Domain Wall Dynamics Research Articles

Tuning planar transverse domain wall dynamics in bilayer nanostructures using transverse magnetic fields, Rashba, and spin-Hall effects

Abstract This work deals with the tunability of a planar transverse domain wall with an arbitrary azimuthal angle, achieved by applying a transverse magnetic field of tunable strength and fixed orientation. To be precise, we investigate the static and dynamic features of a planar transverse domain wall within a bilayer nanostructure consisting of a ferromagnetic layer and a non-magnetic heavy metal layer, employing the Landau-Lifshitz-Gilbert equation as our theoretical framework. The domain wall dynamics are analyzed through the collective coordinate method and regular perturbation asymptotic approach, accounting for the combined effects of axial and transverse magnetic fields, spin-polarized electric currents, Rashba effect, and spin-Hall effect. Our study comprehensively analyses the planar transverse domain wall profile, characterized by sharply defined boundaries between adjacent domains and a precise distribution of the transverse magnetic field. In addition, we detail the linear polar angle distribution within the domain wall region, the capability to freely tune the domain wall width, and the enhanced domain wall velocity in steady-state regime. The analytical results are further numerically illustrated, offering valuable insights into manipulating and controlling domain wall dynamics.

Stacking selected polarization switching and phase transition in vdW ferroelectric α-In2Se3 junction devices

The structure and dynamics of ferroelectric domain walls are essential for polarization switching in ferroelectrics, which remains relatively unexplored in two-dimensional ferroelectric α-In2Se3. Interlayer interactions engineering via selecting the stacking order in two-dimensional materials allows modulation of ferroelectric properties. Here, we report stacking-dependent ferroelectric domain walls in 2H and 3R stacked α-In2Se3, elucidating the resistance switching mechanism in ferroelectric semiconductor-metal junction devices. In 3R α-In2Se3, the in-plane movement of out-of-plane ferroelectric domain walls yield a large hysteresis window. Conversely, 2H α-In2Se3 devices favor in-plane domain walls and out-of-plane domain wall motion, producing a small hysteresis window. High electric fields induce a ferro-paraelectric phase transition of In2Se3, where 3R In2Se3 reaches the transition through intralayer atomic gliding, while 2H In2Se3 undergoes a complex process comprising intralayer bond dissociation and interlayer bond reconstruction. Our findings demonstrate tunable ferroelectric properties via stacking configurations, offering an expanded dimension for material engineering in ferroelectric devices.

Tuning domain wall dynamics in a notched ferromagnetic nanostrip with Rashba effect

This work delineates a comprehensive investigation of the static and kinetic depinning of a domain wall in a notched ferromagnetic nanostrip. More precisely, we consider a 180° Bloch-type domain wall and examine its behavior under the action of an applied magnetic field, spin-polarized electric current, and Rashba field. Moreover, we assume an artificial notch positioned at the edges of the nanostrip, serving as a pinning site for the wall. We characterize domain walls’ pinning and depinning dynamics in the steady-state regime by using the classical Schryer and Walker trial-function approach. The results demonstrate that the static depinning limits of external stimuli are more significant than the kinetic depinning. It is also observed that higher Rashba field strength increases the static depinning fields/currents while decreasing kinetic depinning ones. Furthermore, both static and kinetic depinning thresholds are elevated with higher damping, whereas an increase in the non-adiabatic spin-transfer parameter leads to a reduction. Finally, we present numerical illustrations of the analytical results, showing good qualitative agreement with the literature.

Magnetic domain walls interacting with dislocations in micromagnetic simulations

Defects, impurities, and embedded particles in ferromagnetic materials are long known to be responsible for the Barkhausen effect due to the jerky field-driven motion of domain walls and have more recently been shown to play a role also in domain wall dynamics in nanoscale ferromagnetic structures used in spintronics devices. Simulating the magnetic domain wall dynamics in the micromagnetic framework offers a straightforward route to study such systems and phenomena. However, the related work in the past suffers from material imperfections being introduced without proper physical foundation. Here, we implement dislocation stress fields in micromagnetic simulations through the induced anisotropy fields by inverse magnetostriction. The effects of individual dislocations on domain wall dynamics in thin films of different Fe surface lattice planes are characterized numerically. As a demonstration of the applicability of the implementation, we consider disorder fields due to randomly positioned dislocations with different densities, and study the avalanche-like transient approach towards the depinning transition of a domain wall driven by a slowly increasing external magnetic field.

Exploring Fast Domain Wall Motion and DMI Realization in Compensated Ferrimagnetic Nanowires

Abstract Recent advancements in spintronics have spurred interest in current-induced domain wall motion (CIDWM) as a promising avenue for next-generation memory technologies. While previous research has predominantly focused on thin ferromagnetic films, recent attention has shifted towards ferrimagnetic materials due to their potential for magnetization compensation and efficient domain wall (DW) motion. In this study, we investigated the dynamics of DWs in compensated ferrimagnetic Pt/GdxFe1-x nanowires through experimental characterization and analysis. Our results reveal fast DW motion around the magnetic compensation point, indicating the influence of spin-orbit torque induced by current flow. We systematically explore the Dzyaloshinskii-Moriya interaction (DMI) field across different compositions of GdFe, observing elevated DMI field values near the compensation compositions. Additionally, we examine the impact of wire width and pulse duration on DW velocity, demonstrating higher velocities in narrower wires and shorter pulse durations. In the 1 μm wire, a DW velocity of around 3200 m/s was achieved by applying a 3 ns short pulse current. Our findings elucidate the intricate interplay between film composition, magnetic properties, wire width, pulse duration, and DW dynamics, providing valuable insights for the design and optimization of ferrimagnetic materials for future magnetic memory technologies.

Irreducible cosmological backgrounds of a real scalar with a broken symmetry

We explore the irreducible cosmological implications of a singlet real scalar field. Our focus is on theories with an approximate and spontaneously broken Z2 symmetry where quasistable domain walls can form at early times. This seemingly simple framework bears a wealth of phenomenological implications that can be tackled by means of different cosmological and astrophysical probes. We elucidate the connection between domain wall dynamics and the production of dark matter and gravitational waves. In particular, we identify three main benchmark scenarios. The gravitational wave signal observed by pulsar timing arrays can be generated by the domain walls if the mass of the singlet is ms∼PeV. For lower masses, but with ms≳10 GeV, scalars produced in the annihilation of the domain walls can be dark matter with a distinctive feature in their power spectrum. Finally, the thermal bath provides an unavoidable source of unstable scalars via the freeze-in mechanism whose subsequent decays can be tested by their imprints on cosmological and terrestrial observables. Published by the American Physical Society 2024

MODVORTEx: computer vision-driven automation for magnetic domain wall velocity analysis

Abstract This paper presents Magneto Optic Domain Velocity Observation and Real-Time Extraction (MODVORTEx), a comprehensive software solution for automating domain wall (DW) velocity measurements in magnetic materials using magneto-optic Kerr effect microscopy. Building upon our previous work on bubble domain structures, we introduce a versatile graphical user interface (GUI) that accommodates arbitrary domain shapes and employs advanced computer vision techniques. The software provides different methods for DW detection and velocity calculation, catering to various domain structures of arbitrary shape. Our approach significantly reduces the time and effort required for data extraction, transforming a process that previously took days of manual work into a task completable within minutes. We provide the details of the algorithmic implementation which is organized into pre-processing, DW detection, displacement measurement, and velocity extraction. This tool is applicable to a wide range of scenarios, including bubble domain dynamics, Dzyaloshinskii–Moriya interaction studies in perpendicular magnetic anisotropy systems, current-driven DW motion in patterned strips etc. By providing both GUI and Application Programing Interface, our software offers flexibility for integration into existing measurement systems and adaptability for specific research needs. This automation promises to accelerate research in spintronics and magnetic materials, enabling more comprehensive and accurate studies of DW dynamics.

Multicore memristor from electrically readable nanoscopic racetracks.

The manipulation and detection of mobile domain walls in nanoscopic magnetic wires underlies the development of multibit memories. The studies of such domain walls have focused on macroscopic wires that allow for optical detection by using magneto-optic effects. In this study, we demonstrated the electrical tracking with a spatial resolution of better than 40 nm of multiple mobile domain walls in nanoscopic racetracks, using a set of anomalous Hall detectors integrated into the racetracks. Electrical time-series signals from the Hall detectors allow for the static and dynamic phase space visualization of the dynamics of a domain wall or multiple domain walls that can be described by a multicore memristor model. The domain wall dynamics and stochasticity can be controlled in racetracks even to deep submicron dimensions.

Low-field-driven large strain in lead zirconate titanium-based piezoceramics incorporating relaxor lead magnesium niobate for actuation

Studies on the piezoelectric materials capable of efficiently outputting high electrostrains at low electric fields are driven by the demand for precise actuation in a wide range of applications. Large electrostrains of piezoceramics in operation require high driving fields, which limits their practical application due to undesirable nonlinearities and high energy consumption. Herein, a strategy is developed to enhance the electrostrains of piezoceramics while maintaining low hysteresis by incorporating lead magnesium niobate relaxors into lead zirconate titanium at the morphotropic phase boundary. An ultrahigh inverse piezoelectric coefficient d33*\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{33}^{*}$$\\end{document} of 1380 pm/V with a reduced hysteresis of 11.5% is achieved under a low electric field of 1 kV/mm, outperforming the major lead-based piezoelectric materials. In situ synchrotron X-ray diffraction and domain wall dynamics characterization with sub-microsecond temporal resolution reveal that the outstanding performances originate from facilitated domain wall movement, which in turn is due to reduced lattice distortion and miniaturized domain structures. These findings not only address the pending challenges of effective actuation under reduced driving conditions but also lay the foundation for a more systematic approach to exploring the origin of large electrostrains.

Exploration of Rayleigh loop vis-to-vis high applied magnetic field hysteresis loops phenomena in barium hexaferrite-Copper ferrite ferrimagnetic composites

Recent research interest has surged in magnetic composite materials, driven by the increasing demand for permanent magnets, magnetic fluids, and magnetic sensors, in various technological applications. Among all these materials, the 1BaFe12O19 + (x) CuFe2O4 composites have developed as particularly promising in terms of its magnetic properties. However, despite its potential, detailed insights into the magnetic characteristics of this composite remain scarce in the existing literature. In this article, we address this gap by thoroughly investigating the magnetic properties of the 1BaFe12O19 + (x) CuFe2O4 composite across a range of compositions (x = 1 to 6). This present study focused on both low and high applied magnetic fields, examining the material’s behavior in Rayleigh region as well as under intense magnetic influences. At low magnetic fields, the M−H loop exhibits distinctive elliptical or lens shape. Notably, the susceptibility (χm) initially increases but then declines after reaching a critical threshold with increasing magnetic field strength. The analysis of different magnetic parameters, including maximum magnetization (Mm), remanent magnetization (Mr), coercive field (Hc), and the ratio of remanent to maximum magnetization (Mr/Mm), derived from the M−H loops across different applied magnetic fields have been reported here. According to present research, these magnetic parameters show a growing trendency with increasing applied magnetic field strength until they get close to saturation. Results are correlated with the magnetic domain wall dynamics.

Interplay between Point and Extended Defects and Their Effects on Jerky Domain-Wall Motion in Ferroelectric Thin Films

Defects have a significant influence on the polarization and electromechanical properties of ferroelectric materials. Statistically, they can be seen as random pinning centers acting on an elastic manifold, slowing domain-wall propagation and raising the energy required to switch polarization. Here we show that the “dressing” of defects can lead to unprecedented control of domain-wall dynamics. We engineer defects of two different dimensionalities in ferroelectric oxide thin films—point defects externally induced via He2+ bombardment, and extended quasi-one-dimensional a domains formed in response to internal strains. The a domains act as extended strong pinning sites (as expected) imposing highly localized directional constraints. Surprisingly, the induced point defects in the He2+ bombarded samples orient and align to impose further directional pinning, screening the effect of a domains. This defect interplay produces more uniform and predictable domain-wall dynamics. Such engineered interactions between defects are crucial for advancements in ferroelectric devices. Published by the American Physical Society 2024

Microwave magnetic excitations in U-type hexaferrite Sr4CoZnFe36O60 ceramics

Microwave (MW) transmission, absorption, and reflection loss spectra of the ferrimagnetic U-type hexaferrite Sr4CoZnFe36O60 ceramics were studied from 100 MHz to 35 GHz at temperatures between 10 and 390 K. Nine MW magnetic excitations with anomalous behavior near ferrimagnetic phase transitions were revealed. They also change under the application of the weak bias magnetic field (0–700 Oe) at room temperature. Six pure magnetic modes are assigned to dynamics of the magnetic domain walls and inhomogeneous magnetic structure of the ceramics, to the natural ferromagnetic resonance (FMR), and to the higher-frequency magnons. Three modes are considered the magnetodielectric ones with the dominating influence of the magnetic properties on their temperature and field dependences. The presence of the natural FMR in all ferrimagnetic phases proves the existence of the non-zero internal magnetization and magnetocrystalline anisotropy. Splitting of the FMR into two components without magnetic bias was observed in the collinear phase and is attributed to a change in the magnetocrystalline anisotropy during phase transition. The high-frequency FMR component critically slows down to phase transition. At room temperature, FMR splitting and essential suppression of the higher-frequency modes were revealed under the weak bias field (300–700 Oe). The highly nonlinear MW response and FMR splitting are caused by the gradual evolution of the polydomain magnetic structure to a monodomain one. The high number of magnetic excitations observed in the MW region confirms the suitability of using hexaferrite Sr4CoZnFe36O60 ceramics as MW absorbers, shielding materials and highly tunable filters.

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

Interlayer coupled domain wall dynamics induced by external magnetic field in synthetic antiferromagnets

The response of a magnetic domain wall to an external magnetic field in a perpendicularly magnetized synthetic antiferromagnet is studied using both micromagnetic simulations and a reduced model. It is found that the external field induces a sizable displacement between the position of the domain wall in each layer, which can be larger than the domain wall width for a sufficiently strong field. We also study the dynamic evolution of the system when this field is applied or removed. In both cases we find a complex response with two distinct phases that involve both internal domain wall rotation and coupled interlayer domain wall oscillations. As a result of this dynamics spin waves are radiated. The emitted radiation is characterized by a broadband spectrum and can be detected far away from the domain wall.

Effect of Ir growth pressure on the domain wall dynamics in Ta/Pt/Co/Ir/Ta stacks

Effect of Ir growth pressure on the domain wall dynamics in Ta/Pt/Co/Ir/Ta stacks

Temperature and medium structurization effect on spontaneous evolution of domains and bubbles in magnetic nanostructures

Spontaneous evolutions of domains in magnetic nanowires and of magnetic bubbles in open ferromagnetic nanolayers are investigated using micromagnetic simulations. We compare temperature dependent dynamics of domain wall (DW) systems in Permalloy (Py) nanowires and systems of chiral DWs in ultra-thin nanowires with perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interaction (DMI). In Py nanowires DWs collide and, in majority of cases, the collision leads to the DW annihilation in disagreement with the expectation of topological protection of sums of all the magnetic charges attached to the nanowire edges which are carried by DWs. For our purpose of discussing the DW collision in the presence of thermal excitations, we revisit the problem of field-driven collisions of DWs in Py nanowires at zero temperature. We claim that thermal fluctuations can counteract the collision-induced annihilation of DWs, thought further improvement of stabilization of domain structures is achievable via structurization of the magnetic nanowires (dividing them into grains). In PMA-DMI nanowires, thermally-excited chiral DWs can be randomly approaching or moving away while not being annihilated. A problem related to the motion of chiral DWs is the spontaneous motion of magnetic bubbles in open PMA-DMI planes. The magnetic bubbles expand or shrink to vanishing dependent on strength of the DMI interaction. Such a motion appears to be be strongly influenced by temperature and by structural discontinuities of the magnetic layer.

Primordial black holes from axion domain wall collapse

The QCD axion can solve the Strong CP Problem and be the dark matter of our universe. If the PQ symmetry breaking scale associated with the axion is below the inflationary reheating temperature, axion strings and domain walls populate the universe. Most of these strings and walls decay away into axion dark matter, but a small subset of the walls will be self-enclosed surfaces that are not attached to any strings. These enclosed walls can collapse in on themselves, compressing a large amount of energy into a small volume and potentially forming primordial black holes (PBHs). We study the number density and dynamics of these self-enclosed walls, taking into account their size distribution, Hubble expansion, asphericities, and all stages of domain wall dynamics using a combination of semi-analytic and numerical approaches. We find that axion models with a high axion decay constant fa, such as those of interest in early matter-dominated cosmologies, yield a PBH abundance potentially observable by future gravitational lensing surveys. We note that the formalism developed here is also useful for predicting relic PBH abundances in other models that exhibit unstable domain walls.

Understanding the grain size dependence of functionalities in lead-free (Ba,Ca)(Zr,Ti)O3

Grain size effects in ferroelectric ceramics have long been exploited to tailor their functional properties. However, the underlying mechanism for the grain size effects is not yet fully understood. Here, we study the grain size dependence of domain wall activities in a lead-free piezoceramics system, (Ba,Ca)(Zr,Ti)O3, with grain sizes in the range of 4 − 22 μm. The dielectric permittivity is highest at intermediate grain sizes (∼12 μm) where there are moderate lattice distortion and the most active domain wall motion under low voltages. Despite the larger fraction of switched domains in the material with larger distortion (∼22 μm), as revealed by in situ electric-field synchrotron X-ray diffraction, time-resolved characterizations demonstrate an easier and faster domain wall dynamics in the sample with moderate lattice distortion. Our analysis and phase-field simulations show that the grain size dependence of the domain wall dynamics of polycrystalline ferroelectrics is dictated by the interaction between an external electric field and the grain size-related change in intergranular stress, and this interaction is most effective in stimulating the movement of non-180° domain wall at intermediate grain sizes during the initial phase of polarization reversal. Our results provide a new fundamental understanding to guide the future design of materials for improving functionalities.

Current-driven fast magnetic octupole domain-wall motion in noncollinear antiferromagnets

Antiferromagnets (AFMs) have the natural advantages of terahertz spin dynamics and negligible stray fields, thus appealing for use in domain-wall applications. However, their insensitive magneto-electric responses make controlling them in domain-wall devices challenging. Recent research on noncollinear chiral AFMs Mn3X (X = Sn, Ge) enabled us to detect and manipulate their magnetic octupole domain states. Here, we demonstrate a current-driven fast magnetic octupole domain-wall (MODW) motion in Mn3X. The magneto-optical Kerr observation reveals the Néel-like MODW of Mn3Ge can be accelerated up to 750 m s-1 with a current density of only 7.56 × 1010 A m-2 without external magnetic fields. The MODWs show extremely high mobility with a small critical current density. We theoretically extend the spin-torque phenomenology for domain-wall dynamics from collinear to noncollinear magnetic systems. Our study opens a new route for antiferromagnetic domain-wall-based applications.

Spin-orbit torque-driven domain wall motion in the absence of Dzyaloshinskii-Moriya interactions

The fine structure and dynamics of magnetic domain walls in ultrathin films with perpendicular magnetization, in the presence of a secondary anisotropy, is analysed owing to micromagnetics. Two cases are considered, a cubic anisotropy typical for (111) oriented garnet epitaxial films, and an orthorhombic anisotropy as found in, e.g., Co/W(110) films. The statics is solved first, showing that, in general, domain walls are not of the pure Bloch type. The dynamics under the spin Hall effect induced by a current flowing in an adjacent layer is then monitored. Finite and non-negligible domain wall velocities are predicted in both cases, in the absence of Dzyaloshinskii-Moriya interactions, with distinct behaviours regarding the current density and its orientation with respect to the secondary anisotropy axes. The relevance of these results to recent reports of current-driven domain wall dynamics in insulating ultrathin garnet films, capped with platinum, is discussed.