Surface-modulated magnonic crystals are the natural link between continuous films with sinusoidal spin-wave eigenmodes and one-dimensional magnonic crystals composed of individual nanowires. Nevertheless, the transformation process of the spin-wave modes in this transition remains yet unclear. Here, spin-wave modes in their entire transition from a flat film to a 'full' (one-dimensional) magnonic crystal are studied by ferromagnetic resonance (FMR) and micromagnetic simulations. For this purpose, the surface of a pre-patterned thin permalloy film was sequentially ion milled resulting in hybrid structures, referred to as surface-modulated magnonic crystals, with increasing modulation depth. After each step, FMR measurements were carried out in backward-volume and Damon-Eshbach geometry. The evolution of each spin-wave resonance is studied together with the corresponding mode profile obtained by micromagnetic simulations. Simple rules describing the transition of the modes from the film to the modes of the full magnonic crystal are provided unraveling the complexity of spin-wave states in these hybrid systems.

Theoretical results for the magnetization dynamics of a magnonic crystal formed by grooves on the surface of a ferromagnetic film, called a surface-modulated magnonic crystal, are presented. For such a system, the role of the periodic dipolar field induced by the geometrical modulation is addressed by using the plane-wave method. The results reveal that, under the increasing of the depth of the grooves, zones with magnetizing and demagnetizing fields act on the system in such a way that magnonic band gaps are observed in both Damon-Eshbach and backward volume geometries. Particularly, in the backward volume configuration, high-frequency band gaps and lowfrequency flat modes are obtained. By taking into account the properties of the internal field induced by the grooves, the flattening of the modes and their shift towards low frequencies are discussed and explained. To test the validity of the model, the theoretical results of this work are confirmed by micromagnetic simulations, and good agreement between both methods is achieved. The theoretical model allows for a detailed understanding of the physics underlying these kinds of systems, thereby providing an outlook for potential applications on magnonic devices.

The availability of intense soft x-ray beams with tunable energy and polarization has pushed the development of highly sensitive, element-specific, and noninvasive microscopy techniques to investigate condensed matter with high spatial and temporal resolution. The short wavelengths of soft x-rays promise to reach spatial resolutions in the deep single-digit nanometer regime, providing unprecedented access to magnetic phenomena at fundamental length scales. Despite considerable efforts in soft x-ray microscopy techniques, a two-dimensional resolution of 10 nm has not yet been surpassed in direct imaging. Here, we report on a significant step beyond this long-standing limit by combining newly developed soft x-ray Fresnel zone plate lenses with advanced precision in scanning control and careful optical design. With this approach, we achieve an image resolution of 7 nm. By combining this highly precise microscopy technique with the x-ray magnetic circular dichroism effect, we reveal dimensionality effects in an ensemble of interacting magnetic nanoparticles. Such effects are topical in current nanomagnetism research and highlight the opportunities of highresolution soft x-ray microscopy in magnetism research and beyond.

Magnonic crystals with locally alternating properties and specific periodicities exhibit interesting effects, such as a multitude of different spin-wave states and large band gaps. This work aims for demonstrating and understanding the key role of local demagnetizing fields in such systems. To achieve this, hybrid structures are investigated consisting of a continuous thin film with a stripe modulation on top favorable due to the adjustability of the magnonic effects with the modulation size. For a direct access to the spin dynamics, a magnonic crystal was reconstructed from 'bottom-up', i.e., the structural shape as well as the internal field landscape of the structure were experimentally obtained on the nanoscale using electron holography. Subsequently, both properties were utilized to perform dynamic response calculations. The simulations yield the frequency-field dependence as well as the angular dependence of spin waves in a magnonic crystal and reveal the governing role of the internal field landscape around the backward-volume geometry. The complex angle-dependent spin-wave behavior is described for a 360• in-plane rotation of an external field by connecting the internal field landscape with the individual spin-wave localization.

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Artículo de publicación ISISin acceso a texto completoAn all-electrical method is presented to determine the exchange constant of magnetic thin films using ferromagnetic resonance. For films of 20 nm thickness and below, the determination of the exchange constant A, a fundamental magnetic quantity, is anything but straightforward. Among others, the most common methods are based on the characterization of perpendicular standing spin-waves. These approaches are however challenging, due to (i) very high energies and (ii) rather small intensities in this thickness regime. In the presented approach, surface patterning is applied to a permalloy (Ni80Fe20) film and a Co2Fe0.4Mn0.6Si Heusler compound. Acting as a magnonic crystal, such structures enable the coupling of backward volume spin-waves to the uniform mode. Subsequent ferromagnetic resonance measurements give access to the spin-wave spectra free of unquantifiable parameters and, thus, to the exchange constant A with high accuracy

Symmetry and localization properties of defect modes of a one-dimensional bi-component magnonic superlattice are theoretically studied. The magnonic superlattice can be seen as a periodic array of nanostripes, where stripes with different width, termed as defect stripes, are periodically introduced. By controlling the geometry of the defect stripes, a transition from dispersive to practically flat spin-wave defect modes can be observed inside the magnonic band gaps. It is shown that the spin-wave profile of the defect modes can be either symmetric or antisymmetric, depending on the geometry of the defect. Due to the localized character of the defect modes, a particular magnonic superlattice is proposed, wherein the excitation of either symmetric or antisymmetric flat magnonic modes is enabled at the same time. Also, it is demonstrated that the relative frequency position of the antisymmetric mode inside the band gap does not significantly change with the application of an external field, while the symmetric modes move to the edges of the frequency band gaps. The results are complemented by numerical simulations, where an excellent agreement is observed between both methods. The proposed theory allows exploring different ways to control the dynamic properties of the defect modes in metamaterial magnonic superlattices, which can be useful for applications on multifunctional microwave devices operating over a broad frequency range.

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