André Drews

Time-resolved X-ray microscopy of spin-torque-induced magnetic vortex gyration

Time-resolved x-ray microscopy is used to image the influence of alternating high-density currents on the magnetization dynamics of ferromagnetic vortices. Spin-torque-induced vortex gyration is observed in micrometer-sized permalloy squares. The phases of the gyration in structures with different chirality are compared to an analytical model and micromagnetic simulations, considering both alternating spin-polarized currents and the currents Oersted field. In our case the driving force due to spin-transfer torque is about 70% of the total excitation while the remainder originates from the currents Oersted field. This finding has implications to magnetic storage devices using spin-torque driven magnetization switching and domain-wall motion.

Harmonic oscillator model for current-and field-driven magnetic vortices

Institut fu¨r Angewandte Physik und Zentrum fu¨r Mikrostrukturforschung,Universita¨t Hamburg, Jungiusstr. 11, 20355 Hamburg, Germany(Dated: February 2, 2008)In experiments the distinction between spin-torque and Oersted-field driven magnetization dynamics is stillan open problem. Here, the gyroscopic motion of current- andfield-driven magnetic vortices in small thin-film elements is investigated by analytical calculations an d by numerical simulations. It is found that for smallharmonic excitations the vortex core performs an elliptical rotation around its equilibrium position. The globalphase of the rotation and the ratio between the semi-axes aredetermined by the frequency and the amplitude ofthe Oersted field and the spin torque.

Numerical methods for the stray-field calculation: A comparison of recently developed algorithms

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor-grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can be subdivided into integral methods (fast Fourier transform methods, tensor-grid method) which solve the stray field directly and in differential equation methods (finite-element method) which compute the stray field as the solution of a partial differential equation. It turns out that for cuboid structures the integral methods, which work on cuboid grids (fast Fourier transform methods and tensor-grid methods), outperform the finite-element method in terms of the ratio of computational effort to accuracy. Among these three methods the tensor-grid method is the fastest for a given spatial discretization. However, the use of the tensor-grid method in the context of full micromagnetic codes is not well investigated yet. The finite-element method performs best for computations on curved structures.

Current-and field-driven magnetic antivortices for nonvolatile data storage

We demonstrate by micromagnetic simulations that magnetic antivortices are potential candidates for fast nonvolatile data-storage elements. These storage elements are excited simultaneously by alternating spin-polarized currents and their accompanying Oersted fields. Depending on the antivortex-core polarization p and the orientation of the in-plane magnetization c around the core, the superposition of current and field leads to either a suppression of gyration (logical “zero”) or an increased gyration amplitude (logical “one”). Above an excitation threshold the gyration culminates in the switching of the antivortex core. The switching can be seen as a cp-dependent writing of binary data, allowing to bring the antivortex into a distinct state. Furthermore a read-out scheme using an inductive loop situated on top of the element is investigated.

Current- and field-driven magnetic antivortices

Antivortices in ferromagnetic thin-film elements are in-plane magnetization configurations with a core pointing perpendicular to the plane. By using micromagnetic simulations, we find that magnetic antivortices gyrate on elliptical orbits similar to magnetic vortices when they are excited by alternating magnetic fields or by spin-polarized currents. The phase between high-frequency excitation and antivortex gyration is investigated. In case of excitation by spin-polarized currents the phase is determined by the polarization of the antivortex, while for excitation by magnetic fields the phase depends on the polarization as well as on the in-plane magnetization. Simultaneous excitation by a current and a magnetic field can lead to a maximum enhancement or to an entire suppression of the amplitude of the core gyration, depending on the angle between excitation and in-plane magnetization. This variation of the amplitude can be used to experimentally distinguish between spin-torque and Oersted-field driven motion of an antivortex core.

A Fast Finite-Difference Method for Micromagnetics Using the Magnetic Scalar Potential

We propose a method for the stray-field computation of ferromagnetic microstructures via the magnetic scalar potential. The scalar potential is computed using the convolution theorem and the fast Fourier transform. For the discrete convolution an analytical expression for the scalar potential of a uniformly magnetized cuboid is presented. A performance gain of up to 55% compared to common simulation codes is achieved and the memory consumption is reduced by 30%. Since the stray-field computation is the most time consuming part of micromagnetic simulations, this performance gain strongly influences the overall performance. The low memory consumption allows simulations with a high number of simulation cells. This enables simulations of large systems like arrays of coupled magnetic vortices or simulations with high spatial resolution. In conjunction with modern hardware, simulations of microstructures with atomic resolution become feasible.

Vortices and antivortices as harmonic oscillators

It is shown that the current- and field-induced gyration of magnetic vortices and antivortices follows the analytical model of a two-dimensional harmonic oscillator. Quantities of the harmonic oscillator, i.e., resonance frequency, damping constant, gyration amplitude, and phase, can be linked to material parameters and sample dimensions. This description is useful for the investigation of vortex-switching and vortex-antivortex annihilation processes.

Controlled pinning and depinning of domain walls in nanowires with perpendicular magnetic anisotropy

We investigate switching and field-driven domain wall motion in nanowires with perpendicular magnetic anisotropy comprising local modifications of the material parameters. Intentional nucleation and pinning sites with various geometries inside the nanowires are realized via a local reduction of the anisotropy constant. Micromagnetic simulations and analytical calculations are employed to determine the switching fields and to characterize the pinning potentials and the depinning fields. Nucleation sites in the simulations cause a significant reduction of the switching field and are in excellent agreement with analytical calculations. Pinning potentials and depinning fields caused by the pinning sites strongly depend on their shapes and are well explained by analytical calculations.

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau–Lifshitz–Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Direct imaging of phase relation in a pair of coupled vortex oscillators

We study the magnetization dynamics in a stray-field coupled pair of ferromagnetic squares in the vortex state. Micromagnetic simulations give an idea of the mediating stray field during vortex gyration. The frequency-dependent phase relation between the vortices in the spatially separated squares is studied using time-resolved scanning transmission x-ray microscopy while one element is harmonically excited via an alternating magnetic field. It is shown that the normal modes of coupled vortex-core motion can be understood as an attractive (low-frequency) and a repulsive (high-frequency) mode of the effective magnetic moments of the microstructures.