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Magnetic vortex is topologically nontrivial and commonly found in ferromagnetic nanodisks. So far, three classes spin-wave eigenmodes, i.e., gyrotropic, azimuthal and radial modes, have been identified in ferromagnetic nanodisks. Here, using micromagnetic simulation and analytical calculation, we reveal twisted spin-wave modes in a thick permalloy (Ni0.8Fe0.2) nanodisk. The twisted spin-waves carry topological charges, which sign depends on the core polarity of the magnetic vortex in the nanodisk. By applying rotating magnetic fields at one end of the sample, we observe continuous generation of twisted spin-waves that have characteristic spiral phase front and carry topological charge l = 1, -1, 2 and -2. The dispersion relation of twisted spin-waves is derived analytically and the result is in good agreement with micromagnetic numerical calculations.

We are concerned about the averaging principle for the stochastic Burgers equation with slow-fast time scale. This slow-fast system is driven by L\'{e}vy processes. Under some appropriate conditions, we show that the slow component of this system strongly converges to a limit, which is characterized by the solution of stochastic Burgers equation whose coefficients are averaged with respect to the stationary measure of the fast-varying jump-diffusion. To illustrate our theoretical result, we provide some numerical simulations., Comment: 16 pages, 2 figures, 21 references, the paper is submitted

Twisted spin waves attracted research attentions lately and the orbital angular momentum they carry may be utilized in communication and computing technologies. In this work, we manifest by micromagnetic simulations that twisted spin wave modes naturally exist in thick ferromagnetic disks. The twisted spin waves can be readily stimulated using rotating magnetic field when it is tuned to the eigenfrequency of corresponding modes. We analytically derive dispersion relation of the twisted spin waves and the results agree well with the numerical studies. Lastly, we demonstrate that the topological charge of twisted spin waves can be controlled by the exciting field.

We propose a new method to generate magnetic skyrmions through spin-wave focusing in chiral ferromagnets.A lens is constructed to focus spin waves by a curved interface between two ferromagnetic thin films with different perpendicular magnetic anisotropies. Based on the principle of identical magnonic path length, we derive the lens contour that can be either elliptical or hyperbolical depending on the magnon refractive index. Micromagnetic simulations are performed to verify the theoretical design. It is found that under proper condition magnetic skyrmions emerge near the focus point of the lens where the spin-wave intensity has been significantly enhanced. A close investigation shows that a magnetic droplet first forms and then converts to the skyrmion accompanying with a change of topological charge. Phase diagram about the amplitude and duration-time of the exciting field for skyrmion generation is obtained. Our findings would be helpful for designing novel spintronic devices combining the advantages of skyrmionics and magnonics., Comment: 5 pages, 4 figures

In this work, we study a class of non-autonomous two-time-scale stochastic reaction-diffusion equations driven by Poisson random measures, in which the coefficients satisfy the polynomial growth condition and local Lipschitz condition. First, the existence and uniqueness of the mild solution are proved by constructing auxiliary equations and using the technique of stopping time. Then, consider that the time dependent of the coefficients, the averaged equation is redefined by studying the existence of time-dependent evolution family of measures associated with the frozen fast equation. Further, the slow component strongly converges to the solution of the corresponding averaged equation is verified by using the classical Khasminskii method., Comment: 32 pages. arXiv admin note: text overlap with arXiv:1904.10621

This paper investigates a non-autonomous slow-fast system, which is generalized by stochastic differential equations (SDEs) with locally Lipschitz coefficients, subjected to standard Brownian motion (Bm) and fractional Brownian motion (fBm) with Hurst parameter 1/2

We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system., Comment: 0

We theoretically investigate the radial-spin-wave induced magnetic vortex switching in the presence of Dzyaloshinskii-Moriya interaction (DMI). From micromagnetic simulations, we observe a circular-to-radial vortex phase transition by increasing the DMI strength. The radial spin-wave excitation spectrum for each magnetization configuration is analyzed, showing that the frequency of spin-wave mode with a given radial node number monotonically increases (decreases) with the DMI parameter of the radial (circular) vortex. Interestingly, we find that the DMI can significantly facilitate the polarity switching of the circular vortex driven by radial spin waves. Our work provides a new insight into the DMI effect on the vortex dynamics and is helpful for designing fast all-magnonic memory devices., Comment: 6 pages, 5 figures

In this paper, we develop the averaging principle for a class of two-time-scale stochastic reaction-diffusion equations driven by Wiener processes and Poisson random measures. We assume that all coefficients of the equation have polynomial growth, and the drift term of the equation is non-Lipschitz. Hence, the classical formulation of the averaging principle under the Lipschitz condition is no longer available. To prove the validity of the averaging principle, the existence and uniqueness of the mild solution are proved firstly. Then, the existence of time-dependent evolution family of measures associated with the fast equation is studied, by which the averaged coefficient is obtained. Finally, the validity of the averaging principle is verified., Comment: 23 pages. arXiv admin note: text overlap with arXiv:1807.08068

It is well known that azimuthal spin wave modes of magnetic vortex state in permalloy nanodisks have circular symmetry. Intuitively, magnetic materials having magnetocrystalline anisotropy is not compatible with the circular symmetry of the azimuthal modes. In this article, however, we report cubic azimuthal modes in heterogeneous nanodisks consisting of a permalloy core and a Fe shell. The fourfold symmetry of azimuthal modes is due to the exchange, and magneto-static, interactions between the permalloy core and the Fe shell. In comparison to results of circular azimuthal mode, the vortex switching occurs considerably faster under the excitation of cubic azimuthal mode. The gyration path of vortex core turns into square under the influence of induced cubic anisotropy in the Py region. We find out periodic oscillation of the vortex core size and the gyration speed as well. Our findings may offer a new route for spintronic applications using heterogeneous magnetic nanostructures., Comment: 10 pages, 4 figures