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This chapter describes spin-wave excitations in nanosized dots and rings in the presence of the vortex state. The special attention is paid to the manifestation of the competition between exchange and dipolar interactions in the spin-wave…

The spin dynamics are calculated for a model system consisting of magnetically soft, layered nanomagnets, in which two ferromagnetic (F) cylindrical dots, each with a magnetic vortex ground state, are separated by a non-magnetic spacer (N).…

Within the framework of the Landau-Lifshitz-Gilbert equation, using permalloy parameters, we study the statics and dynamics of flat circular magnetic nano-structures with an in-plane magnetic vortex configuration, putting particular…

We investigate spin-wave modes in confined ferromagnetic resonators with spherical and cylindrical geometries across the exchange-dominated, dipole-exchange, and dipolar interaction regimes. Starting from the linearized…

We have studied spin excitations in nanosized magnetic films in the Heisenberg model with magnetic dipole and exchange interactions by the spin operator diagram technique. Dispersion relations of spin waves in thin magnetic films (in…

We present a finite-difference micromagnetic approach for determining the normal modes of spin-waves propagating in extended magnetic films and strips, which is based on the linearized Landau-Lifshitz equation and uses the dynamic matrix…

We calculated the main dynamic parameters of the spin polarized current induced magnetic vortex oscillations in nanopillars, such as the range of current density, where a vortex steady oscillations exist, the oscillation frequency and orbit…

The Landau-Lifshitz equation governing magnetization dynamics is written in terms of the amplitudes of normal modes associated with the micromagnetic system's appropriate ground state. This results in a system of nonlinear ordinary…

We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg-Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by…

A vortex-antivortex (VA) dipole may be generated due to a spin-polarized current flowing through a nano-aperture in a magnetic element. We study the vortex dipole dynamics using the Landau-Lifshitz equation in the presence of an in-plane…

A two-dimensional easy-plane ferromagnetic substrate, interacting with a dipolar tip which is magnetised perpendicular with respect to the easy plane is studied numerically by solving the Landau-Lifshitz Gilbert equation. Due to the…

Stacked spin-vortex pairs in magnetic multilayered nanopillars, with vertical separation between the vortices small compared to the vortex core size, exhibit spin dynamics absent in individual vortices. This dynamics is nonlinear and is due…

This study conducts a comprehensive investigation into the reversal mechanism of magnetic vortex cores in a nanopillar system composed of two coupled ferromagnetic dots under zero magnetic field conditions. The research employs a…

We present an experimental investigation of radial spin-wave modes in magnetic nano-disks with a vortex ground state. The spin-wave amplitude was measured using a frequency-resolved magneto optical network analyzer, allowing for…

We study dynamical and thermal effects that are induced in nanoparticle systems by a rotating magnetic field. Using the deterministic Landau-Lifshitz equation and appropriate rotating coordinate systems, we derive the equations that…

We study the magnetization dynamics in a nanocontact magnetic vortex oscillators as function of temperature. Low temperature experiments reveal that the dynamics at low and high currents differ qualitatively. At low currents, we excite a…

Relaxation schemes for finding normal modes of nonlinear excitations are described, and applied to the vortex-spinwave scattering problem in classical two-dimensional easy-plane Heisenberg models. The schemes employ the square of an…

We introduce a topological gauge vector potential which influences spin wave excitations over arbitrary non-uniform, slowly moving magnetization distribution. The time-component of the gauge potential plays a principal role in magnetization…

Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their…

Vortices and antivortices are typical non uniform magnetization configurations that can be achieved in spin-torque oscillators with in-plane materials. Dynamics of a vortex-antivortex pair, namely vortex dipole, were predicted and already…