Domain Wall Dynamics Research Articles

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.

Dynamic peculiarities of interphase boundaries and domain walls for non-spin domains

The analysis of magnetization oscillations (de Haas – van Alphen effect; dHvA effect) and features of the Fermi surface shape in three (3D)- and two-dimensional (2D) metals shows that the dynamic phenomena — the dynamics of domain walls and interphase boundaries during diamagnetic phase transitions — are described by a new nonlinear partial differential equation. The equation is a result of the inclusion of the case of multiple extremal cross sections of the Fermi surface in these metals. Our consideration indicates the possibility of the appearance of metastable non-spin domains (Condon domains) and first-order phase transitions to the ordered phase in the regime of dHvA oscillations for the two-frequency case. Sine–Gordon, Klein–Gordon, double sine–Gordon, time-dependent Ginzburg–Landau equations, and the telegraph equation are limiting cases of the derived equation. We show that particular moving kink-soliton solutions of the equation describe traveling wave fronts being moving domain walls and interphase boundaries in the Condon domain phase.

Dynamics of domain walls in curved antiferromagnetic wires

The influence of the curvature on the dynamical properties of transversal domain walls in a thin antiferromagnetic wire is studied theoretically. Equations of motion for antiferromagnetic domain wall are obtained within the collective variable approach ($q-\Phi$ model). It is shown that (i) for the case of localized bend, curvature results in a pinning potential for domain wall. (ii) The gradient of the curvature results in a driving force on the domain wall and it effectively moves without any external stimuli. Although we showcase our approach on the specific parabola and Euler spiral geometries, the approach is general and valid for a wide class of geometries. All analytical predictions are confirmed by numerical simulations.

Domain-wall dynamics in Bose-Einstein condensates with synthetic gauge fields.

Interactions in many-body physical systems, from condensed matter to high-energy physics, lead to the emergence of exotic particles. Examples are mesons in quantum chromodynamics and composite fermions in fractional quantum Hall systems, which arise from the dynamical coupling between matter and gauge fields1,2. The challenge of understanding the complexity of matter-gauge interaction can be aided by quantumsimulations, for which ultracold atoms offer a versatile platform via the creation of artificial gauge fields. An important step towards simulating the physics of exotic emergent particles is the synthesis of artificial gauge fields whose state depends dynamically on the presence of matter. Here we demonstrate deterministic formation of domain walls in a stable Bose-Einstein condensate with a gauge field that is determined by the atomic density. The density-dependent gauge field is created by simultaneous modulations of an optical lattice potential and interatomic interactions, and results in domains of atoms condensed into two different momenta. Modelling the domain walls as elementary excitations, we find that the domain walls respond to synthetic electric field with a charge-to-mass ratio larger than and opposite to that of the bare atoms. Our work offers promising prospects to simulate the dynamics and interactions of previously undescribed excitations in quantum systems with dynamical gauge fields.

Compactified AdS black holes, Chamblin-Reall background, and their dual non-conformal relativistic fluids

The Chamblin-Reall background is a static solution of Einstein gravity coupled with a background scalar field and a dynamical domain wall, with the potential of the scalar field being of Liouville type. It can be got by dimensionally reducing a higher dimensional background with a constant potential. Compactified AdS black holes are black hole backgrounds constructed by wrapping one or more spatial directions of a higher dimensional AdS black hole on a torus and then integrating them out. The compactified AdS black hole background is asymptotically flat, non-conformal, and of Chamblin-Reall type. In this work, we derive all the 7 dynamical second-order transport coefficients for the relativistic fluids dual to compactified AdS black holes of various dimensions via fluid/gravity correspondence. Through this work, we achieve three main goals: (1) We prove that all the gravitational backgrounds that can be used to extract analytical results for second-order transport coefficients hitherto are all Chamblin-Reall type backgrounds. (2) We generalize the results in previous studies on the second-order transport coefficients of the relativistic fluids dual to 5-dimensional Chamblin-Reall model into general dimensions. (3) We offer a thorough study on the Kanitscheider-Skenderis proposal and find its physical accounts.

Distinctive Nb–O hybridization at domain walls in orthorhombic KNbO3 ferroelectric perovskite

Niobate-based ferroelectric perovskites have been an important group of functional materials. Since the formation and dynamics of domain walls are decisive to the properties of ferroelectrics, in this study, a representative orthorhombic niobate-based ferroelectric perovskite, i.e., KNbO3, is studied by using first-principles calculation. Three types of domain walls with permissible walls located at crystallographic planes, including uncharged 180°, 120°, and 90° domain walls, are selected for simulation. The formation energy, intrinsic energy barrier of domain-wall motion, and the electronic configuration are systematically analyzed. We discover that the formation energy is associated with the variation of Nb–O hybridization at the domain wall, while the intrinsic energy barrier of the domain-wall motion depends on the dynamical change of Nb–O hybridization along the transition path. Therefore, we propose that the Nb–O hybridization plays a critical role in the formation and motion of domain walls in niobate-based ferroelectrics.

Enhancement of the Walker limit by bulk Dzyaloshinskii-Moriya interaction

In this work, dynamics of chiral domain walls in long and narrow magnetic heterostructures based on non-centrosymmetric chiral magnets with bulk Dzyaloshinskii-Moriya interactions (DMI) and perpendicular magnetic anisotropy is systematically investigated. The driving forces can be out-of-plane magnetic fields and in-plane currents, correspondingly both steady and precessional flows are considered. Their dividing points (the Walker critical field and current density) are obtained as functions of bulk DMI strength ($D_{\mathrm{b}}$) and the ratio ($\kappa$) of total (crystalline plus shape) anisotropy in the hard axis over that in the easy one. When far beyond Walker breakdown, the dependence curve of wall velocity on external in-plane bias field takes parabolic shape around the compensation point where the total in-plane field disappears. The center shift is determined by $D_{\mathrm{b}}$, $\kappa$, and the wall's topological charge, thus can be used to measure the bulk DMI strength in chiral magnets.

Tuning of Magnetoimpedance Effect and Magnetic Properties of Fe-Rich Glass-Coated Microwires by Joule Heating.

The influence of Joule heating on magnetic properties, giant magnetoimpedance (GMI) effect and domain wall (DW) dynamics of Fe75B9Si12C4 glass-coated microwires was studied. A remarkable (up to an order of magnitude) increase in GMI ratio is observed in Joule heated samples in the frequency range from 10 MHz to 1 GHz. In particular, an increase in GMI ratio, from 10% up to 140% at 200 MHz is observed in Joule heated samples. Hysteresis loops of annealed samples maintain a rectangular shape, while a slight decrease in coercivity from 93 A/m to 77 A/m, after treatment, is observed. On the other hand, a modification of MOKE hysteresis loops is observed upon Joule heating. Additionally, an improvement in DW dynamics after Joule heating is documented, achieving DW propagation velocities of up to 700 m/s. GMI ratio improvement along with the change in MOKE loops and DW dynamics improvement have been discussed considering magnetic anisotropy induced by Oersted magnetic fields in the surface layer during Joule heating and internal stress relaxation. A substantial GMI ratio improvement observed in Fe-rich Joule-heated microwires with a rectangular hysteresis loop and fast DW propagation, together with the fact that Fe is a more common and less expensive metal than Co, make them suitable for use in magnetic sensors.

Relativistic domain-wall dynamics in van der Waals antiferromagnet MnPS3

The discovery of two-dimensional (2D) magnetic van der Waals (vdW) materials has flourished an endeavor for fundamental problems as well as potential applications in computing, sensing and storage technologies. Of particular interest are antiferromagnets, which due to their intrinsic exchange coupling show several advantages in relation to ferromagnets such as robustness against external magnetic perturbations. Here we show that, despite of this cornerstone, the magnetic domains of recently discovered 2D vdW MnPS3 antiferromagnet can be controlled via magnetic fields and electric currents. We achieve ultrafast domain-wall dynamics with velocities up to ~3000 m s−1 within a relativistic kinematic. Lorentz contraction and emission of spin-waves in the terahertz gap are observed with dependence on the edge termination of the layers. Our results indicate that the implementation of 2D antiferromagnets in real applications can be further controlled through edge engineering which sets functional characteristics for ultrathin device platforms with relativistic features.

Exchange spring-like inhomogeneous states in a ferromagnetic wire with current

Transverse structure of magnetization in a ferromagnetic film induced by magnetic field of electric current has been analyzed. Two steps of arising exchange spring evolution are shown. The first one (weak current) is gradual twisting of magnetization aside from the wire axis. Above some critical current the transient area is compressed and localized near the middle plane. In presence of additional conductive layer the transient structure becomes asymmetric resulting to non-zero lateral component of the net magnetization. It is shown also that the mentioned asymmetry can provide additional displacement of domain walls after the electric current pulses. Keywords: spintronics, domain wall dynamics, exchange spring, ferromagnet.

A comparative study of the domain wall motion in ferrimagnets (Fe,Co)1-x(Gd,Tb)x.

Magnetic domain walls (DWs) in rare-earth-transition-metal (RE-TM) ferrimagnetic alloys can be used as information carriers in nonvolatile spintronic devices. Due to the rich combinations of RE-TM elements (such as CoGd, FeGd, CoTb, and FeTb in our case), it is intriguing to reveal the characteristics of DW dynamics in these wide choices of RE-TM compounds. Through a systematic study of the DW motion in thin films with different compositions of stacking order Pt(3 nm)/(Fe,Co)1-x(Gd,Tb)x(∼8 nm)/Ta(3 nm), we show that the partially compensated ferrimagnets CoGd and FeGd can exhibit a faster DW motion under various (in-plane and out-of-plane) magnetic fields driven by current-induced spin-orbit torques. In stark contrast with the fast motion of domain walls in Gd-based ferrimagnets, we find that the CoTb system exhibits much slower DW dynamics, and the FeTb system shows no motion, but evolved into a multi-domain state upon applying current pulses. Our results demonstrate that ferrimagnets CoGd and FeGd are more suitable candidates for achieving ultrafast DW motion, which could be useful for developing spintronic memory and logic devices.

Dynamics of high-velocity domain wall motion and spin wave excitation in trilayer structures

Propagation of dipolar-coupled transverse domain walls in a permalloy/non-magnetic/permalloy trilayer was investigated using micromagnetic modeling. Circulating stray fields meant that the walls adopted a composite structure with behavior analogous to walls seen in nanotubes. Wall velocities were sensitive to the chirality of the stray field circulation, with velocities of the most favored chirality enhanced by 32% compared with velocities seen in the individual constituent layers just below their Walker breakdown field. Additionally, Walker breakdown was completely suppressed within the trilayer for both chiralities, despite occurring in the constituent layers when modelled in isolation, leading to a maximum of 317% velocity enhancement. Wall velocity saturated around 1100 m/s due to the Cherenkov-like emission of spin waves, comparable to the magnonic regime of nanotubes. By reproducing the advantageous domain wall dynamics of nanotubes within a planar system, we demonstrate that ultrafast magnetic switching may feasibly be realized within a lithographically produced system.

Domain wall dynamics in two-dimensional van der Waals ferromagnets

Domain wall motion is in the core of many information technologies ranging from storage [Beach et al., J. Magn. Magn. Mater. 320, 1272–1281 (2008)], processing [Tatara et al., Phys. Rep. 468, 213–301 (2008)], and sensing [Ralph and Stiles, J. Magn. Magn. Mater. 320, 1190–1216 (2008)] up to novel racetrack memory architectures [Parkin et al., Science 320, 190–194 (2008)]. The finding of magnetism in two-dimensional (2D) van der Waals (vdW) materials [Huang et al., Nature 546, 270 (2017); Gong et al., Nature 546, 265–269 (2017); Guguchia et al., Sci. Adv. 4, eaat3672 (2018); Klein et al., Science 360, 1218–1222 (2018)] has offered a new frontier for the exploration and understanding of domain walls at the limit of few atom-thick layers. However, to use 2D vdW magnets for building spintronics nanodevices such as domain-wall based logic [Allwood et al., Science 309, 1688–1692 (2005); Luo et al., Nature 579, 214–218 (2020); Xu et al., Nat. Nanotechnol. 3, 97–100 (2008)], it is required to gain control of their domain wall dynamics by external driving forces such as spin-polarized currents or magnetic fields, which have so far been elusive. Here, we show that electric currents as well as magnetic fields can efficiently move domain walls in the recently discovered 2D vdW magnets CrI3 and CrBr3 at low temperatures and robust down to monolayer. We realize field- and current-driven domain wall motion with velocities up to 1020 m s−1, which are comparable to the state-of-the-art materials for domain-wall based applications [Yang et al., Nat. Nanotechnol. 10, 221–226 (2015); Woo et al., Nat. Mater. 15, 501–506 (2016); Vélez et al., Nat. Commun. 10, 4750 (2019); Siddiqui et al., Phys. Rev. Lett. 121, 057701 (2018); Ryu et al., Nat. Nanotechnol. 8, 527–533 (2013)]. Domain walls keep their coherence driven by the spin-transfer torque induced by the current and magnetic fields up to large values of about 12×109 A cm−2 and 5 T, respectively. For larger magnitudes of current or field, a transition to a hydrodynamic spin-liquid regime is observed with the emission of a periodic train of spin-wave solitons with modulational instability [Rabinovich and Trubetskov, Oscillations and Waves: In Linear and Nonlinear Systems, Mathematics and its Applications (Springer Netherlands, 2011)]. The emitted waveform achieves terahertz (THz) frequency in a wide range of fields and current densities, which opens up perspectives for reconfigurable magnonic devices. Moreover, we found that these spin-waves can transport spin angular momentum through the layers over distances as long as 10 μm without losses for the transport of spin information. Our results push the boundary of what is currently known about the dynamics of domain walls in 2D vdW ferromagnets and unveil strategies to design ultrathin, high-speed, and high-frequency spintronic devices.

Domain-wall motion driven by a rotating field in a ferrimagnet

We theoretically study a ferrimagnetic domain-wall motion driven by a rotating magnetic field. We find that, depending on the magnitude and the frequency of the rotating field, the dynamics of a ferrimagnetic domain wall can be classified into two regimes. First, when the frequency is lower than a certain critical frequency set by the field magnitude, there is a stationary solution for the domain-wall dynamics, where a domain-wall in-plane magnetization rotates in-phase with the external field. The field-induced precession of the domain wall gives rise to the translational motion of the domain wall via the gyrotropic coupling between the domain-wall angle and position. In this so-called phase-locking regime, a domain-wall velocity increases as the frequency increases. Second, when the frequency exceeds the critical frequency, a domain-wall angle precession is not synchronous with the applied field. In this phase-unlocking regime, a domain wall velocity decreases as the frequency increases. Moreover, the direction of the domain-wall motion is found to be reversed across the angular compensation point where the net spin density of the ferrimagnet changes its sign. Our work suggests that the dynamics of magnetic solitons under time-varying biases may serve as platform to study critical phenomena.

Engineering of domain wall propagation in magnetic microwires with graded magnetic anisotropy

We report on the influence of graded magnetic anisotropy designed by stress-annealing of magnetic microwire at variable annealing temperature on domain wall propagation. We found that the domain wall propagation in a medium with graded magnetic anisotropy is substantially nonuniform. Domain wall can be trapped in the microwire region with strong enough stress-annealing induced magnetic anisotropy. On the other hand, faster domain wall propagation and a decrease in the domain wall length are observed in the region with moderate stress-annealing induced magnetic anisotropy. Beneficial effect of stress-annealing on the domain wall dynamics is associated with the induced transverse magnetic anisotropy in the outer domain which affects the travelling domain wall in a similar way as application of transversal bias magnetic field. Observed decreasing of the half-width of the electromagnetic force (EMF) peak in stress-annealed microwires can be associated to the decreasing of the characteristic domain wall length.

Collective dynamics of domain walls: An antiferromagnetic spin texture in an optical cavity

Spin canting and complex spin textures in antiferromagnetic materials can often be described in terms of Dzyaloshinskii-Moriya interactions (DMI). Values for DMI parameters are not easily measurable directly, and often inferred from other quantities. In this work, we examine how domain wall dynamics in an antiferromagnetic optomagnonic system can display unique features directly related to the existence of DMI. Our results indicate that the presence of DMI enables spin interactions with cavity photons in a geometry which otherwise allows no magneto-optical coupling, and on the other hand modulates frequencies in a geometry where coupling is already realized in the absence of DMI. This result may be used to measure the DMI constant in optomagnonic experiments by comparing resonances obtained with different polarisations of the exciting field.

A second-order numerical method for Landau-Lifshitz-Gilbert equation with large damping parameters

A second order accurate numerical scheme is proposed and implemented for the Landau-Lifshitz-Gilbert equation, which models magnetization dynamics in ferromagnetic materials, with large damping parameters. The main advantages of this method are associated with the following features: (1) It only solves linear systems of equations with coefficient matrices independent of the magnetization, and fast solvers are available, so that the numerical efficiency has been greatly improved, in comparison with the existing Gauss-Seidel project method. (2) The second-order accuracy in time is achieved, and it is unconditionally stable for large damping parameters. Moreover, both the second-order accuracy and the great efficiency improvement will be verified by several numerical examples in the 1D and 3D simulations. In the presence of large damping parameters, it is observed that this method is unconditionally stable and finds physically reasonable structures while many existing methods have failed. For the domain wall dynamics, the linear dependence of wall velocity with respect to the damping parameter and the external magnetic field will be obtained through the reported simulations.