Unidirectional sub-100 ps magnetic vortex core reversal

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

Multiscale Model Approach for Magnetization Dynamics Simulations

Simulations of magnetization dynamics in a multiscale environment enable rapid evaluation of the Landau-Lifshitz-Gilbert equation in a mesoscopic sample with nanoscopic accuracy in areas where such accuracy is required. We have developed a multiscale magnetization dynamics simulation approach that can be applied to large systems with spin structures that vary locally on small length scales. To implement this, the conventional micromagnetic simulation framework has been expanded to include a multiscale solving routine. The software selectively simulates different regions of a ferromagnetic sample according to the spin structures located within in order to employ a suitable discretization and use either a micromagnetic or an atomistic model. To demonstrate the validity of the multiscale approach, we simulate the spin wave transmission across the regions simulated with the two different models and different discretizations. We find that the interface between the regions is fully transparent for spin waves with frequency lower than a certain threshold set by the coarse scale micromagnetic model with no noticeable attenuation due to the interface between the models. As a comparison to exact analytical theory, we show that in a system with Dzyaloshinskii-Moriya interaction leading to spin spiral, the simulated multiscale result is in good quantitative agreement with the analytical calculation

Multiscale and multimodel simulation of Bloch point dynamics

We present simulation results on the structure and dynamics of micromagnetic point singularities with atomistic resolution. This is achieved by embedding an atomistic computational region into a standard micromagnetic algorithm. Several length scales are bridged by means of an adaptive mesh refinement and a seamless coupling between the continuum theory and a Heisenberg formulation for the atomistic region. The code operates on graphical processing units and is able to detect and track the position of strongly inhomogeneous magnetic regions. This enables us to reliably simulate the dynamics of Bloch points, which means that a fundamental class of micromagnetic switching processes can be analyzed with unprecedented accuracy. We test the code by comparing it with established results and present its functionality with the example of a simulated field-driven Bloch point motion in a soft-magnetic cylinder

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetization tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii)