Monitoring magnetic nanoparticle clustering and immobilization with thermal noise magnetometry using optically pumped magnetometers.

Thermal noise magnetometry (TNM) is a recently developed magnetic characterization technique where thermally induced fluctuations in magnetization are measured to gain insight into nanomagnetic structures like magnetic nanoparticles (MNPs). Due to the stochastic nature of the method, its signal amplitude scales with the square of the volume of the individual fluctuators, which makes the method therefore extra attractive to study MNP clustering and aggregation processes. Until now, TNM signals have exclusively been detected by using a superconducting quantum interference device (SQUID) sensor. In contrast, we present here a tabletop setup using optically pumped magnetometers (OPMs) in a compact magnetic shield, as a flexible alternative. The agreement between results obtained with both measurement systems is shown for different commercially available MNP samples. We argue that the OPM setup with low complexity complements the SQUID setup with high sensitivity and bandwidth. Furthermore, the OPM tabletop setup is well suited to monitor aggregation processes because of its excellent sensitivity in lower frequencies. As a proof of concept, we show the changes in the noise spectrum for three different MNP immobilization and clustering processes. From our results, we conclude that the tabletop setup offers a flexible and widely adoptable measurement unit to monitor the immobilization, aggregation, and clustering of MNPs for different applications, including interactions of the particles with biological systems and the long-term stability of magnetic samples.

Finite difference magnetoelastic simulator.

We describe an extension of the micromagnetic finite difference simulation software MuMax3 to solve elasto-magneto-dynamical problems. The new module allows for numerical simulations of magnetization and displacement dynamics in magnetostrictive materials and structures, including both direct and inverse magnetostriction. The theoretical background is introduced, and the implementation of the extension is discussed. The magnetoelastic extension of MuMax3 is freely available under the GNU General Public License v3.

Creep turns linear in narrow ferromagnetic nanostrips.

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.

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 ß are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (ß/α>1) in magnetic vortex cores or Skyrmions.

Vinamax: a macrospin simulation tool for magnetic nanoparticles.

We present Vinamax, a simulation tool for nanoparticles that aims at simulating magnetization dynamics on very large timescales. To this end, each individual nanoparticle is approximated by a macrospin. Vinamax numerically solves the Landau-Lifshitz equation by adopting a dipole approximation method, while temperature effects can be taken into account with two stochastic methods. It describes the influence of demagnetizing and anisotropy fields on magnetic nanoparticles at finite temperatures in a space- and time-dependent externally applied field. Vinamax can be used in biomedical research where nanoparticle imaging techniques are under development, e.g., to validate other higher-level models and study their limitations.

Correlation between spin structure oscillations and domain wall velocities.

Magnetic sensing and logic devices based on the motion of magnetic domain walls rely on the precise and deterministic control of the position and the velocity of individual magnetic domain walls in curved nanowires. Varying domain wall velocities have been predicted to result from intrinsic effects such as oscillating domain wall spin structure transformations and extrinsic pinning due to imperfections. Here we use direct dynamic imaging of the nanoscale spin structure that allows us for the first time to directly check these predictions. We find a new regime of oscillating domain wall motion even below the Walker breakdown correlated with periodic spin structure changes. We show that the extrinsic pinning from imperfections in the nanowire only affects slow domain walls and we identify the magnetostatic energy, which scales with the domain wall velocity, as the energy reservoir for the domain wall to overcome the local pinning potential landscape.

Coupled vortex oscillations in spatially separated permalloy squares.

We experimentally study the magnetization dynamics of pairs of micron-sized permalloy squares coupled via their stray fields. The trajectories of the vortex cores in the Landau-domain patterns of the squares are mapped in real space using time-resolved scanning transmission x-ray microscopy. After excitation of one of the vortex cores with a short magnetic-field pulse, the system behaves like coupled harmonic oscillators. The coupling strength depends on the separation between the squares and the configuration of the vortex-core polarizations. Considering the excitation via a rotating in-plane magnetic field, it can be understood that only a weak response of the second vortex core is observed for equal core polarizations.

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.

Magnetic antivortex-core reversal by circular-rotational spin currents.

Topological singularities occur as antivortices in ferromagnetic thin-film microstructures. Antivortices behave as two-dimensional oscillators with a gyrotropic eigenmode which can be excited resonantly by spin currents and magnetic fields. We show that the two excitation types couple in an opposing sense of rotation in the case of resonant antivortex excitation with circular-rotational currents. If the sense of rotation of the current coincides with the intrinsic sense of gyration of the antivortex, the coupling to the Oersted fields is suppressed and only the spin-torque contribution locks into the gyrotropic eigenmode. We report on the experimental observation of purely spin-torque induced antivortex-core reversal. The dynamic response of an isolated antivortex is imaged by time-resolved scanning transmission x-ray microscopy on its genuine time and length scale.

Vortex core switching by coherent excitation with single in-plane magnetic field pulses.

The response of magnetic vortex cores to subnanosecond in-plane magnetic field pulses was studied by time-resolved x-ray microscopy. Vortex core reversal was observed and the switching events were located in space and time. This revealed a mechanism of coherent excitation by the leading and trailing edges of the pulse, lowering the field amplitude required for switching. The mechanism was confirmed by micromagnetic simulations and can be understood in terms of gyration around the vortex equilibrium positions, displaced by the applied field.

Polarization selective magnetic vortex dynamics and core reversal in rotating magnetic fields.

We report on the observation of magnetic vortex dynamics in response to rotating magnetic fields in submicron platelets. Unlike linear fields or spin polarized currents, which excite both vortex core polarization states, an in-plane rotating field can selectively excite one of the polarization states. We demonstrate by direct imaging with time-resolved scanning x-ray microscopy that the rotating field only excites the gyrotropic mode if the rotation sense of the field coincides with the vortex gyration sense and that such a field can selectively reverse the vortex polarization.

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 current's 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 current's Oersted field. This finding has implications to magnetic storage devices using spin-torque driven magnetization switching and domain-wall motion.