Research efforts addressing spin waves (magnons) in micro- and nanostructured ferromagnetic materials have increased tremendously in recent years. Corresponding experimental and theoretical work in magnonics faces significant challenges in that spin-wave dispersion relations are highly anisotropic and different magnetic states might be realized via, for example, the magnetic field history. At the same time, these features offer novel opportunities for wave control in solids going beyond photonics and plasmonics. In this topical review we address materials with a periodic modulation of magnetic parameters that give rise to artificially tailored band structures and allow unprecedented control of spin waves. In particular, we discuss recent achievements and perspectives of reconfigurable magnonic devices for which band structures can be reprogrammed during operation. Such characteristics might be useful for multifunctional microwave and logic devices operating over a broad frequency regime on either the macro- or nanoscale.

https://iopscience.iop.org/article/10.1088/0953-8984/26/12/123202/pdf

Review and prospects of magnonic crystals and devices with reprogrammable band structure

Magnons—the quanta of spin waves—propagating in magnetic materials with wavelengths at the nanometer-scale and carrying information in the form of an angular momentum, can be used as data carriers in next-generation, nano-sized low-loss information processing systems. In this respect, artificial magnetic materials with properties periodically varied in space, known as magnonic crystals, are especially promising for controlling and manipulating the magnon currents. In this article, different approaches for the realization of static, reconfigurable, and dynamic magnonic crystals are presented along with a variety of novel wave phenomena discovered in these crystals. Special attention is devoted to the utilization of magnonic crystals for processing of analog and digital information. Magnonic crystals for data processing 2

https://iopscience.iop.org/article/10.1088/1361-6463/aa6a65/pdf

Magnonic crystals for data processing

Artificial spin ices consist of nanomagnets arranged on the sites of various periodic and aperiodic lattices. They have enabled the experimental investigation of a variety of fascinating phenomena such as frustration, emergent magnetic monopoles and phase transitions that have previously been the domain of bulk spin crystals and theory, as we discuss in this Review. Artificial spin ices also show promise as reprogrammable magnonic crystals and, with this in mind, we give an overview of the measurements of fast dynamics in these magnetic metamaterials. We survey the variety of geometries that have been implemented, in terms of both the form of the nanomagnets and the lattices on which they are placed, including quasicrystalline systems and artificial spin systems in 3D. Different magnetic materials can also be incorporated to modify anisotropies and blocking temperatures, for example. With this large variety of systems, the way is open to discover new phenomena, and we complete this Review with possible directions for the future. Artificial spin ices are metamaterials displaying fascinating phenomena arising from the collective behaviour of nanoscale magnets. We review recent developments in terms of emergent magnetic monopoles, phase transitions, dynamics and geometries, and discuss future directions for research and potential applications.

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Advances in artificial spin ice

Magnetic materials hosting correlated electrons play an important role for information technology and signal processing. The currently used ferro-, ferri- and antiferromagnetic materials provide microscopic moments (spins) that are mainly collinear. Recently more complex spin structures such as spin helices and cycloids have regained a lot of interest.The interest has been initiated by the discovery of the skyrmion lattice phase in noncentrosymmetric helical magnets. In this review we address how spin helices and skyrmion lattices enrich the microwave characteristics of magnetic materials and give rise to bottom-up magnonic crystals. When discussing perspectives for microwave electronics and magnonics we focus particularly on insulating materials as they avoid eddy current losses, offer low spin-wave damping, and allow for electric field control. Thereby, they further fuel the vision of magnonics operated at low energy consumption.

https://iopscience.iop.org/article/10.1088/1361-6463/aa7573/pdf

Collective spin excitations of helices and magnetic skyrmions: review and perspectives of magnonics in non-centrosymmetric magnets

Recent results in magnonics – a topical and rapidly developing branch of spintronics and magnetoelectronics – are presented. The paper describes measurement techniques and theoretical approaches used to explore physical processes associated with the spin-wave propagation in complex nano- and micro-dimensional magnetic structures. The results of the application of magnetic structures in signal processing and transmission systems are discussed. In particular, results on spin wave propagation in distributed magnetic periodic structures, lumped systems, coupled waveguide structures, and controllable magnonic structures are considered. Specific examples of circuitry based on magnonic structures are discussed, and possibilities for further developing this circuitry are explored.

https://iopscience.iop.org/article/10.3367/UFNe.0185.201510m.1099/pdf

Magnonics: a new research area in spintronics and spin wave electronics

We investigate the magnonic band structure of in-plane magnetized two-dimensional magnonic crystals composed of cobalt dots embedded into a permalloy antidot lattice. Our analysis is based on the results of numerical calculations carried out by the plane wave method. The complex magnonic band structure found in square-lattice magnonic crystals is explained on the basis of the spin wave dispersion relations calculated in the empty lattice model. We show that four principal effects influence the formation of a magnonic band structure in planar two-dimensional bi-component magnonic crystals: a folding effect, Bragg scattering, hybridization between various spin wave modes, and a demagnetizing field. While the first two effects are found for other types of waves in periodic composites, the third one exists in an anisotropic medium and the last one is specific to spin waves propagating in magnonic crystals with magnetization in the film plane. The strong anisotropy in the dispersion relation of spin waves in thin ferromagnetic films results in the crossing and anti-crossing of the fast, Damon–Eshbach-like mode with a number of other spin waves folded to the first Brillouin zone. The demagnetizing field can induce the formation of channels for spin waves which are propagating perpendicular to the external magnetic field direction, but this property exists only in the limiting range of the thicknesses and the lattice constants of the bi-component magnonic crystals. Based on the model analysis we propose a modification of the magnonic crystal structure by changing its thickness, lattice constant and aspect ratio along the direction of the applied magnetic field to significantly modify the magnonic band structure and obtain partial magnonic band gaps.

https://iopscience.iop.org/article/10.1088/0022-3727/46/49/495003/pdf

Magnonic band structures in two-dimensional bi-component magnonic crystals with in-plane magnetization

Large magnonic band gaps and spectra evolution in three-dimensional magnonic crystals based on magnetoferritin nanoparticles

All-electrical spin-wave spectroscopy and frequency-resolved magneto-optical Kerr-effect measurements are combined to study spin waves propagating through a magnetic antidot lattice nanopatterned from a Ni80Fe20 thin film. Spin waves are injected from a plain film into the antidot lattice and the transmission across the interface is explored in detail for different wavelengths. We find that spin waves with a wavelength much greater than the lattice periodicity are not described well by recently discussed approaches. Instead the spin-wave dispersion is consistent with an effective magnetization smaller than the saturation magnetization measured on the unstructured ferromagnetic material. Consistently, we find that the transmission coefficients are modeled well by assuming an effectively continuous metamaterial for spin waves characterized by the reduced magnetization. The experimental data and interpretation are substantiated theoretically using the plane-wave method and micromagnetic modeling. The results are interesting for the development of frequency-selective mirrors in magnonics through lateral nanopatterning.

Tunable metamaterial response of a Ni 80 Fe 20 antidot lattice for spin waves

We investigate spin waves in two-dimensional superlattices in the form of an infinite ferromagnetic slab of finite thickness with periodically embedded ferromagnetic inclusions. One of the reasons of the interest in magnonic superlattices is the possibility of tailoring their spectrum to produce magnonic gaps, crucial for the prospective applications. The objective of this study is to find the optimal values of structural parameters for which low-frequency magnonic gaps will occur and have a maximum width. We provide some guidelines for designing superlattices with a desired spectrum. We focus on the role of the symmetry of the lattice versus other geometrical factors, including the filling fraction and the superlattice constant. We compare the spectra of superlattices with inclusions of circular, hexagonal, and square cross sections.

The impact of the lattice symmetry and the inclusion shape on the spectrum of 2D magnonic crystals

The Landau-Lifshitz equation with a scalar damping constant predicts that the damping of spin waves propagating in an infinite homogeneous magnetic medium does not depend on the direction of propagation. This is not the case in materials with a periodic arrangement of magnetic constituents (known as magnonic crystals). In this paper, the plane wave method is extended to include damping in the calculation of the dispersion and relaxation of spin waves in three-dimensional magnonic crystals. A model material system is introduced and calculations are then presented for magnonic crystals realized in the direct and inverted structure and for two different filling fractions. The ability of magnonic crystals to support the propagation of spin waves is characterized in terms of a figure of merit, defined as the ratio of the spin wave frequency to the decay constant. The calculations reveal that in magnonic crystals with a modulated value of the relaxation constant, the figure of merit depends strongly on the frequency and wave vector of the spin waves, with the dependence determined by the spatial distribution of the spin wave amplitude within the unit cell of the magnonic crystal. Bands and directions of exceptionally long spin wave propagation have been identified. The results are also discussed in terms of the use of magnonic crystals as metamaterials with designed magnetic permeability.

Sławomir Mamica

Papers

Magnonic band structures in two-dimensional bi-component magnonic crystals with in-plane magnetization

Large magnonic band gaps and spectra evolution in three-dimensional magnonic crystals based on magnetoferritin nanoparticles

Tunable metamaterial response of a Ni 80 Fe 20 antidot lattice for spin waves

The impact of the lattice symmetry and the inclusion shape on the spectrum of 2D magnonic crystals

Investigation of spin wave damping in three-dimensional magnonic crystals using the plane wave method