Sciences Research Council under Project EP/L019876/1 and Project EP/P505526/1

An effect of the curvature induced anisotropy on the spectrum of spin waves in a curved magnetic nanowire

This is the final version of the article. Available from the American Institute of Physics via the DOI in this record.Within the framework of the solid state theory, an expression for the spectrum of spin waves propagating in a thin magnetic nanowire curled into a helix (spiral) is obtained. Its modification under the effect of a periodic modulation of the helical pitch is analyzed. In particular, it is shown that the periodic modulation of the helix pitch leads to the appearance of band gaps in the spectrum of spin waves. The influence of the modulation depth of the helical pitch on a size of the first gap is considered. © 2013 American Institute of Physics.This work was supported in part by the project NoWaPhen (FP7 GA 247556)

Chiral magnonic resonators: Rediscovering the basic magnetic chirality in magnonics

This is the author accepted manuscript. the final version is available from the American Institute of Physics via the DOI in this recordData availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.The outlook for producing useful practical devices within the paradigm of magnonics rests on our ability to emit, control, and detect coherent exchange spin waves on the nanoscale. Here, we argue that all these key functionalities can be delivered by chiral magnonic resonators—soft magnetic elements chirally coupled, via magneto–dipole interaction, to magnonic media nearby. Starting from the basic principles of chiral coupling, we outline how they could be used to construct devices and explore underpinning physics, ranging from basic logic gates to field programmable gate arrays, in-memory computing and artificial neural networks, and extending from one- to two- and three-dimensional architectures.Engineering and Physical Sciences Research Council (EPSRC)European Union FP7European Union Horizon 202

Bloch oscillations of backward volume magnetostatic spin waves

This is the final version. Available from the American Physical Society via the DOI in this recordWe have used numerical micromagnetic simulations to propose a feasible candidate system in which Bloch oscillations of spin waves could be observed experimentally. Our simulations demonstrate these phenomena for backward volume magnetostatic spin waves (BVMSWs) in a film of yttrium-iron-garnet in a spatially varying bias magnetic field comprising a sinusoidal and gradient contributions. Despite the complex character of the BVMSW dispersion relation, the spin-wave packets are distinctly confined by the field gradient, while showing only minor broadening over the simulation time.Engineering and Physical Sciences Research Council (EPSRC)European Union Horizon 202

Electric-field control of spin-wave power flow and caustics in thin magnetic films

This is the final version of the article. Available from American Physical Society via the DOI in this record.An external electric field can modify the strength of the spin-orbit interaction between spins of ions in magnetic crystals. This influence leads to a spin-wave frequency shift that is linear in both the applied electric field and the wave vector of the spin wave. Here we study theoretically the external electric field as a means of control of the spin-wave power flow in thin ferromagnets. The spin-wave group velocity and focusing patterns are obtained from the slowness (isofrequency) curves by evaluating their curvature at each point of the reciprocal space. We show that the combination of the magnetodipole interaction and the electric field can result in nonreciprocal unidirectional caustic beams of dipole-exchange spin waves. We demonstrate that the degree of asymmetry of the spin-wave power flow can be tuned with the external electric field. Our findings open a novel avenue for spin-wave manipulation and development of electrically tunable magnonic devices.his research was conducted in the framework of the MagIC Project: 644348-H2020-MSCA-RISE-2014; V.N.K. and A.S.S. also acknowledge support of the State Fund for Fundamental Research of Ukraine (Project: F71/59-2017)

Emission of coherent spin waves from a magnetic layer excited by a uniform microwave magnetic field

This is the author accepted manuscript. The final version is available from IOP Publishing via the DOI in this record.We have developed an analytical theory of the Schlömann spin wave generation from a ferromagnetic layer sandwiched between two semi-infinite media of another ferromagnetic material and pumped by a uniform microwave magnetic field. Our calculations show that, under identical conditions, such a non-uniformity can boost more than twice the emitted spin wave amplitude relative to that emitted from an isolated magnetic interface. The theory provides further support in favour of the dominant role played in the process by the local difference of the microwave magnetic susceptibilities of the adjacent magnetic materials.Engineering and Physical Sciences Research CouncilEuropean Union’s Horizon 2020 researchMarie Skłodowska-Curi

Magnetic interfaces as sources of coherent spin waves

This is the final version of the article. Available from APS via the DOI in this recordWe have developed a simple but general analytical theory that elucidates the mechanism of spin-wave generation from interfaces between ferromagnetic media pumped by a uniform microwave magnetic field. Our calculations show that, provided there is a finite coupling between the two media, the amplitude of the emitted spin waves depends linearly on the difference between their magnetic susceptibilities. The theory is successfully applied to interpret qualitatively three recent experimental studies in which such a spin-wave emission was observed. Furthermore, we describe how our approach can be extended to several more complicated spin-wave excitation schemes employing electric, elastic, and optical stimuli.The research leading to these results has received funding from the Engineering and Physical Sciences Research Council of the United Kingdom (Project No. EP/L019876/1) and from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie Grant Agreement No. 644348 (MagIC)

Scattering of exchange spin waves from a helimagnetic layer sandwiched between two semi-infinite ferromagnetic media

This is the final version. Available from the publisher via the DOI in this record.We have calculated the scattering (reflection and transmission) coefficients of linear exchange spin waves normally incident upon a helimagnetic layer sandwiched between two semi-infinite ferromagnetic media. Our calculations show that, despite the helimagnetic order induced in the layer by the Dzyaloshinskii-Moriya interaction (DMI), the scattering is reciprocal and insensitive to the presence of the helimagnetic order in the layer. This comes as a result of the disappearance of the DMI from the boundary conditions in the considered geometry under the small-amplitude approximation and from the specific form of the nonreciprocity of the spin-wave dispersion relation in the helimagnetic material. We show that the helimagnetic layer’s interfaces act as a system of two semicrossed polarizers for the circularly polarized spin waves incident from the ferromagnetic media. This results from the ellipticity of the magnetic precession induced by the easy-plane anisotropy in the helimagnetic layer. Our calculations also reveal the importance of evanescent solutions to correctly describe the spin-wave scattering in samples with elliptical precession. Our findings will aid development of magnonic devices containing helimagnetic constituents.European Union’s Horizon 202

Graded index lenses for spin wave steering

This is the final version. Available from the American Physical Society via the DOI in this record. We use micromagnetic modelling to demonstrate the operation of graded index lenses designed to steer forward-volume magnetostatic spin waves by 90 and 180 degrees. The graded index profiles require the refractive index to diverge in the lens center, which, for spin waves, can be achieved by modulating the saturation magnetization or external magnetic field in a ferromagnetic film by a small amount. We also show how the 90$^\circ$ lens may be used as a beam divider. Finally, we analyse the robustness of the lenses to deviations from their ideal profiles.Royal Society (Charity)Engineering and Physical Sciences Research Council (EPSRC