Using a stereographical projection to the plane we construct an O(N log(N)) algorithm to approximate scattered data in N points by orthogonal, compactly supported wavelets on the surface of a 2-sphere or a local subset of it. In fact, the sphere is not treated all at once, but is split into subdomains whose results are combined afterwards. After choosing the center of the area of interest the scattered data points are mapped from the sphere to the tangential plane through that point. By combining a k-nearest neighbor search algorithm and the two dimensional fast wavelet transform a fast approximation of the data is computed and mapped back to the sphere. The algorithm is tested with nearly 1 million data points and yields an approximation with 0.35% relative errors in roughly 2 minutes on a standard computer using our MATLAB implementation. The method is very flexible and allows the application of the full range of two dimensional wavelets.
The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space- and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. The experimental results are in good qualitative agreement with numerical simulations.
We report results of the switching properties of Stoner-like magnetic particles subject to short magnetic field pulses, obtained by numerical investigations. We discuss the switching properties as a function of the external field pulse strength and direction, the pulse length and the pulse shape. For field pulses long compared to the ferromagnetic resonance precession time the switching behavior is governed by the magnetic damping term, whereas in the limit of short field pulses the switching properties are dominated by the details of the precession of the magnetic moment. In the latter case, by choosing the right field pulse parameters, the magnetic damping term is of minor importance and ultrafast switching can be achieved. Switching can be obtained in an enlarged angular range of the direction of the applied field compared to the case of long pulses.
For the next generation of high data rate magnetic recording above 1 Gbit/s, a better understanding of the switching processes for both recording heads and media will be required. In order to maximize the switch-ing speed for such devices, the magnetization precession after the magnetic field pulse termination needs to be suppressed to a maximum degree. It is demonstrated experimentally for ferrite films that the appropriate adjustment of the field pulse parameters and/or the static applied field may lead to a full suppression of the magnetization precession immediately upon termination of the field pulse. The suppression is explained by taking into account the actual direction of the magnetization with respect to the static field direction at the pulse termination.
The first observation of self-focusing of dipolar spin waves in garnet film media is reported. In particular, we show that the quasi-stationary diffraction of a finite-aperture spin wave beam in a focusing medium leads to the concentration of the wave power in one focal point rather than along a certain line (channel). The obtained results demonstrate the wide applicability of non-linear spin wave media to study non-linear wave phenomena using an advanced combined microwave-Brillouin light scattering technique for a two-dimensional mapping of the spin wave amplitudes.
A new advanced space- and time-resolved Brillouin light scattering (BLS) technique is used to study diffraction of two-dimensional beams and pulses of dipolar spin waves excited by strip-line antennas in tangentially magnetized garnet films. The new technique is an effective tool for investigations of two-dimensional spin wave propagation with high spatial and temporal resolution. Linear effects, such as the unidirectional exci-tation of magnetostatic surface waves and the propagation of backward volume magnetostatic waves (BVMSW) in two preferential directions due to the non-collinearity of their phase and group velocities are investigated in detail. In the nonlinear regime stationary and non-stationary self-focusing effects are studied. It is shown, that non-linear diffraction of a stationary BVMSW beam, having a finite transverse aperture, leads to self-focusing of the beam at one spatial point. Diffraction of a finite-duration (non-stationary) BVMSW pulse leads to space-time self-focusing and formation of a strongly localized two-dimensional wave packet (spin wave bullet). Numerical modeling of the diffraction process by using a variational approach and direct numerical integration of the two-dimensional non-linear Schrödinger equation provides a good qualitative description of the observed phenomena.
A new advanced space- and time-resolved Brillouin light scattering technique is used to study diffraction of two-dimensional beams and pulses of dipolar spin waves excited by strip-line antennas in tangentially magnetized garnet films. The technique is an effective tool for investigations of two-dimensional spin wave propagation with high spatial and temporal resolution. Nonlinear effects such as stationary and nonstationary self-focusing are investigated in detail. It is shown, that nonlinear diffraction of a stationary backward volume magnetostatic wave (BVMSW) beam, having a finite transverse aperture, leads to selffocusing of the beam at one spatial point. Diffraction of a finite-duration (non-stationary) BVMSW pulse leads to space-time self-focusing and formation of a strongly localized two-dimensional wave packet (spin wave bullet).
Absract: We report on measurements of the two-dimensional intensity distribtion of linear and non-linear spin wave excitations in a LuBiFeO film. The spin wave intensity was detected with a high-resolution Brillouinlight scatteringspectroscopy setup. The observed snake-like structure of the spin wave intensity distribution is understood as a mode beating between modes with different lateral spin wave intensity distributions. The theoretical treatment of the linear regime is performed analytically, whereas the propagation of non-linear spin waves is simulated by a numerical solution of a non-linear Schrödinger equation with suitable boundary conditions.