In the emerging field of magnonics, spin waves are foreseen as signal carriers for future spintronic information processing and communication devices, owing to both the very low power losses and a high device miniaturization potential predicted for short-wavelength spin waves. Yet, the efficient excitation and controlled propagation of nanoscale spin waves remains a severe challenge. Here, we report the observation of high-amplitude, ultrashort dipole-exchange spin waves (down to 80 nm wavelength at 10 GHz frequency) in a ferromagnetic single layer system, coherently excited by the driven dynamics of a spin vortex core. We used time-resolved x-ray microscopy to directly image such propagating spin waves and their excitation over a wide range of frequencies. By further analysis, we found that these waves exhibit a heterosymmetric mode profile, involving regions with anti-Larmor precession sense and purely linear magnetic oscillation. In particular, this mode profile consists of dynamic vortices with laterally alternating helicity, leading to a partial magnetic flux closure over the film thickness, which is explained by a strong and unexpected mode hybridization. This spin-wave phenomenon observed is a general effect inherent to the dynamics of sufficiently thick ferromagnetic single layer films, independent of the specific excitation method employed.

The magnetic vortex structure, an important ground state configuration in micron and sub-micron sized ferromagnetic thin film platelets, is characterized by a curling in-plane magnetization and, in the center, a minuscule region with out-of-plane magnetization, the vortex core, which points either up or down. It has already been demonstrated that the vortex core polarity can be reversed with external AC magnetic fields, frequency-tuned to the (sub-GHz) gyrotropic eigenmode or to (multi-GHz) azimuthal spin wave modes, where reversal times in the sub-ns regime can be realized. This fast vortex core switching may also be of technological interest as the vortex core polarity can be regarded as one data bit. Here we experimentally demonstrate that unidirectional vortex core reversal by excitation with sub-100 ps long orthogonal monopolar magnetic pulse sequences is possible in a wide range of pulse lengths and amplitudes. The application of such short digital pulses is the favourable excitation scheme for technological applications. Measured phase diagrams of this unidirectional, spin wave mediated vortex core reversal are in good qualitative agreement with phase diagrams obtained from micromagnetic simulations. The time dependence of the reversal process, observed by time-resolved scanning transmission X-ray microscopy indicates a switching time of 100 ps and fits well with our simulations. The origin of the asymmetric response to clockwise and counter clockwise excitation which is a prerequisite for reliable unidirectional switching is discussed, based on the gyromode -spin wave coupling.

We demonstrate a non-linear interference due to an active 'dual frequency' excitation of both, the sub-GHz vortex gyromode and multi-GHz magneto-static spin waves in ferromagnetic micrometer sized platelets in the vortex state. When the sub-GHz vortex gyromode is excited simultaneously a significant broadband reduction of the switching threshold for spin wave mediated vortex core reversal is observed in both, experiments and micromagnetic simulations. Consequently, the magnetic field amplitudes required for vortex core reversal can be lowered by nearly one order of magnitude. Moreover, additional spin wave resonance frequencies are found which emerge only if the vortex gyromode is actively excited simultaneously which can be explained by frequency doubling and by the broken symmetry of the vortex state.

Time-resolved scanning transmission x-ray microscopy (TR-STXM) has been used for the direct imaging of spin wave dynamics in thin film yttrium iron garnet (YIG) with spatial resolution in the sub 100 nm range. Application of this x-ray transmission technique to single crystalline garnet films was achieved by extracting a lamella (13x5x0.185 µm 3 ) of liquid phase epitaxy grown YIG thin film out of a gadolinium gallium garnet substrate. Spin waves in the sample were measured along the Damon-Eshbach and backward volume directions of propagation at gigahertz frequencies and with wavelengths in a range between 100 nm and 10 µm. The results were compared to theoretical models. Here, the widely used approximate dispersion equation for dipole-exchange spin waves proved to be insufficient for describing the observed Damon-Eshbach type modes. For achieving an accurate description, we made use of the full analytical theory taking mode-hybridization effects into account.

Three-dimensional linear spin-wave eigenmodes of a vortex-state Permalloy disk are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The simulations confirm that the increase of the disk thickness leads to the appearance of additional exchange-dominated so-called gyrotropic flexure modes having nodes along the disk thickness, and eigenfrequencies that decrease when the thickness is increased. We observe the formation of a gap in the mode spectrum caused by the hybridization of the first flexure mode with one of the azimuthal spin-wave modes of the disk. A qualitative change of the transverse profile of this azimuthal mode is found, demonstrating that in a thick vortex-state disk the influence of the "transverse" and the "azimuthal" coordinates cannot be separated. The threedimensional character of the eigenmodes is essential to explain the recently observed asymmetries in an experimentally obtained phase diagram of vortex-core reversal in relatively thick Permalloy disks. DOI: 10.1103/PhysRevLett.117.037208 The study of spin-wave (SW) excitations in micro-and nanosized magnetic elements is one of the most important topics in modern magnetism. The dynamic spin-wave eigenmodes of finite-size magnetic elements not only determine the high-frequency properties of these elements, but also provide valuable information about remagnetization processes in nanomagnetic objects, as the change of the magnetic ground state of an element is, usually, happening through the softening of one of the SW eigenmodes of this element. When the ground state of magnetization in a magnetic element is spatially uniform the spatial distribution of the spin-wave excitations can, usually, be factorized, and represented as a product of three functions of three independent coordinates (separation ansatz).The situation becomes much more complicated in the case when the magnetic element is thick, so that it has to be treated as three-dimensional (3D), and the magnetization ground state of the element is spatially nonuniform. In that case the possibilities of traditional analytic methods are limited; however, the essential information about SW excitations can be obtained from micromagnetic simulations. As it will be shown below, in a 3D spatially nonuniform case the dependence of the spin-wave mode profile on some of the spatial coordinates gets mixed, and the above discussed separation ansatz traditionally used in the analytic theory does not work anymore.A relatively simple example of a magnetic element having spatially nonuniform ground state of static magnetization is a vortex-state magnetic disk [1][2][3]. In a cylindrical nanodisk with thickness h of a few tens of nanometers and diameter 2R of typically several hundred nanometers the magnetic ground state is a vortex. There the magnetization curls in the plane of the disk with a clockwise (CW) or counterclockwise (CCW) circulation. At the center of the disk in an area with a typical diameter of 10 to 20 nm the magnetization turns out of the plane [3] form...