Jonathan Leliaert

The design and verification of MuMax3

We report on the design, verification and performance of MUMAX3, an open-source GPU-accelerated micromagnetic simulation program. This software solves the time- and space dependent magnetization evolution in nano- to micro scale magnets using a finite-difference discretization. Its high performance and low memory requirements allow for large-scale simulations to be performed in limited time and on inexpensive hardware. We verified each part of the software by comparing results to analytical values where available and to micromagnetic standard problems. MUMAX3 also offers specific extensions like MFM image generation, moving simulation window, edge charge removal and material grains.

Influence of material defects on current-driven vortex domain wall mobility

Many future concepts for spintronic devices are based on the current-driven motion of magnetic domain walls through nanowires. Consequently a thorough understanding of the domain wall mobility is required. However, the magnitude of the nonadiabatic component of the spin-transfer torque driving the domain wall is still debated today as various experimental methods give rise to a large range of values for the degree of nonadiabaticity. Strikingly, experiments based on vortex domain wall motion in magnetic nanowires consistently result in lower values compared to other methods. Based on the micromagnetic simulations presented in this contribution we can attribute this discrepancy to the influence of distributed disorder which vastly affects the vortex domain wall mobility, but is most often not taken into account in the models adopted to extract the degree of nonadiabaticity.

Regarding the Néel relaxation time constant in magnetorelaxometry

Magnetorelaxometry (MRX) is a sensitive measurement technique frequently employed in biomedical applications for imaging magnetic nanoparticles (MNP). In this article, we employ a first principles model to investigate the effects of different iron oxide MNP sample properties on the Neel relaxation time constant τN in magnetorelaxometry. Using this model, we determined that dipolar interactions start to have an impact on the MRX signal from Fe concentrations of 100u2009mmol/l and result in a smaller τN. Additionally, the micromagnetic damping constant, closely related to τN, was found to be between 0.0005 and 0.002 by comparison to an MRX measurement of iron oxide particles. This is significantly lower compared to the bulk value of 0.07 for this material.

Current-driven domain wall mobility in polycrystalline Permalloy nanowires: A numerical study

A complete understanding of domain wall motion in magnetic nanowires is required to enable future nanowire based spintronics devices to work reliably. The production process dictates that the samples are polycrystalline. In this contribution, we present a method to investigate the effects of material grains on domain wall motion using the GPU-based micromagnetic software package MuMax3. We use this method to study current-driven vortex domain wall motion in polycrystalline Permalloy nanowires and find that the influence of material grains is fourfold: an extrinsic pinning at low current densities, an increasing effective damping with disorder strength, shifts in the Walker breakdown current density, and the possibility of the vortex core to switch polarity at grain boundaries.

A numerical approach to incorporate intrinsic material defects in micromagnetic simulations

Spintronics devices like racetrack memory rely on the controlled movement of domain walls in magnetic nanowires. The effects of distributed disorder on this movement have not yet been studied extensively. Defects give rise to a pinning potential that can be characterized in terms of a depth and an interaction range. We investigate how the effects of defects can be realistically introduced in micromagnetic simulations by comparing the properties of the pinning potential to experimental results in the literature. We show that the full 3-dimensional simulations can be replaced by equivalent 2-dimensional ones and propose two approaches to include defects.

Dynamical Magnetic Response of Iron Oxide Nanoparticles Inside Live Cells

Magnetic nanoparticles exposed to alternating magnetic fields have shown a great potential acting as magnetic hyperthermia mediators for cancer treatment. However, a dramatic and unexplained reduction of the nanoparticle magnetic heating efficiency has been evidenced when nanoparticles are located inside cells or tissues. Recent studies suggest the enhancement of nanoparticle clustering and/or immobilization after interaction with cells as possible causes, although a quantitative description of the influence of biological matrices on the magnetic response of magnetic nanoparticles under AC magnetic fields is still lacking. Here, we studied the effect of cell internalization on the dynamical magnetic response of iron oxide nanoparticles (IONPs). AC magnetometry and magnetic susceptibility measurements of two magnetic core sizes (11 and 21 nm) underscored differences in the dynamical magnetic response following cell uptake with effects more pronounced for larger sizes. Two methodologies have been employed for experimentally determining the magnetic heat losses of magnetic nanoparticles inside live cells without risking their viability as well as the suitability of magnetic nanostructures for in vitro hyperthermia studies. Our experimental results-supported by theoretical calculations-reveal that the enhancement of intracellular IONP clustering mainly drives the cell internalization effects rather than intracellular IONP immobilization. Understanding the effects related to the nanoparticle transit into live cells on their magnetic response will allow the design of nanostructures containing magnetic nanoparticles whose dynamical magnetic response will remain invariable in any biological environments, allowing sustained and predictable in vivo heating efficiency.

Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry

PURPOSEnThe performance of an increasing number of biomedical applications is dependent on the accurate knowledge of the spatial magnetic nanoparticle (MNP) distribution in the body. Magnetorelaxometry (MRX) imaging is a promising and noninvasive technique for the reconstruction of this distribution. To date, no accurate and quantitative measure is available to compare and optimize different MRX imaging models and setups independent of the MNP distribution. In this paper, the authors employ statistical parameters to develop quantitative MRX imaging models. Using these models, a straightforward optimization of setups and models is possible resulting in improved MNP reconstructions.nnnMETHODSnA MRX imaging setup is considered with different coil configurations, each corresponding to a MRX imaging model. The models can be represented by a sensitivity matrix. These are compared by employing the matrices as inputs to statistical parameters such as conditional entropy and mutual information (MI). These parameters determine the best model to reconstruct the MNP amount for each volume-element (voxel) in the sample. The matrix is transformed by multiplying the columns with different weightings depending on the performance of the MRX imaging model with respect to the other models. This transformed matrix is compared to the original sensitivity matrix without weightings.nnnRESULTSnCompared to the original sensitivity matrix, an increased numerical stability and improved noise robustness for the transformed sensitivity matrix are observed. The reconstruction of the MNP shows improvements: a correlation to the actual MNP distribution of 99.2%, whereas the original matrix only had 82.5%. By selecting the MRX models with the smallest MI, the authors are able to reduce the measurement time by 65% and still obtain an improved imaging accuracy and noise robustness. The statistical parameters allow a direct measure of the relative information content within the setup such that the optimal voxel size for the MRX setup is determined to be between 5 and 15 mm, while other sizes show a significant change in the statistical parameters.nnnCONCLUSIONSnThe use of statistical parameters in MRX imaging models results in quantitative models which can optimize MRX setups in a very fast and elegant way such that improved MNP imaging can be realized. Finally, the presented measure allows to quantitatively and accurately compare different MRX models and setups independent of the MNP distribution.

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 underxa0development, e.g., to validate other higher-level models and study their limitations.

Thermal effects on transverse domain wall dynamics in magnetic nanowires

Magnetic domain walls are proposed as data carriers in future spintronic devices, whose reliability depends on a complete understanding of the domain wall motion. Applications based on an accurate positioning of domain walls are inevitably influenced by thermal fluctuations. In this letter, we present a micromagnetic study of the thermal effects on this motion. As spin-polarized currents are the most used driving mechanism for domain walls, we have included this in our analysis. Our results show that at finite temperatures, the domain wall velocity has a drift and diffusion component, which are in excellent agreement with the theoretical values obtained from a generalized 1D model. The drift and diffusion component are independent of each other in perfect nanowires, and the mean square displacement scales linearly with time and temperature.

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.