Matthias Kammerer

Magnetic vortex core reversal by excitation of spin waves

Micron-sized magnetic platelets in the flux-closed vortex state are characterized by an in-plane curling magnetization and a nanometer-sized perpendicularly magnetized vortex core. Having the simplest non-trivial configuration, these objects are of general interest to micromagnetics and may offer new routes for spintronics applications. Essential progress in the understanding of nonlinear vortex dynamics was achieved when low-field core toggling by excitation of the gyrotropic eigenmode at sub-GHz frequencies was established. At frequencies more than an order of magnitude higher vortex state structures possess spin wave eigenmodes arising from the magneto-static interaction. Here we demonstrate experimentally that the unidirectional vortex core reversal process also occurs when such azimuthal modes are excited. These results are confirmed by micromagnetic simulations, which clearly show the selection rules for this novel reversal mechanism. Our analysis reveals that for spin-wave excitation the concept of a critical velocity as the switching condition has to be modified.

Gyrokinetic turbulence simulations at high plasma beta

Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for β values up to and beyond the kinetic ballooning threshold. The β scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of β values just below the respective ideal limit. The magnetic transport scales like β2 and is well described by a Rechester–Rosenbluth-type ansatz.Electromagnetic gyrokinetic turbulence simulations employing Cyclone Base Case parameters are presented for β values up to and beyond the kinetic ballooning threshold. The β scaling of the turbulent transport is found to be linked to a complex interplay of linear and nonlinear effects. Linear investigation of the kinetic ballooning mode is performed in detail, while nonlinearly, it is found to dominate the turbulence only in a fairly narrow range of β values just below the respective ideal limit. The magnetic transport scales like β2 and is well described by a Rechester–Rosenbluth-type ansatz.

Exceptional points in linear gyrokinetics

When performing linear gyrokinetic simulations, it is found that various types of microinstabilities, which are usually considered as strictly separated, can actually be transformed into each other via continuous variations of the plasma parameters. This behavior can be explained in terms of so-called exceptional points, which have their origin in the non-Hermiticity of the linear gyrokinetic operator and also occur in many other branches of physics. As a consequence, in large regions of parameter space, the designation of unstable modes should be done very carefully or even be avoided altogether.

Fast eigenvalue calculations in a massively parallel plasma turbulence code

Magnetic fusion aims at providing CO2 free energy for the 21st century and well beyond. However, the success of the international fusion experiment ITER (currently under construction) will depend to a large degree on the value of the so-called energy confinement time. One of the most advanced tools describing the underlying physical processes is the highly scalable (up to at least 32,768 cores) plasma turbulence code GENE. GENE solves a set of nonlinear partial integro-differential equations in five-dimensional phase space by means of the method of lines, with a 4th order explicit Runge-Kutta scheme for time integration. To maximize its efficiency, the code computes the eigenspectrum of the linearized equation to determine the largest possible timestep which maintains the stability of the method. This requires the computation of the largest (in terms of its magnitude) eigenvalue of a complex, non-Hermitian matrix whose size may range from a few millions to even a billion. SLEPc, the Scalable Library for Eigenvalue Problem Computations, is used to effectively compute this part of the spectrum. Additionally, eigenvalue computations can provide new insight into the properties of plasma turbulence. The latter is driven by a number of different unstable modes, including dominant and subdominant ones, that can be determined employing SLEPc. This computation is more challenging from the numerical point of view, since these eigenvalues can be considered interior, and also because the linearized operator is available only in implicit form. We analyze the feasibility of different strategies for computing these modes, including matrix-free spectral transformation as well as harmonic projection methods.

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.

Enhanced Nonadiabaticity in Vortex Cores due to the Emergent Hall Effect

We present a combined theoretical and experimental study, investigating the origin of the enhanced nonadiabaticity of magnetic vortex cores. Scanning transmission x-ray microscopy is used to image the vortex core gyration dynamically to measure the nonadiabaticity with high precision, including a high confidence upper bound. We show theoretically, that the large nonadiabaticity parameter observed experimentally can be explained by the presence of local spin currents arising from a texture induced emergent Hall effect. This study demonstrates that the magnetic damping α and nonadiabaticity parameter β are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (β/α>1) in magnetic vortex cores or Skyrmions.

Low-amplitude magnetic vortex core reversal by non-linear interaction between azimuthal spin waves and the vortex gyromode

We show, by experiments and micromagnetic simulations in vortex structures, that an active “dual frequency” excitation of both the sub-GHz vortex gyromode and multi-GHz spin waves considerably changes the frequency response of spin wave mediated vortex core reversal. Besides additional minima in the switching threshold, a significant broadband reduction of the switching amplitudes is observed, which can be explained by non-linear interaction between the vortex gyromode and the spin waves. We conclude that the well known frequency spectra of azimuthal spin waves in vortex structures are altered substantially, when the vortex gyromode is actively excited simultaneously.

Direct imaging of current induced magnetic vortex gyration in an asymmetric potential well

Employing time-resolved x-ray microscopy, we investigate the dynamics of a pinned magnetic vortex domain wall in a magnetic nanowire. The gyrotropic motion of the vortex core is imaged in response to an exciting ac current. The elliptical vortex core trajectory at resonance reveals asymmetries in the local potential well that are correlated with the pinning geometry. Using the analytical model of a two-dimensional harmonic oscillator, we determine the resonance frequency of the vortex core gyration and, from the eccentricity of the vortex core trajectory at resonance, we can deduce the stiffness of the local potential well.

Delayed magnetic vortex core reversal

When switching the vortex core in a magnetic disc by a short excitation with an in-plane field, there is an initial global excitation of the magnetization due to a precession of the magnetization in the spatially homogeneous field. Then an energy transport from this global excitation towards the center of the disc takes place leading to a concentration of the energy close to the vortex core which suffices to switch the core. Because this transport requires time, there is a delay between the end of the excitation and the switching. This is demonstrated for switching by in-plane rotating GHz rf-bursts.

Micromagnetic Simulations on GPU, A Case Study: Vortex Core Switching by High-Frequency Magnetic Fields

Since magnetic vortex cores have two ground states, they are candidates for digital memory bits in future magnetic random access memory (MRAM) devices. Vortex core switching can be induced by exciting the gyrotropic eigenmode, e.g., by applying cyclic magnetic helds with typically a sub-gigahertz frequency. However, recent studies reveal that other modes exist that can be excited at higher frequencies, but still lead to switching with relatively small held amplitudes. Here, we perform a full scan of the frequency/amplitude parameter space to explore such excitation modes. The enormous amount of simulations can only be performed in an acceptable time span when the micromagnetic (CPU) simulations are drastically accelerated. To this aim, we developed MUMAX, a GPU-based software tool that speeds up micromagnetic simulations with about two orders of magnitude compared to standard CPU micromagnetic tools. By exploiting MUMAXs numerical power we were able to explore new switching opportunities at moderate held amplitudes in the frequency range between 5 and 12 GHz.