Domain Wall Dynamics Research Articles

Thickness-dependent spin bistable transitions in single-crystalline molecular 2D material

The advent of two-dimensional (2D) crystals has led to numerous scientific breakthroughs. Conventional 2D systems have in-plane covalent bonds and a weak out-of-plane van-der-Waals bond. Here we report a new type of 2D material composed of discrete magnetic molecules, where anisotropic van-der-Waals interactions bond the molecules into a 2D packing. Through mechanical exfoliation, we can obtain single-crystalline molecular monolayers, which can be readily integrated into other 2D systems. Optical spectroscopy suggests the few-layered molecules preserve the temperature-induced spin-crossover switching observed in the bulk form but show a drastic increase in thermal hysteresis unique to these thin 2D molecule assemblies. The trapping of spin bistability with decreasing layer number can arise from domain wall dynamics in reduced dimensions. Our results establish molecular solids with strong anisotropy of intermolecular interactions as precursors to a new class of 2D materials, affording possibilities to control molecular functionalities through substrate and interlayer interactions.

Simulation on spin wave transmission and domain wall dynamics in a permalloy nanostrip

Spin waves (SWs), the magnons, can potentially be used for fast and energy efficient information processing and the interaction of SWs with a magnetic domain wall (DW), which is quite complex, can play a key role in the development of magnonic devices. Manipulation of SW amplitude and phase is the key step in realization of spin wave devices. The SW transmission through DW is strongly dependent on the magnetization angle inside the DW and spatial movement of DW is coupled to this interaction. Magnonic spin transfer torque and linear momentum transfer of SW, collectively, control the motion of the DW and the rotation of magnetization inside the DW. In the present work, micromagnetic simulations were performed considering a ferromagnetic permalloy nanostrip with perpendicular magnetic anisotropy (PMA) using mumax3 platform to study SW transmission through DW. The correlation between rotation in magnetization tilt angle (δϕ) inside an initially Néel-type DW and SW-transmission ratio (TD) was investigated at different SW-frequencies ranging from 18 GHz to 28 GHz. Applied SW amplitude at each frequency was sufficiently large for transverse DW to show oscillatory motion along the length of the strip. The results showed that the dependence of TD on rotation in magnetization angle (δϕ) decreases as the frequency of SW is increased and it approaches a nearly isotropic behavior at higher frequencies.

Exploring Physics of Ferroelectric Domain Walls in Real Time: Deep Learning Enabled Scanning Probe Microscopy.

The functionality of ferroelastic domain walls in ferroelectric materials is explored in real-time via the in situ implementation of computer vision algorithms in scanning probe microscopy (SPM) experiment. The robust deep convolutional neural network (DCNN) is implemented based on a deep residual learning framework (Res) and holistically nested edge detection (Hed), and ensembled to minimize the out-of-distribution drift effects. The DCNN is implemented for real-time operations on SPM, converting the data stream into the semantically segmented image of domain walls and the corresponding uncertainty. Further the pre-defined experimental workflows perform piezoresponse spectroscopy measurement on thus discovered domain walls, and alternating high- and low-polarization dynamic (out-of-plane) ferroelastic domain walls in a PbTiO3 (PTO) thin film and high polarization dynamic (out-of-plane) at short ferroelastic walls (compared with long ferroelastic walls) in a lead zirconate titanate (PZT) thin film is reported. This work establishes the framework for real-time DCNN analysis of data streams in scanning probe and other microscopies and highlights the role of out-of-distribution effects and strategies to ameliorate them in real time analytics.

Tensile stress and low temperature influence changes in geometry of propagating domain wall in magnetic glass-coated bistable microwires

Dynamics of magnetic domain walls in bistable glass-coated microwires under the influence of axial tensile stress and temperature are studied. Recent work dealing with domain wall geometry confirmed that increased damping of domain wall motion results in shortening of the wall. Results of further research into the effects of applied axial tensile stress and low temperature on domain wall geometry are presented. Magnetoelastic anisotropy changes in microwire samples due to applied tensile stress showed additional voltage peaks in induced signals from the pick-up coil, representing local increase in domain wall velocity. This local velocity increase appears to contradict pinning center predictions.

Domain-wall dynamics driven by thermal and electrical spin-transfer torque

According to spin Seebeck effect, a thermal spin current will be produced when a temperature gradient is applied to the metallic ferromagnet. Similar to the electrical spin transfer torque (ESTT) induced by spin-polarized current, there is also a thermal spin transfer torque (TSTT) caused by the thermal spin current, which can be attributed to the s-d interaction between the conduction electrons and the local magnetization. In this paper, the generalized analytical expressions of thermal spin current and TSTT are derived based on the spinor Boltzmann equation (SBE) under the local equilibrium approximation. This generalized TSTT has different terms compared to the previous phenomenological form, and the phenomenological coefficients can be determined theoretically within our framework. Combined with the SBE under the applied electric field and temperature gradient, we solve the Landau-Lifshitz-Gilbert-Levy equation to study the domain wall (DW) motion driven by the ESTT and TSTT. We investigated the temperature-dependent DW motion, the total spin torque, and TSTT in permalloys. We found that the velocity of the DW can be promoted by increasing temperature and temperature gradient, which provide a path to effectively utilize the Joule heating in spintronics devices.

Domain wall dynamics driven by a circularly polarized magnetic field in ferrimagnet: effect of Dzyaloshinskii–Moriya interaction

Domain wall dynamics driven by a circularly polarized magnetic field in ferrimagnet: effect of Dzyaloshinskii–Moriya interaction

Dynamics of Dzyaloshinskii domain walls for ferrimagnets with compensation of angular momentum

Dzyaloshinskii domain walls in chiral ferrimagnets, with a violation of spatial inversion symmetry due to Dzyaloshinskii–Moriya interaction, are studied theoretically. The dynamics of domain walls with non-small velocity is investigated by means of qualitative and numerical analysis of the sigma-model equation, generalized for accounting for chiral interactions and not complete compensation of sublattice angular momenta. Domain wall critical velocity, the maximal velocity that the domain wall can move, its energy and linear momentum are determined. Domain wall dispersion relation, the dependence of the energy on the linear momentum, is constructed. Forced motion of domain walls with accounting for weak dissipation processes is investigated by means of collective variable approach. We found quite a complicated picture of the dynamics of domain walls in chiral ferrimagnet that can be of interest for general theory of magnetic solitons and useful for applications. In addition to the increasing of the critical velocity of the domain wall when approaching angular momentum compensation point, which is the well-known sequence of the exchange enhancement effect, even the qualitative picture of domain wall states is changing. The main difference is that a few different types of domain walls appear, forming a sequence of states with a characteristic complication of the wall structure (formation of cluster domain walls) together with an increase in their energy. Both factors, the exchange enhancement of the limiting domain wall velocity and the destruction of integrability, turn out to be important here. In particular, the critical velocities of cluster domain walls, as well as the maximal values of their linear momenta, appear to be higher (sometimes, a few times higher) than for standard domain walls. This effect is absent for domain walls, known for non-integrable models of ferromagnets. The presence of cluster domain walls can be of interest for the problem, how to increase the maximal velocity of motion for domain walls.

Impedance spectroscopy of ferroelectrics: The domain wall pinning element

We introduce an equivalent-circuit element based on the theory of interface pinning in random systems to analyze the contribution of domain wall motion below the coercive field to the impedance of a ferroelectric, as a function of amplitude E0 and frequency f of an applied ac electric field. We demonstrate our model on a bulk PbZrxTi1−xO3 (PZT) reference sample and then investigate capacitor stacks, containing ferroelectric 0.5(Ba0.7Ca0.3)TiO3–0.5Ba(Zr0.2Ti0.8)O3 (BCZT) thin films, epitaxially grown by pulsed laser deposition on Nb-doped SrTiO3 single crystal substrates and covered with Au electrodes. Impedance spectra from f=10 Hz to 1 MHz were collected at different E0. Deconvolution of the spectra is achieved by fitting the measured impedance with an equivalent-circuit model of the capacitor stacks, and we extract for E0=2.5 kV/cm, a frequency-dependent permittivity of εr′(f)=458+7.3ln⁡(1Hz/2πf) for the BCZT films from the obtained fit parameters. From an extended Rayleigh analysis, we obtain a coupling strength of 0.187 cm/kV between dielectric nonlinearity and dielectric dispersion in the BCZT films and identify different domain-wall-motion regimes. Finally, we construct a schematic diagram of the different domain-wall-motion regimes and discuss the corresponding domain-wall dynamics. Our approach can be utilized to replace purely phenomenological constant phase elements (CPEs) in modeling the impedance response of ferroelectrics and extracting material properties.

Field-driven side-by-side magnetic domain wall dynamics in ferromagnetic nanostrips

There has been a plethora of studies on domain wall dynamics in magnetic nanostrips, mainly because of its versatile non-linear physics and potential applications in data storage devices. However, most of the studies focus on out-of-plane domain walls or in-plane head-to-head (tail-to-tail) domain walls. Here, we numerically study the field-driven dynamics of in-plane side-by-side domain walls in ferromagnetic strips, which can be stable in the presence of an in-plane easy-axis anisotropy transverse to the strip. The domain walls move in a rigid-body manner at low field, and show complex Walker breakdown behavior at high field. We observe a multi-step Walker breakdown through vortex nucleation in wide strips. In the presence of Dzyaloshinskii-Moriya interaction (DMI), the first Walker breakdown field first decreases then increases with interfacial DMI, while keeps increasing with bulk DMI. These findings complement the current understanding on domain wall dynamics.

Dynamics of domain walls in ferroelectrics and relaxors

AbstractThe dynamic contribution of domain walls (DWs) to application‐relevant dielectric and piezoelectric properties of ferroelectrics and relaxor‐based oxide ceramics has been in the focus since the earliest studies on these complex multifunctional materials. Despite the vital importance of DWs in the material design for targeted applications, the understanding of these interfaces has been significantly advanced only recently owing to the concurrent development of analytical methodologies probing the structure of samples in situ and at different length scales. In this contribution, we present two recent cases that have raised particular attention and controversy. The first is on the electrically conductive DWs in BiFeO3 (BFO), whereas the second is on low‐angle DWs characteristic for relaxor ferroelectric Pb(Mg1/3Nb2/3)O3−xPbTiO3 (PMN–PT). Using nonlinear piezoelectric measurements with the support from multiscale structural analysis, we illustrate with the two case studies how, on one hand, the local electrical conductivity in BFO and, on the other hand, the structural disorder inherent to PMN–PT affect DW dynamics, leading to emerging macroscopic effects. By clarifying some of the aspects of these particular interfaces, we hope that the presented results will provide guidance to analytical approaches for identifying the key microscopic mechanisms contributing to macroscopic functional properties of ferroelectric and related materials.

Influence of mechanical stress on magnetization processes in amorphous FINEMET alloy

The influence of mechanical stress on magnetization processes in an amorphous metal alloy have been investigated. The rapidly quenched amorphous metallic ribbons with nominal composition Fe73.5Cu1Nb3Si13.5B9 (precursor of FINEMET) were chosen for this study. The significant differences in the magnetic properties of the studied material were observed at different degrees of mechanical stress applied to the sample. The origin of these effects arises from changes in the dynamics of domain walls. They are primarily caused by variation of their fundamental properties (thickness, energy per unit area of the domain wall) as well as changes in the properties of internal stress areas, which are obstacles to their movement. Impact of stress areas was demonstrated by analysis of influence of mechanical load on the internal demagnetization factor.

Dynamics of Domain Walls in the Region of Compensated Angular Momentum in Ferrimagnetic Films with Plane Anisotropy

Dynamics of Domain Walls in the Region of Compensated Angular Momentum in Ferrimagnetic Films with Plane Anisotropy

Dynamical phase-field model of coupled electronic and structural processes

Many functional and quantum materials derive their functionality from the responses of both their electronic and lattice subsystems to thermal, electric, and mechanical stimuli or light. Here we propose a dynamical phase-field model for predicting and modeling the dynamics of simultaneous electronic and structural processes and the accompanying mesoscale pattern evolution under static or ultrafast external stimuli. As an illustrative example of application, we study the transient dynamic response of ferroelectric domain walls excited by an ultrafast above-bandgap light pulse. We discover a two-stage relaxational electronic carrier evolution and a structural evolution containing multiple oscillational and relaxational components across picosecond to nanosecond timescales. The phase-field model offers a general theoretical framework which can be applied to a wide range of functional and quantum materials with interactive electronic and lattice orders and phase transitions to understand, predict, and manipulate their ultrafast dynamics and rich mesoscale evolution dynamics of domains, domain walls, and charges.

Magnetic Bloch oscillations and domain wall dynamics in a near-Ising ferromagnetic chain

When charged particles in periodic lattices are subjected to a constant electric field, they respond by oscillating. Here we demonstrate that the magnetic analogue of these Bloch oscillations are realised in a ferromagnetic easy axis chain. In this case, the “particles” undergoing oscillatory motion in the presence of a magnetic field are domain walls. Inelastic neutron scattering reveals three distinct components of the low energy spin-dynamics including a signature Bloch oscillation mode. Using parameter-free theoretical calculations, we are able to account for all features in the excitation spectrum, thus providing detailed insights into the complex dynamics in spin-anisotropic chains.

Effect of Chiral Damping on the dynamics of chiral domain walls and skyrmions

Friction plays an essential role in most physical processes that we experience in our everyday life. Examples range from our ability to walk or swim, to setting boundaries of speed and fuel efficiency of moving vehicles. In magnetic systems, the displacement of chiral domain walls (DW) and skyrmions (SK) by Spin Orbit Torques (SOT), is also prone to friction. Chiral damping (αc), the dissipative counterpart of the Dzyaloshinskii Moriya Interaction (DMI), plays a central role in these dynamics. Despite experimental observation, and numerous theoretical studies confirming its existence, the influence of chiral damping on DW and SK dynamics has remained elusive due to the difficulty of discriminating from DMI. Here we unveil the effect that αc has on the flow motion of DWs and SKs driven by current and magnetic field. We use a static in-plane field to lift the chiral degeneracy. As the in-plane field is increased, the chiral asymmetry changes sign. When considered separately, neither DMI nor αc can explain the sign reversal of the asymmetry, which we prove to be the result of their competing effects. Finally, numerical modelling unveils the non-linear nature of chiral dissipation and its critical role for the stabilization of moving SKs.

Depinning Exponents of Thin Film Domain Walls Depend on Disorder Strength.

Domain wall dynamics in ferromagnets is complicated by internal degrees of freedom of the domain walls. We develop a model of domain walls in disordered thin films with perpendicular magnetic anisotropy capturing such features, and use it to study the depinning transition. For weak disorder, excitations of the internal magnetization are rare, and the depinning transition takes on exponent values of the quenched Edwards-Wilkinson equation. Stronger disorder results in disorder-dependent exponents concurrently with nucleation of an increasing density of Bloch lines within the domain wall.

Strain-driven magnetic domain wall dynamics controlled by voltage in multiferroic heterostructures

Magnetic domain walls (DWs) have significants application potential as information carriers in the construction of novel high-density, high-speed spintronics devices. In this study, the fully coupled micro-magnetic-mechanical finite element method (FEM) was used to demonstrate the behaviour of DW dynamics under voltage-modulated magnetoelastic anisotropy via piezostrain transfer in ferromagnetic (FM)/piezoelectric (PE) multiferroic heterostructures. Continuous and long-distance high-speed DW-motion could be realized in the ferromagnetic layer by utilizing a voltage switching on the piezoelectric layer without applying magnetic fields or spin-polarization currents. Numerical simulations demonstrate that this system has low energy consumption of 1.215fJ for every shift operation and high speed with an average velocity of 234.4m/s when applying a 0.5volts under continuous and long-distance DW motion. This performance can be further improved by optimizing the structural design and material selection. The design and analysis results in this study provide a new and effective method to realize low-power consumption and high-speed spin logic devices based on magnetic DWs.

Dynamics of domain wall induced by voltage-controlled strain-field gradient

This work investigates the strain-gradient-driven domain wall (DW) motion in a ferromagnetic-heavy-metal–piezoelectric heterostructure with perpendicular magnetic anisotropy and the interface Dzyaloshinskii-Moriya interaction (iDMI). The simulation results show that a larger iDMI can lead to greater tilting of the DW surface as the DW approaches the end of the wire. When the DW stops, the tilt angle is zero, and the DW is perpendicular to the nanowire. The DW displacement and the velocity are affected by the iDMI coefficient, strain-gradient amplitude, and Gilbert damping. We also show that such a mechanism can be used to implement a leaky-integrate-fire spiking neuron device with the controllable temporary location of the DW serving as the analog membrane potential of a biological neuron, which is promising for future DW-based artificial neural devices.

Domain wall propagation in Fe-rich magnetic microwires with graded magnetic anisotropy

We observed that stress-annealing of Fe75B9Si12C4 magnetic microwire at variable annealing temperature allows to create graded magnetic anisotropy. We have found that single domain wall (DW) propagation in a media with graded magnetic anisotropy is essentially non-uniform: faster DW propagation is observed in the region with moderate stress-annealing induced magnetic anisotropy. Higher DW velocity in the region with induced magnetic anisotropy is explained by the transverse character of stress-annealing induced magnetic anisotropy which affects the travelling DW in a similar way as application of transversal bias magnetic field. Obtained graded magnetic anisotropy allows engineering the DW dynamics of Fe-rich microwires.

Multiple Walker breakdowns in magnetic multilayers

Herein, we report an exotic domain-wall dynamics showing double Walker breakdowns in magnetic multilayer films composed of two magnetic layers. Such multiple Walker breakdowns are attributed to the internal magnetic dipole field, which is antisymmetric on the domain walls of the lower and upper magnetic layers. A micromagnetic simulation shows four phases of the domain-wall dynamics, which result in a phase diagram with the phase boundaries of the double Walker breakdown fields. Such double Walker breakdowns lead to two minima in the variation of the domain-wall velocity, as often observed experimentally.