Thermal vortex dynamics in thin circular ferromagnetic nanodisks

The dynamics of gyrotropic vortex motion in a thin circular nanodisk of soft ferromagnetic material is considered. The demagnetization field is calculated using two-dimensional Green's functions for the thin film problem and fast Fourier transforms. At zero temperature, the dynamics of the Landau-Lifshitz-Gilbert equation is simulated using fourth order Runge-Kutta integration. Pure vortex initial conditions at a desired position are obtained with a Lagrange multipliers constraint. These methods give accurate estimates of the vortex restoring force constant $k_F$ and gyrotropic frequency, showing that the vortex core motion is described by the Thiele equation to very high precision. At finite temperature, the second order Heun algorithm is applied to the Langevin dynamical equation with thermal noise and damping. A spontaneous gyrotropic motion takes place without the application of an external magnetic field, driven only by thermal fluctuations. The statistics of the vortex radial position and rotational velocity are described with Boltzmann distributions determined by $k_F$ and by a vortex gyrotropic mass $m_G=G^2/k_F$, respectively, where $G$ is the vortex gyrovector.Comment: 18 pages, 17 figure

Electromagnetic modes in dielectric equilateral triangle resonators

Resonant electromagnetic modes are analyzed inside a dielectric cavity of equilateral triangular cross section and refractive index n, surrounded by a uniform medium of refractive index n'. The field confinement is determined only under the requirements needed to maintain total internal reflection of the internal electromagnetic fields, matched to exponentially decaying evanescent waves outside the cavity. Two-dimensional electromagnetics is considered, with no dependence on the coordinate perpendicular to the cross section; hence, independent transverse electric (TE) and transverse magnetic (TM) polarizations are described separately. A linear combination of six plane waves is sufficient within the cavity, whose wavevectors are related by 120-degree rotations and whose phases are related by Fresnel reflection coefficients. Generally, the mode spectrum becomes sparse and the minimum mode frequency increases rapidly as the index ratio N=n/n' approaches 2. For specified quantum numbers and N, the TM modes are lower in frequency than the TE modes. Assuming the evanescent boundary waves escape at the triangle vertices, TE modes generally are found to have greater confinement of the fields inside the cavity and much higher quality factors than TM modes.Comment: 16 pages, 17 figures (color version available at http://www.phys.ksu.edu/~wysin/publist.htm

Geometrical pinning of magnetic vortices induced by a deficit angle on a surface: anisotropic spins on a conic space background

We study magnetic vortex-like excitations lying on a conic space background. Two types of them are obtained. Their energies appear to be linearly dependent on the conical aperture parameter, besides of being logarithmically divergent with the sample size. In addition, we realize a geometrical-like pinning of the vortex, say, it is energetically favorable for it to nucleate around the conical apex. We also study the problem of two vortices on the cone and obtain an interesting effect on such a geometry: excitations of the same charge, then repealing each other, may nucleate around the apex for suitable cone apertures. We also pay attention to the problem of the vortex pair and how its dissociation temperature depends upon conical geometry.Comment: 13 pages, 06 figures, Latex. Version accepted for PHYSICS LETTERS

Statistics of Gyrotropic Vortex Dynamics in Submicron Magnetic Disks

Topological vortex excitations in thin magnetic nanodisks have attracted a lot of attention because of their dynamic stability and various charge-like properties, which make them suitable objects for data storage. They also have a natural gyrotropic orbital motion that can be described rather well by an approximate Thiele gyrotropic equation for the magnetization dynamics. The gyrotropic oscillation makes them available as a basis for natural oscillators at close to gigahertz frequencies. This gyrotropic motion is excited naturally even by thermal fluctuations. In addition, the gyrotropic oscillation frequency can be affected by external perturbations, which allows possibilities for the design of nanoscale detectors. The vortex moves in an effective potential, strongly determined by the shape anisotropy of the magnetic disk, which then determines the force appearing in the Thiele equation of motion. The motion of an individual vortex within a disk of circular or elliptical shape is considered theoretically, including stochastic thermal effects together with the deterministic gyrotropic effects. From simulations of the motion at different parameter values, a picture of the typical vortex position and velocity distribution within the disk is developed and compared with what is expected from the Thiele equation

Magnetic vortex dynamics in the non-circular potential of a thin elliptic ferromagnetic nanodisk with applied fields

Citation: Wysin, G. M. (2017). Magnetic vortex dynamics in the non-circular potential of a thin elliptic ferromagnetic nanodisk with applied fields. Aims Materials Science, 4(2), 421-438. doi:10.3934/matersci.2017.2.421Spontaneous vortex motion in thin ferromagnetic nanodisks of elliptical shape is dominated by a natural gyrotropic orbital part, whose resonance frequency omega(G) = (k) over bar /G depends on a force constant and gyrovector charge, both of which change with the disk size and shape and applied in-plane or out-of-plane fields. The system is analyzed via a dynamic Thiele equation and also using numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equations for thin systems, including temperature via stochastic fields in a Langevin equation for the spin dynamics. A vortex is found to move in an elliptical potential with two principal axis force constants k(x) and k(y), whose ratio determines the eccentricity of the vortex motion, and whose geometric mean (k) over bar = root k(x)k(y) determines the frequency. The force constants can be estimated from the energy of quasi-static vortex configurations or from an analysis of the gyrotropic orbits. k(x) and k(y) get modified either by an applied field perpendicular to the plane or by an in-plane applied field that changes the vortex equilibrium location. Notably, an out-of-plane field also changes the vortex gyrovector G, which directly influences omega(G). The vortex position and velocity distributions in thermal equilibrium are found to be Boltzmann distributions in appropriate coordinates, characterized by the force constants