We report on reversible electric-field-driven magnetic domain wall motion in a Cu/Ni multilayer on a ferroelectric BaTiO_3 substrate. In our heterostructure, strain-coupling to ferroelastic domains with in-plane and perpendicular polarization in the BaTiO_3 substrate causes the formation of domains with perpendicular and in-plane magnetic anisotropy, respectively, in the Cu/Ni multilayer. Walls that separate magnetic domains are elastically pinned onto ferroelectric domain walls. Using magneto-optical Kerr effect microscopy, we demonstrate that out-of-plane electric field pulses across the BaTiO_3 substrate move the magnetic and ferroelectric domain walls in unison. Our experiments indicate an exponential increase of domain wall velocity with electric field strength and opposite domain wall motion for positive and negative field pulses. Magnetic fields do not affect the velocity of magnetic domain walls, but independently tailor their internal spin structure, causing a change in domain wall dynamics at high velocities.

Lagrangian-based collective coordinate models for magnetic domain wall (DW) motion rely on an ansatz for the DW profile and a Lagrangian approach to describe the DW motion in terms of a set of time-dependent collective coordinates: the DW position, the DW magnetization angle, the DW width and the DW tilting angle. Another approach was recently used to derive similar equations of motion by averaging the Landau-Lifshitz-Gilbert equation without any ansatz, and identifying the relevant collective coordinates afterwards. In this paper, we use an updated version of the semi-analytical equations to compare the Lagrangian-based collective coordinate models with micromagnetic simulations for field-and STT-driven (spin-transfer torque-driven) DW motion in Pt/CoFe/MgO and Pt/Co/AlOx nanostrips. Through this comparison, we assess the accuracy of the different models, and provide insight into the deviations of the models from simulations. It is found that the lack of terms related to DW asymmetry in the Lagrangian-based collective coordinate models significantly contributes to the discrepancy between the predictions of the most accurate Lagrangian-based model and the micromagnetic simulations in the field-driven case. This is in contrast to the STT-driven case where the DW remains symmetric. (C) 2017 Elsevier B.V. All rights reserved.

A magnetic logic concept based on magnetic switching in three stripe domains separated by pinned magnetic domain walls is proposed. The relation between the inputs and the output of the logic operator is determined by the energetics of the domain walls, which can be switched between two distinctive states by an external magnetic field. Together with magnetic read-out along two orthogonal directions, non-volatile AND, OR, NAND, and NOR gates can be created. The logic concept is experimentally demonstrated using CoFeB films on BaTiO3 substrates, and micromagnetic simulations are used to analyze the energetics of the system.

Miniaturization of magnonic devices for wave-like computing requires emission of short-wavelength spin waves, a key feature that cannot be achieved with microwave antennas. In this paper, we propose a tunable source of short-wavelength spin waves based on highly localized and strongly pinned magnetic domain walls in ferroelectric-ferromagnetic bilayers. When driven into oscillation by a microwave spin-polarized current, the magnetic domain walls emit spin waves with the same frequency as the excitation current. The amplitude of the emitted spin waves and the range of attainable excitation frequencies depend on the availability of domain wall resonance modes. In this respect, pinned domain walls in magnetic nanowires are particularly attractive. In this geometry, spin wave confinement perpendicular to the nanowire axis produces a multitude of domain wall resonances enabling efficient spin wave emission at frequencies up to 100 GHz and wavelengths down to 20 nm. At high frequency, the emission of spin waves in magnetic nanowires becomes monochromatic. Moreover, pinning of magnetic domain wall oscillators onto the same ferroelectric domain boundary in parallel nanowires guarantees good coherency between spin wave sources, which opens perspectives towards the realization of Mach-Zehnder type logic devices and sensors.

Fast domain wall (DW) propagation through perpendicularly magnetized nanostrips with a Dzyaloshinskii-Moriya interaction (DMI) offers promising opportunities for the development of magnetic memory and logic devices. However, as the DW speed increases, the DW magnetization is also progressively affected which ultimately leads to an unstable DW and a drop in the velocity, i.e. the Walker breakdown. In this paper, we introduce a semi-analytical approach to describe and quantify changes to the internal degrees of freedom of the DW. By spatially averaging the Landau-Lifshitz-Gilbert equation, we derive equations of motion and identify seven DW variables in addition to the DW position. This contrasts analytical models where such variables are introduced in an ansatz for the DW shape. We apply this to a field driven DW motion and we study the effect of DMI in detail. Our method helps characterize the opposing and reinforcing effects of the different interactions involved, contributing to our understanding of the Walker breakdown.

Various proposals for future magnetic memories, data processing devices, and sensors rely on a precise control of the magnetization ground state and magnetization reversal process in periodically patterned media. In finite dot arrays, such control is hampered by the magnetostatic interactions between the nanomagnets, leading to the non-uniform magnetization state distributions throughout the sample while reversing. In this paper, we evidence how during reversal typical geometric arrangements of dots in an identical magnetization state appear that originate in the dominance of either Global Configurational Anisotropy or Nearest-Neighbor Magnetostatic interactions, which depends on the fields at which the magnetization reversal sets in. Based on our findings, we propose design rules to obtain the uniform magnetization state distributions throughout the array, and also suggest future research directions to achieve non-uniform state distributions of interest, e.g., when aiming at guiding spin wave edge-modes through dot arrays. Our insights are based on the Magneto-Optical Kerr Effect and Magnetic Force Microscopy measurements as well as the extensive micromagnetic simulations.

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.

Strong coupling of magnetic domain walls onto straight ferroelastic boundaries of a ferroelectric layer enables full and reversible electric-field control of magnetic domain wall motion. In this paper, the dynamics of this new driving mechanism is analyzed using micromagnetic simulations. We show that transverse domain walls with a near-180 degrees spin structure are stabilized in magnetic nanowires and that electric fields can move these walls with high velocities. Above a critical velocity, which depends on material parameters, nanowire geometry and the direction of domain wall motion, the magnetic domain walls depin abruptly from the ferroelastic boundaries. Depinning evolves either smoothly or via the emission and annihilation of a vortex or antivortex core (Walker breakdown). In both cases, the magnetic domain wall slows down after depinning in an oscillatory fashion and eventually comes to a halt. The simulations provide design rules for hybrid ferromagnetic-ferroelectric domain-wall-based devices and indicate that material disorder and structural imperfections only influence Walker-breakdown-like depinning at high domain wall velocities.

We introduce a non-volatile digital logic and memory concept in which the binary data is stored in the transverse magnetic domain walls present in in-plane magnetized nanowires with sufficiently small cross sectional dimensions. We assign the digital bit to the two possible orientations of the transverse domain wall. Numerical proofs-of-concept are presented for a NOT-, AND- and OR-gate, a FAN-out as well as a reading and writing device. Contrary to the chirality based vortex domain wall logic gates introduced in Omari and Hayward (2014 Phys. Rev. Appl. 2 044001), the presented concepts remain applicable when miniaturized and are driven by electrical currents, making the technology compatible with the in-plane racetrack memory concept. The individual devices can be easily combined to logic networks working with clock speeds that scale linearly with decreasing design dimensions. This opens opportunities to an all-magnetic computing technology where the digital data is stored and processed under the same magnetic representation.

We investigate the frequency of thermally excited vortex oscillations in Co-Fe-B magnetic tunnel junction (MTJ) pillars in the presence of defects. Under a variable in-plane magnetic field, a characteristic behavior is observed: the frequency oscillates from a maximum at certain field values to a steep minimum, which tends towards zero frequency. These frequency variations are described qualitatively well by an analytical model based on the Thiele equation taking into account a single Gaussian pinning potential. It is thus possible to calculate the in-plane depinning field for certain pinning potential parameters. For steep potentials, the depinning is hysteretic and jumps between the pinned and unpinned regime occur due to the presence of an energy barrier. A sharp frequency minimum occurs at an applied field, where a large flat region in the energy landscape is present. From the experiments, the pinning potentials are estimated to be between −0.2eV and −0.4eV. We also perform micromagnetic simulations of the vortex oscillations in the presence of a distribution of pinning centers. The simulations confirm the validity of the Thiele-approach showing that the vortex remains sufficiently rigid.

Several future spintronic devices are based on domain wall propagation through magnetic nanowires. Next to experiments and simulations, theoretical models are an indispensable tool to understand the magnetic domain wall mobility. In this paper, we extract the collective coordinates and derive the equations of motion that describe the domain wall dynamics directly from averaging the underlying micromagnetic equations. This way, five collective coordinates naturally emerge in the equations of motion: the domain wall displacement, the magnetization tilting, the domain wall width, effective demagnetizing factors and the domain wall asymmetry. While not predictive by itself, the approach enables a direct macroscopic interpretation of micromagnetic simulations, largely enhancing the complementarity between theory and simulations. We apply the method to study the field and current driven domain wall dynamics in nanowires with high perpendicular anisotropy. We suggest the existence of an intrinsic depinning threshold for such domain wall dynamics, even when taking into account non-adiabatic contributions to the spin-transfer torques. Furthermore, we show that the domain wall asymmetry has a resonant behaviour at high excitation strengths.

Control of magnetic domain-wall motion by electric fields has recently attracted scientific attention because of its potential for magnetic logic and memory devices. Here, we report on a new driving mechanism that allows for magnetic domain-wall motion in an applied electric field without the concurrent use of a magnetic field or spin-polarized electric current. The mechanism is based on elastic coupling between magnetic and ferroelectric domain walls in multiferroic heterostructures. Pure electric-field-driven magnetic domain-wall motion is demonstrated for epitaxial Fe films on BaTiO3 with in-plane and out-of-plane polarized domains. In this system, magnetic domain-wall motion is fully reversible and the velocity of the walls varies exponentially as a function of out-of-plane electric-field strength.

We investigate magnetic domain wall (MDW) dynamics induced by applied electric fields in ferromagnetic-ferroelectric thin-film heterostructures. In contrast to conventional driving mechanisms where MDW motion is induced directly by magnetic fields or electric currents, MDW motion arises here as a result of strong pinning of MDWs onto ferroelectric domain walls (FDWs) via local strain coupling. By performing extensive micromagnetic simulations, we find several dynamical regimes, including instabilities such as spin wave emission and complex transformations of the MDW structure. In all cases, the time-averaged MDW velocity equals that of the FDW, indicating the absence of Walker breakdown.

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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.

SUMMARYIn a large variety of research areas, convolution products that relate a physical quantity in some observation points with their sources are encountered. When the sources and the observation points coincide, the numerical evaluation of the physical quantity typically leads to order N2 numerical problems. Here, fast Fourier transforms are widely used to reduce the computations to order Nlog N complexity. When adopting Fourier transforms (FFT) for finite physical problems, zero padding is required. Hence, in 2D and 3D problems, an optimization of the evaluation of the convolution product includes a non‐execution of Fourier transforms on arrays containing only zeros in the forward 2D or 3D FFT scheme and their corresponding arrays in the inverse 2D or 3D FFT scheme. This paper describes the implementation of such an approach on graphical processing units (GPUs) and compares the time gains on GPU and on CPU. It is found that on CPU, the speedup corresponds with the theoretical limit, while in the GPU implementation, the memory bandwidth limits the speedup ratio. Copyright © 2013 John Wiley & Sons, Ltd.

We propose an alternative micromagnetic approach to determine the spin wave dispersion relations in magnonic structures. Characteristic of the method is that a limited area of the system is continuously excited with a spatially uniform oscillating field, tuned at a given frequency. After a transitory time, the regime magnetization dynamics is collected and a spatial Fourier analysis on it determines the frequency vs wave vector relation. Combining several simulations in any predetermined range of frequencies, at any resolution, we investigate the dispersion relations for different kinds of magnonic crystals: a dot array, an antidot array and a bicomponent film. Especially compared to traditional pulse-excitation methods, this technique has many advantages. First, the excitation power is concentrated at a single frequency, allowing the corresponding spin waves to propagate with very low attenuation, resulting in a higher k-space resolution. Second, the model allows to include very large wave vector components, necessary to describe the high-frequency response of non-quantized spin waves in quasi-continuous systems. Finally, we address some possible experimental opportunities with respect to excitation/detection techniques over large distances and the observation of the odd/even symmetry of spin waves using Brillouin light scattering.

We investigate the magnetization reversal of a magnetic dot array by means of magneto-optical Kerr effect and magnetic force microscopy measurements as well as micromagnetic simulations. We find that the finite dimensions of the dot array introduce a global configurational anisotropy that promotes state transitions first in dots near the sample boundaries. From there, the reversal process expands towards the sample body by means of collective magnetization processes originating in the magnetostatic coupling between the dots. These processes are characterized by transition avalanches and the formation of magnetization chains. These findings are important in the development of applications that rely on a robust control of dot magnetization states in dot arrays.