The influence of the magnetostatic interaction on vortex dynamics in arrays of ferromagnetic disks is investigated by means of a broadband ferromagnetic-resonance setup. Transmission spectra reveal a strong dependence of the resonance frequency of vortex-core motion on the ratio between the center-to-center distance and the element size. For a decreasing ratio, a considerable broadening of the absorption peak is observed following an inverse sixth power law. An analogy between the vortex system and rotating dipoles is confirmed by micromagnetic simulations.
A wide variety of coupled harmonic oscillators exist in nature. Coupling between different oscillators allows for the possibility of mutual energy transfer between them and the information-signal propagation. Low-energy input signals and their transport with negligible energy loss are the key technological factors in the design of information-signal processing devices. Here, utilizing the concept of coupled oscillators, we experimentally demonstrated a robust new mechanism for energy transfer between spatially separated dipolar-coupled magnetic disks - stimulated vortex gyration. Direct experimental evidence was obtained by a state-of-the-art experimental time-resolved soft X-ray microscopy probe. The rate of energy transfer from one disk to the other was deduced from the two normal modes' frequency splitting caused by dipolar interaction. This mechanism provides the advantages of tunable energy transfer rates, low-power input signals and negligible energy loss in the case of negligible intrinsic damping. Coupled vortex-state disks might be implemented in applications for information-signal processing.
Lattice vibration modes are collective excitations in periodic arrays of atoms or molecules. These modes determine novel transport properties in solid crystals. Analogously, in periodical arrangements of magnetic vortex-state disks, collective vortex motions have been predicted. Here, we experimentally observe wave modes of collective vortex gyration in one-dimensional (1D) periodic arrays of magnetic disks using time-resolved scanning transmission x-ray microscopy. The observed modes are interpreted based on micromagnetic simulation and numerical calculation of coupled Thiele equations. Dispersion of the modes is found to be strongly affected by both vortex polarization and chirality ordering, as revealed by the explicit analytical form of 1D infinite arrays. A thorough understanding thereof is fundamental both for lattice vibrations and vortex dynamics, which we demonstrate for 1D magnonic crystals. Such magnetic disk arrays with vortex-state ordering, referred to as magnetic metastructure, offer potential implementation into information processing devices.
The influence of the magnetostatic interaction on vortex dynamics in arrays of ferromagnetic disks is investigated by means of a broadband ferromagnetic-resonance setup. Transmission spectra reveal a strong dependence of the resonance frequency of vortex-core motion on the ratio between the center-tocenter distance and the element size. For a decreasing ratio, a considerable broadening of the absorption peak is observed following an inverse sixth power law. An analogy between the vortex system and rotating dipoles is confirmed by micromagnetic simulations. DOI: 10.1103/PhysRevLett.105.037201 PACS numbers: 75.75.Àc, 75.25.Àj, 75.40.Gb, 76.50.+g Vortex dynamics can be observed in many physical systems such as ferromagnets, superconductors, and Bose-Einstein condensates. Explanations of flow phenomena in modern fluid mechanics are often predicated on the dynamics of vortices. In recent years, small ferromagnetic structures with vortex magnetization configuration have gained intense scientific interest because of their dynamics on the subnanosecond time scale and potential technological applications, such as ultrafast and highdensity digital storage devices [1][2][3][4]. Even medical applications have lately been discussed [5]. Understanding the influence of the various internal and external parameters on the dynamic properties of the magnetic vortex is an important issue for further development. The gyrotropic mode and switching of single vortex cores have been studied intensely [6][7][8][9][10]. However, investigation of the interaction between several vortices [11][12][13][14] is still required. Coupling of magnetic vortices, e.g., provides a model system in fundamental research and could also determine the packing density in storage devices.To describe the magnetic behavior of an array of ferromagnetic disks, the magnetostatic interaction between single elements has to be considered when the interelement distance is less than the lateral size of one disk [15]. An increase of the initial susceptibility and a decrease of the vortex nucleation and annihilation fields are observed [16]. Analytical and numerical calculations using the rigid vortex model predict a shift of the eigenfrequency of vortexcore motions in adjacent ferromagnetic disks depending on the core polarizations and the distance between the disk centers [11,17].Here, we experimentally study the influence of the magnetostatic interaction on the resonance frequency of vortices trapped in arrays of 4 Â N ferromagnetic disks by varying the distance and the size of the elements. Energy absorption in radio-frequency magnetic fields has been determined via a broadband ferromagnetic-resonance (FMR) setup using a vector-network analyzer. The vortex resonance frequency strongly depends on the magnetostatic coupling within the array. The relative broadening of the absorption peak due to resonant vortex-core motion varies with the inverse sixth power of the normalized center-to-center distance. This kind of distance dependence is a prominent feature of the f...
A parallel geometric multigrid solver on hierarchically distributed grids is presented. Using a tree-structure for grid distribution onto the processing entities, the multigrid cycle is performed similarly to the serial algorithm, using additional vertical communication during transfer operations. The workload is gathered to fewer processes on coarser levels. Involved parallel structures are described in detail and the multigrid algorithm is formulated, discussing parallelization details. A performance study is presented that shows close to optimal efficiency for weak scaling up to 262k processes in 2 and 3 space dimensions.
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